Susceptibility Weighted Imaging in MRI: Basic Concepts and Clinical Applications [1 ed.] 9780470043431

Table of contents :
Susceptibility
Weighted Imaging in MRI
Susceptibility Weighted Imaging in MRI
Basic Concepts and Clinical
Applications
E. Mark Haacke
J €
urgen R. Reichenbach
Contents
Preface
Contributors
Part I
Basic Concepts
Introduction to Susceptibility Weighted Imaging
Magnetic Susceptibility
B ¼ m 0 ð H þ M Þ
v ¼ g B
ð 2 : 2 Þ
B ¼ m 0 ð 1 þ x Þ H or B ¼
ð 2 : 4 Þ
v ð x Þ ¼ g ð B 0 þ G x x Þ
ð 2 : 6 Þ
B ð x Þ ¼ B 0 þ D B ð x Þ þ G x x
ð 2 : 7 Þ
v ð x Þ ¼ g ð B 0 þ D B ð x Þ þ G x x Þ
v ð x Þ ¼ g B 0 þ G x x þ
ð 2 : 9 Þ
v ð x 0 Þ ¼ g ð B 0 þ G x x 0 Þ
D v ¼ g ð d B o Þ
w ¼ g D B t
w / ð Hct ð 1 Y Þ 2 : 62 10 6 Þ
Gradient Echo Imaging
k x ¼
2 p G x t 0 t T acq = 2
ð 3 : 1 Þ
w ð x ; t Þ ¼ 2 p k x x ¼ g G x x t 0 t T ac
2 p G x T acq = 2 þ
w ð x ; t Þ ¼ g G x x ð t TE Þ j t TE j T acq = 2 ð 3 : 4
k x ¼ g G x T acq = 2
k x ¼
2 p G x t T acq = 2
ð 3 : 5 Þ
ð 3 : 6 Þ
α φ
TE 3
TE 1
G R
ADC
2 p G R D t ¼
ð 3 : 7 Þ
ð 3 : 8 Þ
2 p D G S t S ¼
ð 3 : 9 Þ
M ? ð t Þ ¼ M 0 e t = T * 2
M ? ¼ M 0 sin a
w ¼ g D B TE ¼ g D x B 0 TE
w ¼ g G x v t 2
Phase and Its Relationship to Imaging Parameters and
Susceptibility
w t ð Þ ¼ v t þ w 0
x þ j r j sin w ^ y
w t ð Þ ¼ v t
ð 4 : 1 Þ
ð 4 : 2 Þ
r ¼ r x þ r y ¼ j r j cos w ^
ð 4 : 4 Þ
þ y 2 p
ð Þ
ð 4 : 5 Þ
ð 4 : 6 Þ
ð 4 : 7 Þ
w r ; t ð Þ ¼ g B 0 B ð r ; t Þ
ð Þ t ¼ g D B r ; t
ð Þ t
ð 4 : 8 Þ
w r ð Þ ¼ g D B r
ð Þ TE
ð 4 : 9 Þ
D w ¼ g D B TE
D w ¼ g D B vt TE g D x v t B 0 TE
ð Þ e i w 1 r ð Þ ¼ r 1m r
ð Þ e i g D B r
ð Þ e i w 2 r ð Þ ¼ r 2m r
ð Þ e i g D B r
ð Þ e e = T 2 r ð Þ )
ð Þ ¼ e i g e D B r
ð Þ e i w p p r ð Þ
ð Þ e i w q q r ð Þ
ð Þ
(a)
(b)
(c)
r ð x Þ ¼ f n ð x Þ r ð x Þ
f ð x Þ ¼ ½ p þ w ð x Þ
f ð x Þ ¼
p w ð x Þ
f ð x Þ ¼
p þ w ð x Þ
p w ð x Þ
f ð x Þ ¼ g w ð x Þ
1 þ exp ½ a ð w ð x Þ b Þ
P I ð Þ ¼
p D w ð Þ ¼
F ½ f ð x x 0 Þ ¼ ð
¼ ð
ð
F ½ f ð x Þ
Understanding T * 2 -Related
Signal Loss
M xy t ð Þ ¼ M xy t ¼ 0
ð Þ e t = T 2
¼ R 2 þ R 0 2
ð 5 : 2 Þ
ð 5 : 3 Þ
ð 5 : 4 Þ
ð 5 : 5 Þ
ð 5 : 7 Þ
ð 5 : 8 Þ
M sph t ð Þ ¼ ð p
ð Þ e i dv sph r ; u
dv cyl r ; u ; f ð Þ ¼ g B 0
M C t ð Þ ¼ ð 2
ð Þ e i dv C r ; u ; f
ð Þ ¼ M 0 e 0 : 3 l dv net t ð Þ 2 e t = T 2
ð Þ ¼ M 0 e l dv net
M t ð Þ ¼ M SE e j t t SE j = T 0 2
Processing Concepts and SWI Filtered Phase Images
ð Þ
ð Þ þ 2 m r
ð Þ p
I m r ð Þ ¼ I D r
ð Þ e i w r ð Þ
ð Þ e i w r ð Þ ¼ j I D r
ð Þ j e i w des r
ð Þ
ð 6 : 4 Þ
1 j w j
ð 6 : 6 Þ
ð 6 : 7 Þ
ð 6 : 8 Þ
ð 6 : 9 Þ
w ¼ ff
w 0 ¼ ff
MR Angiography and Venography of the Brain
D w g D x B 0 TE
exp ½ i dw s ; u ð r Þ ¼ exp ½ i w ð r þ D u Þ i w ð r D u Þ ¼ U D
U D u ¼ A ð r þ D u Þ = A ð r þ D u Þ ; U * D u ¼ A * ð r D u Þ =
LFG u ð r Þ ¼ dw s ; u ð r Þ = ð g TE 2 j D u jÞ ¼ arg ð U D u U * D
LFG 2 x ð r Þ þ LFG 2 y ð r Þ þ LFG 2 z ð r Þ
ð 7 : 5 Þ
Brain Anatomy with Phase
Part II
Current Efforts in Clinical Translational
Research Using SWI
SWI Venographic Anatomy of the Cerebrum
Deep Medullary Veins
Novel Approaches to Imaging Brain Tumors
Traumatic Brain Injury
Imaging Cerebral Microbleeds with SWI
Imaging Ischemic Stroke and Hemorrhage with SWI
Visualizing Deep Medullary Veins with SWI in Newborn and Young Infan
Susceptibility Weighted Imaging in Multiple Sclerosis
Cerebral Venous Diseases and Occult Intracranial Vascular Malformations
Sturge–Weber Syndrome
Visualizing the Vessel Wall Using Susceptibility Weighted
g D B TE K e TE = T * 2
p K e
Imaging Breast
Calcification Using SWI
Susceptibility Weighted Imaging at Ultrahigh
Magnetic Fields
h 2 N I I þ 1
ð Þ
3 k T B 0
D w ¼ g D x B 0 TE
S ð t Þ ¼ ð
W ð r Þ f s ð r Þ r ð r Þ e i y D B ð r Þ t e t = T * 2 ð r Þ
Part III
Advanced Concepts
Improved Contrast in MR Imaging of the Midbrain
Using SWI
ð Þ ¼ R 2o þ k B 0
Measuring Iron
Content with Phase
w ¼ g D B TE
R *
¼ R * 2 ð Fe Þ
¼ D R * 2 ð Fe Þ
(a)
(b)
(e)
(c)
(d)
(f)
(g)
( h )
(a)
(c)
(d)
( e )
( f )
(c)
(e)
( f )
(a)
(b)
(c)
( e )
( f )
(a)
(b)
(c)
(d)
( e )
( f )
(b)
(c)
(d)
(e)
(f)
(a)
(c)
(e)
(f)
(a)
(c)
( e )
( f )
Validation of Phase Iron Detection with Synchrotron
X-Ray Fluorescence
ð Þ
½ ¼ 850 D w
B 0 T ½
½ ¼ 217 D w CSF
½ ¼ 434 D w CSF
B 0 T ½
Rapid Calculation of Magnetic Field Perturbations from Biological Tiss
B ð r Þ ¼ B 0 þ
ð V 0 d 3 r 0 3 M ð r 0 Þ ð r r 0 Þ
ð r r 0 Þ
j j 5
M ð r 0 Þ
j j 3
M ð r Þ ¼
w ð r Þ
m 0 ð 1 þ w ð r ÞÞ
M z ð r Þ
w ð r Þ
m 0 ð 1 þ w ð r ÞÞ
B 0 z ¼)
w ð r Þ
B z ð r Þ ¼ B 0 z þ
ð V 0 d 3 r 0 3 M z ð r 0 Þ ð z z 0 Þ 2
j j 5
M z ð r 0 Þ
j j 3
B d z ð r Þ ¼
ð V 0 d 3 r 0 3 w ð r 0 Þ ð z z 0 Þ 2
j j 5
w ð r 0 Þ
j j 3
ð V 0 d 3 r 0 w ð r Þ G c ; 3D ð r r 0 Þ
3 ð z 2 r 2 Þ
þ k 2 y þ k 2 z q
¼ 4 p
ð u 3D ; f Þ Y ‘ m ð u k ; 3D ; f k Þ
B d z ð r Þ ¼ B 0 = 1 = w ð r Þ
ð Þ
þ k 2 y þ k 2 z
d 2
k 2 z
þ k 2 z þ
B z ; 2D ð r Þ ¼ = 1 = w ð r Þ
ð Þ G c ; 2D
(a)
(b)
(c)
(d)
ð Þ = 6.
B z ð r Þ ¼ B 0 = 1 = w ð r Þ
f g G ð k Þ
(a)
(b)
(c)
(d)
(a)
(b)
(c)
(d)
(a)
(b)
(c)
(d)
w ð r Þ ¼ g B d z ð r Þ TE ¼ g B 0 TE = 1 = w ð
ð Þ
þ k 2 y þ k 2 z
w ð r Þ ¼ g B 0 TE = 1 "
w 1 g 1 þ w 2 g 2 þ
þ w i g i þ þ w n g n Þ
þ k 2 y þ k 2 z
B z ð r Þ ¼
ð Þ
þ w e
w ð r Þ ¼ g B d z ð r Þ TE ¼ g B 0 TE = 1 = w ð r Þ
ð Þ
þ k 2 y þ k 2 z
Þ 2
w i g TE w B 0 g i d w i 2
Þ 2
g TE B 0
SNR 2 i w i w 0 g TE w B 0 g i
w i w 0 g TE w B 0 g i p s i ; phase
SWIM: Susceptibility Mapping as a Means to Visualize Veins and Quant
Oxygen Saturation
j k j 2
a ð k z Þ ¼ ð k z k z 0 Þ = ð b D k z Þ for j k z k zo j < b
g ð k Þ ¼
when j k z k zo j b D k z
b ¼ j k za k zo j = ð D k z Þ
a ð k z Þ ¼ ð k z k zo Þ = j k za k zo j
(a)
(b)
Effects of Contrast Agents in Susceptibility Weighted
T i ð c CA Þ ¼
R i ð c CA Þ ¼
7 t c 2 1 þ ð v S t c 2 Þ 2
3 t c 1 1 þ ð v I t c 1 Þ 2
2 A 2 S ð S þ 1 Þ
t 0 c 2 1 þ ð v S t 0 c 2 Þ 2
6 : 5 t c 2 1 þ ð v S t c 2 Þ 2
1 : 5 t c 1 1 þ ð v I t c 1 Þ 2
þ 2 t c 1
S ð S þ 1 Þ 3 h 2
t 0 c 2 1 þ ð v S t 0 c 2 Þ 2
þ t 0 c 1
D B ð r Þ ¼
cos ð u Þ 2
sin ð u Þ 2
r 2 cos ð 2 f Þ
S ð TE Þ ¼ r v l f v ð T 1 ; TR Þ e i w ð TE ; Y ; c CA w
f v ð a ; TR ; T 1 Þ ¼ sin ð a Þ
f t ð a ; TR ; T 1 Þ ¼ sin ð a Þ
W ð r Þ f ð r Þ r ð r Þ e i g D B ð r Þ TE e TE = T * 2 ð
ð Y Þ ¼ A * þ B * ð 1 Y Þ þ C * ð 1 Y Þ 2
w ð r Þ w CA ð r Þ
D B CA ð r Þ ¼
D w ð r in Þ ¼ 2
g TE B 0 ð cos 2 u 1 = 3 Þ
Oxygen Saturation: Quantification
A ¼ ½ w ð V ein Þ w ð A rt Þ = ½ k Hct ð 1 Y Þ TE ð 3 cos 2 u 1
u ¼ tan 1 ½ d D x = ½ð n 1 Þ D z
¼ 1 = T * 2 ¼ 1 = T * 2o þ A T 2 ð 1 Y Þ ¼ 13 : 29 ð 1 Y Þ þ
Quantification of Oxygen Saturation of Single Cerebral
Veins, the Blood Capillary Network, and Its Dependency on Perfusion
D x ¼ D x do Hct 1 Y
j r j 2
B 0 j r j < a
B 0 j r j > a
ð Þ
6 ð 3 cos 2 u 1 Þ j B 0 j
þ ð 1 l Þ S ext e t = T 2ext h ð 28 : 5 Þ
h ¼ 1 f ð dv t Þ
1 l þ f ð l dv t Þ
f ð x Þ ¼ ð
1 J 0 ð xu Þ
S net ð t Þ ¼ ð 1 l Þ S ext e l f ð d v t Þ e
d v ¼ g
f ð x Þ ¼
p
1 J 0 ðð 3 = 2 Þ xu Þ
Integrating Perfusion Weighted Imaging, MR
Angiography, and Susceptibility Weighted
Imaging
Functional Susceptibility Weighted Magnetic Resonance Imaging
Complex Thresholding Methods for Eliminating
Voxels That Contain Predominantly Noise in Magnetic Resonance Images
p ð M ; f Þ ¼
þ A 2 2 AM cos ð f u Þ
p M ð M Þ ¼
s ð 2 p = 2 Þ .
p M ð M Þ ¼
þ s 2
p ð w Þ ¼
2 p s = A ð Þ 2
exp ð f u Þ 2 2 s = A ð Þ 2
n 0 ð x ; y Þ ¼
L ð A ; u ; s 2 Þ ¼ 2 p s 2
þ A 2 2 AM i cos ð f i u Þ
ð Þ 2 þ y I
ð Þ 2
l ¼ L ð
ð Þ 2
(a)
(b)
(c)
(d)
Automatic Vein Segmentation and Lesion Detection: from SWI-MIPs to MR
¼ j l 2 j j l 3 j
¼ j l 1 j
j l 2 l 3 j
S ¼ k H k F ¼
ð a b Þ 2 þ ð b c Þ 2 þ ð c a Þ 2
Rapid Acquisition Methods
ð Þ d x d y ;
ð Þ
w ð x ; y ; l D T Þ ¼ i v 0 ð x ; y Þð l D T þ TE ð 0 ÞÞ
(a)
(b)
r x ; y ð Þ ¼ X
w ð x ; y Þ ¼ v 0 ð x ; y Þ D T
ð Þ
ð Þ L D T
ð Þ ¼ X
ð Þ L l
ð Þ D T
ð Þ
p n .
High-Resolution Venographic BOLD MRI of Animal Brain at 9.4 T: Impli
v in ¼ 2 p D x 0 ð 1 Y Þ v 0 ð cos 2 u 1 = 3 Þ
v out ¼ 2 p D x 0 ð 1 Y Þ v 0 ð a = r Þ 2 ð sin 2 u Þð cos 2 f Þ
Susceptibility Weighted Imaging in Rodents
f ¼ R pc = ð 1 R pc Þ
Ultrashort TE Imaging:
Phase and Frequency Mapping of Susceptibility Effects in Short T 2 T
M x ð t Þ ¼ M 0
M y ð t Þ ¼ M 0
M z ð t Þ ¼ M 0
ð Þ 1
u ð t Þ ¼ e i
v 1 ð t Þ e
v 1 ð t Þ e i
þ e
v 1 ð t Þ e i
F ð t Þ ¼ v off t ff
F ð t Þ ¼ ff
k ð t Þ ¼
S ð k Þ ¼
S ð k Þ ¼ e i ð 2 v off = g G Þ k ;
I ð x Þ ¼
I ð x ¼ 0 Þ ¼
ð Þ
F ð x ¼ 0 Þ ¼ ff i 1 e i ð v off = g GL Þ
k ð t Þ ¼
S ð k Þ ¼ e i 2 v off
p ;
S ð k Þ ¼ e þ i 2 v off
I ð x ¼ 0 Þ ¼
p d k þ ð
p d k ¼ 2
p d k
I ð x ¼ 0 Þ ¼
F ð x ¼ 0 Þ
I ð x ¼ 0 Þ ¼
F ð x ¼ 0 Þ
F ð x ¼ 0 Þ v off
ð Þ d k x d k y
I ð x ¼ y ¼ 0 Þ ¼
S ð k r Þ ¼ e i 2 v off
s 0 ð r Þ½ð 1 = T * 2 Þ i 2 ð f f 0 Þ
ð 1 = T * 2 Þ 2 þ 4 ð f f 0 Þ 2
Real ½ s 0 ð r Þ ð 1 = T * 2 Þ þ Imag ½ s 0 ð r Þ 2 ð f f 0 Þ
ð 1 = T * 2 Þ 2 þ 4 ð f f 0 Þ 2
j S ð r ; f Þj ¼ j s 0 ð r Þj
ð 1 = T * 2 Þ 2 þ 4 ð f f 0 Þ 2
dt ¼ M g B
ð Þ
d M dt ¼ M g B ð 36 : A1 Þ
x 0 ¼
i
ð Þ x 0 þ C þ exp þ t
ð Þ x þ þ C exp t
ð Þ x ð 36 : A3 Þ
M ð t ¼ 0 Þ ¼
M x ð t Þ ¼ M 0
M y ð t Þ ¼ M 0
APPENDIX
Seminal Articles Related to the Development of Susceptibility Weighted
Imaging
Index

Citation preview

Susceptibility Weighted Imaging in MRI

Susceptibility Weighted Imaging in MRI Basic Concepts and Clinical Applications

Edited by

E. Mark Haacke Wayne State University, Detroit, MI, USA The MRI Institute for Biomedical Research, Detroit, MI, USA Case Western Reserve University, Cleveland, OH, USA Loma Linda University, Loma Linda, CA, USA McMaster University, Hamilton, ON, Canada

€ rgen R. Reichenbach Ju Jena University Hospital, Jena, Germany Friedrich Schiller University, Jena, Germany

Copyright Ó 2011 by Wiley-Blackwell. All rights reserved. Wiley-Blackwell is an imprint of John Wiley & Sons, Formed by the merger of Wiley’s global Scientific, Technical, and Medical business with Blackwell Publishing. Published by John Wiley & Sons, Inc., Hoboken, New Jersey Published simultaneously in Canada No part of this publication may be reproduced, stored in a retrieval system, or transmitted in any form or by any means, electronic, mechanical, photocopying, recording, scanning, or otherwise, except as permitted under Section 107 or 108 of the 1976 United States Copyright Act, without either the prior written permission of the Publisher, or authorization through payment of the appropriate per-copy fee to the Copyright Clearance Center, Inc., 222 Rosewood Drive, Danvers, MA 01923, (978) 750-8400, fax (978) 750-4470, or on the web at www.copyright.com. Requests to the Publisher for permission should be addressed to the Permissions Department, John Wiley & Sons, Inc., 111 River Street, Hoboken, NJ 07030, (201) 748-6011, fax (201) 748-6008, or online at http://www.wiley.com/go/permission. Limit of Liability/Disclaimer of Warranty: While the publisher and author have used their best efforts in preparing this book, they make no representations or warranties with respect to the accuracy or completeness of the contents of this book and specifically disclaim any implied warranties of merchantability or fitness for a particular purpose. No warranty may be created or extended by sales representatives or written sales materials. The advice and strategies contained herein may not be suitable for your situation. You should consult with a professional where appropriate. Neither the publisher nor author shall be liable for any loss of profit or any other commercial damages, including but not limited to special, incidental, consequential, or other damages. For general information on our other products and services or for technical support, please contact our Customer Care Department within the United States at (800) 762-2974, outside the United States at (317) 572-3993 or fax (317) 572-4002. Wiley also publishes its books in a variety of electronic formats. Some content that appears in print may not be available in electronic formats. For more information about Wiley products, visit our web site at www.wiley.com. Library of Congress Cataloging-in-Publication Data: Susceptibility weighted imaging in MRI : basic concepts and clinical applications / [edited by] E. Mark Haacke, J€urgen R. Reichenbach p. ; cm. Includes bibliographical references ISBN 978-0-470-04343-1 (cloth) 1. Brain–Magnetic resonance imaging. 2. Cerebrovascular disease–Magnetic resonance imaging. I. E. Mark Haacke, II. Reichenbach, J€urgen R. [DNLM: 1. Magnetic Resonance Imaging–methods. WN 185 M9398 2010] RC386.6.M34M763 2010 616.8’047548–dc22 2010018432 Printed in the United States of America 10 9

8 7 6 5

4 3 2

1

Contents

PREFACE CONTRIBUTORS

PART I 1

BASIC CONCEPTS

Introduction to Susceptibility Weighted Imaging

ix xiii

1 3

J€urgen R. Reichenbach and E. Mark Haacke

2

Magnetic Susceptibility

17

Jaladhar Neelavalli and Yu-Chung Norman Cheng

3

Gradient Echo Imaging

33

J€urgen R. Reichenbach and E. Mark Haacke

4

Phase and Its Relationship to Imaging Parameters and Susceptibility

47

Alexander Rauscher, E. Mark Haacke, Jaladhar Neelavalli, and J€ urgen R. Reichenbach

5

Understanding T2*-Related Signal Loss

73

Jan Sedlacik, Alexander Rauscher, J€urgen R. Reichenbach, and E. Mark Haacke

6

Processing Concepts and SWI Filtered Phase Images

89

Alexander Rauscher and Stephan Witoszynskyj

7

MR Angiography and Venography of the Brain

103

Samuel Barnes, Zhaoyang Jin, Yiping P. Du, Andreas Deistung, and Ju¨rgen R. Reichenbach

v

vi

8

CONTENTS

Brain Anatomy with Phase

121

Jeff Duyn and Oliver Speck

PART II

9

CURRENT EFFORTS IN CLINICAL TRANSLATIONAL RESEARCH USING SWI

SWI Venographic Anatomy of the Cerebrum

137 139

Daniel K. Kido, Jessica Tan, Steven Munson, Udochukwu E. Oyoyo, and J. Paul Jacobson

10

Novel Approaches to Imaging Brain Tumors

151

Sandeep Mittal, Bejoy Thomas, Zhen Wu, and E. Mark Haacke

11

Traumatic Brain Injury

171

Karen Tong, Barbara Holshouser, and Zhen Wu

12

Imaging Cerebral Microbleeds with SWI

191

Muhammad Ayaz, Alexander Boikov, Grant McAuley, Mathew Schrag, Daniel K. Kido, E. Mark Haacke and Wolff Kirsch

13

Imaging Ischemic Stroke and Hemorrhage with SWI

215

Nathaniel Wycliffe, Guangbin Wang, Masahiro Ida, and Zhen Wu

14

Visualizing Deep Medullary Veins with SWI in Newborn and Young Infants

235

J. Paul Jacobson, Udochukwu E. Oyoyo, Daniel K. Kido, John Wuchenich, and Stephen Ashwal

15

Susceptibility Weighted Imaging in Multiple Sclerosis

249

Yulin Ge, Robert I. Grossman, and E. Mark Haacke

16

Cerebral Venous Diseases and Occult Intracranial Vascular Malformations

265

Hans-Joachim Mentzel, Guangbin Wang, Masahiro Ida, and J€urgen R. Reichenbach

17

Sturge–Weber Syndrome

295

Zhifeng Kou, Csaba Juhasz and Jiani Hu

18

Visualizing the Vessel Wall Using Susceptibility Weighted Imaging

307

Yang Qi, Samuel Barnes and E. Mark Haacke

19

Imaging Breast Calcification Using SWI

319

Michael D. Noseworthy, Colm Boylan, and Ali Fatemi-Ardekani

20

Susceptibility Weighted Imaging at Ultrahigh Magnetic Fields Andreas Deistung, Samuel Barnes, Yulin Ge, and J€ urgen R. Reichenbach

329

CONTENTS

PART III 21

ADVANCED CONCEPTS

Improved Contrast in MR Imaging of the Midbrain Using SWI

vii

351 353

Elena Manova and E. Mark Haacke

22

Measuring Iron Content with Phase

369

Manju Liu, Charbel Habib, Yanwei Miao, and E. Mark Haacke

23

Validation of Phase Iron Detection with Synchrotron X-Ray Fluorescence

403

Helen Nichol, Karla Hopp, Bogdan F. Gh. Popescu, and E. Mark Haacke

24

Rapid Calculation of Magnetic Field Perturbations from Biological Tissue in Magnetic Resonance Imaging

419

Jaladhar Neelavalli, Yu-Chung Norman Cheng, and E. Mark Haacke

25

SWIM: Susceptibility Mapping as a Means to Visualize Veins and Quantify Oxygen Saturation

461

Jin Tang, Jaladhar Neelavalli, Saifeng Liu, Yu-Chung Norman Cheng, and E. Mark Haacke

26

Effects of Contrast Agents in Susceptibility Weighted Imaging

487

Andreas Deistung and J€urgen R. Reichenbach

27

Oxygen Saturation: Quantification

517

E. Mark Haacke, Karthik Prabhakaran, Ilaya Raja Elangovan, Zhen Wu, and Jaladhar Neelavalli

28

Quantification of Oxygen Saturation of Single Cerebral Veins, the Blood Capillary Network, and Its Dependency on Perfusion

529

Jan Sedlacik, Song Lai, and J€urgen R. Reichenbach

29

Integrating Perfusion Weighted Imaging, MR Angiography, and Susceptibility Weighted Imaging

543

Meng Li and E. Mark Haacke

30

Functional Susceptibility Weighted Magnetic Resonance Imaging

561

Markus Barth and Daniel B. Rowe

31

Complex Thresholding Methods for Eliminating Voxels That Contain Predominantly Noise in Magnetic Resonance Images

577

Daniel B. Rowe, Jing Jiang, and E. Mark Haacke

32

Automatic Vein Segmentation and Lesion Detection: from SWI-MIPs to MR Venograms

605

Samuel Barnes, Markus Barth and Peter Koopmans

33

Rapid Acquisition Methods

619

Song Lai, Yingbiao Xu and E. Mark Haacke

34

High-Resolution Venographic BOLD MRI of Animal Brain at 9.4 T: Implications for BOLD fMRI Seong-Gi Kim and Sung-Hong Park

637

viii

35

CONTENTS

Susceptibility Weighted Imaging in Rodents

649

Yimin Shen, Zhifeng Kou, and E. Mark Haacke

36

Ultrashort TE Imaging: Phase and Frequency Mapping of Susceptibility Effects in Short T2 Tissues of the Musculoskeletal System

669

Jiang Du, Michael Carl, and Graeme M. Bydder

APPENDIX: Seminal Articles Related to the Development of Susceptibility Weighted Imaging

697

INDEX

717

Preface

Since its inception, magnetic resonance imaging has used tissue properties such as T1, T2, and spin density followed by flow, diffusion characteristics, lipid imaging, and spectroscopy as the technology developed to create images with extraordinary detail of the body and brain; and this list continues to grow. Surprisingly, prior to susceptibility weighted imaging or SWI, the basic property of tissue susceptibility had not been used directly, but rather taken advantage of through local T2* effects in magnitude images. The problem with this approach is that many different sources can cause T2* signal dephasing. The basic field effects created by susceptibility have generally been recognized as a source of artifacts and the usual first response was to remove them. However, such field effects can be used to separate types of materials such as calcium deposits, which are diamagnetic, from microbleeds, which are paramagnetic. In fact, these field effects were used in the original concept of susceptibility weighted imaging to better image small veins and to enhance contrast in tissues. Practically, the phase information available in MR imaging carries all the information that is needed to reconstruct the local magnetic source or susceptibility difference between tissues. Although SWI uses phase as a source of contrast, the more advanced concept is to create a susceptibility map that can be used not only to differentiate paramagnetic from diamagnetic substances but also to quantify the amount of a given substance present that is causing the susceptibility difference, such as local iron differences between tissues. In this book, we refer to the combination of SWI filtered phase and magnetic susceptibility mapping as SWIM for susceptibility weighted imaging and mapping. The work on SWI showed the significance of phase in enhancing contrast in tissues and now SWIM opens the door to quantifying susceptibility in tissues. Clinically, SWI makes it possible to image microbleeds and veins more effectively, while SWIM will provide the methods to quantify oxygen saturation and local iron content. These techniques have or will find applications in neurovascular diseases, neurodegenerative diseases, and iron-related diseases. Multi-echo SWI also offers a means to image the

ix

x

PREFACE

entire vascular system, including arteries and veins alike. The field is still developing, and there are hints that major roadblocks in this area are falling, thanks to technical advances in magnet homogeneity, gradient strengths, and faster imaging methods such as parallel imaging. For example, the need to accommodate or correct air/tissue interfaces is now theoretically possible, high bandwidth imaging avoids geometric distortion, and multiecho imaging may offer a means to ideally phase unwrap data on a pixel by pixel basis. This book contains nearly every aspect of SWI; however, a number of new developments and new findings are being made at the time this book went into publication. As these new concepts in the field of MRI evolve and develop, some of them may be ready for incorporation into the next edition of the book. The main aim of this book is to provide clinicians a detailed overview of the basic concepts and applications related to susceptibility weighted imaging. The book has been organized into three parts. In the first eight chapters, we introduce basic concepts that include the definitions and mechanisms of gradient echo imaging, phase, T2* , and multiecho imaging. This will enable the reader to have an understanding of the basics of the terms used throughout the book. The next 12 chapters represent the current efforts in clinical translational research using SWI. These chapters cover the basic venous structures in the brain followed by the application of SWI in several diseases, such as cancer, traumatic brain injury, vascular dementia, stroke, hemorrhage, multiple sclerosis, venous malformations, Sturge–Weber syndrome, atherosclerosis, and calcifications in breast cancer. The final 16 chapters cover a variety of technically more advanced concepts, including susceptibility mapping (SWIM), oxygen saturation measurements, technical developments, and animal imaging, as well as a list of references related to SWI up to early 2010. Most of the images used in this book have been adapted from published journal articles. Since most of these were either from Journal of Magnetic Resonance Imaging (JMRI) or Magnetic Resonance in Medicine (MRM), both published by John Wiley & Sons Inc., a blanket permission was acquired for their use in this book. Acknowledgement for the figures adapted from other publications are specifically mentioned in their respective captions. The increasing clinical applications of SWI were our inspirations to write and produce this book. We believe its recent growth into SWIM and susceptibility mapping will spearhead even more quantitative measures of iron and new applications ranging from neurodegenerative diseases to hemochromatosis. Many colleagues around the world have made efforts in developing clinical applications of SWI and many, if not most of them, have contributed to this book. We acknowledge the contributions of these experts in the field. Without their enthusiasm and continuous support, including numerous meetings at various conferences, this project would not have been possible. We are indebted to all those people who helped us in bringing out this book, particularly Alexander Boikov, Daniel Haacke, Lisa Hamm, and Judith Farah. Yongquan Ye helped us with his technical expertise in refining several chapters. A very special thanks to Jaladhar Neelavalli for his careful reading of the book, for his meticulous attention to detail, and for coordinating the final efforts that made it possible to get this book to press, in a timely fashion. We acknowledge Wiley for taking on this project and for their expert professional editorial support, particularly that of Dean Gonzalez, Kristen Parrish, and Ms. Sanchari Sil. We are grateful to Thom Moore, editor at Wiley, for his patience and enthusiasm in bringing out this book. A special thanks is due to the people at Siemens Healthcare for having made SWI available as a product for their customers. This was a major

PREFACE

xi

step in taking the methodology into the clinical domain and, in part, is the reason why so many new applications are developing for SWI now. Finally, we would like to thank our families who put up with the added responsibilities during our long hours of work. Their emotional support and patience made this book possible. E. MARK HAACKE € JURGEN R. REICHENBACH

Contributors

STEPHEN ASHWAL, Department of Pediatrics, School of Medicine, Loma Linda University Medical Center, Loma Linda, CA, USA MUHAMMAD AYAZ, Massachusetts General Hospital, Stroke Research Center, Boston, MA; Institute for Exercise and Enviromental Medicine, Texas Health Presbytarian Hospital, University of Texas Southwestern Medical Center, Dallas, TX, USA SAMUEL BARNES, Department of Radiology, Loma Linda University Medical Center, Loma Linda, CA, USA MARKUS BARTH, Centre for Cognitive Neuroimaging, Donders Institute of Brain, Cognition and Behaviour, Radbound University, Nijmegen, The Netherlands ALEXANDER BOIKOV,

Wayne State University, Detroit, MI, USA

COLM BOYLAN, Imaging Research Centre, Brain-Body Institute, St. Joseph’s Healthcare, Diagnostic Imaging, St. Joseph’s Healthcare, Department of Radiology, McMaster University, Hamilton, Ontario, Canada GRAEME M. BYDDER, USA

Department of Radiology, University of California, San Diego, CA,

YU-CHUNG NORMAN CHENG, MR Center/Concourse, Harper Hospital, Wayne State University, Detroit, MI, USA ANDREAS DEISTUNG, Medical Physics Group, Department of Diagnostic and Interventional Radiology, Jena University Hospital, Friedrich Schiller University, Jena, Germany JIANG DU,

Department of Radiology, University of California, San Diego, CA, USA

YIPING P. DU, Department of Psychiatry and Radiology, University of Colorado Denver, Aurora, CO, USA xiii

xiv

CONTRIBUTORS

JEFF DUYN, National Institute of Neurological Disorders and Stroke (NINDS), Bethesda, MD, USA ILAYA RAJA ELANGOVAN, Departments of Radiology and Biomedical Engineering, Wayne State University, Detroit, MI, USA ALI FATEMI-ARDEKANI, Imaging Research Centre, Brain-Body Institute, St. Joseph’s Healthcare, Department of Medical Physics and Applied Radiation Sciences, McMaster University, Hamilton, Ontario, Canada YULIN GE, Department of Radiology, Center for Biomedical Imaging, New York University School of Medicine, New York, NY, USA ROBERT I. GROSSMAN, Department of Radiology, New York University Medical Center, New York, NY, USA E. MARK HAACKE, Department of Radiology, Wayne State University, Detroit, MI, USA; The MRI Institute for Biomedical Research, Detroit, MI, USA; Department of Physics, Case Western Reserve University, Cleveland, OH, USA; Department of Radiology, Loma Linda University, Loma Linda, CA, USA; School of Biomedical Engineering and Department of Electrical and Computer Engineering, McMaster University, Hamilton, ON, Canada. CHARBEL HABIB,

Department of Radiology, Wayne State University, Detroit, MI, USA

BARBARA HOLSHOUSER, Linda, CA, USA

MRI Section, Loma Linda University Medical Center, Loma

KARLA HOPP, Department of Anatomy and Cell Biology, University of Saskatchewan, Saskatoon, Saskatchewan, Canada JIANI HU, MR Research Facility, Department of Radiology, Wayne State University School of Medicine, Detroit, MI, USA MASAHIRO IDA, Department of Radiology and Comprehensive Stroke Unit, Tokyo Metropolitan Ebara Hospital, Tokyo, Japan J. PAUL JACOBSON, Department of Interventional Neuroradiology, Loma Linda University Medical Center, Loma Linda, CA, USA JING JIANG,

Department of Computer Science, Wayne State University, Detroit, MI, USA

ZHAOYANG JIN, Hangzhou Dianzi University, College of Automation, Hangzhou, Zhejiang, P. R. China CSABA JUHASZ,

PET Center, Children’s Hospital of Michigan, Detroit, MI, USA

DANIEL K. KIDO, Department of Radiology, Loma Linda University Medical Center, Loma Linda, CA, USA SEONG-GI KIM, Department of Radiology, Magnetic Resonance Research Center, University of Pittsburgh, Pittsburgh, PA, USA WOLFF KIRSCH, Neurosurgery Center for Research, Training and Education, Loma Linda University, Loma Linda, CA, USA

CONTRIBUTORS

xv

PETER KOOPMANS, Centre for Cognitive Neuroimaging, Donders Institute for Brain, Cognition and Behaviour, Radbound University Nijmegen, Nijmegen, The Netherlands ZHIFENG KOU, MR Research Facility, Department of Radiology, Wayne State University School of Medicine, Detroit, MI, USA SONG LAI, MRI Physics Lab/Radiology, Jefferson Medical College, Thomas Jefferson University, Philadelphia, PA, USA MENG LI, USA

MR Center/Concourse, Harper Hospital, Wayne State University, Detroit, MI,

MANJU LIU, Department of Biomedical Engineering, Wayne State University, Detroit, MI, USA SAIFENG LIU,

McMaster University, Hamilton, Ontario, Canada

ELENA MANOVA,

Department of Radiology, Wayne State University, Detroit, MI, USA

GRANT MCAULEY, Neurosurgery Center for Research, Training and Education, Loma Linda University, Loma Linda, CA, USA HANS-JOACHIM MENTZEL, Department of Diagnostic and Interventional Radiology, Jena University Hospital, Friedrich Schiller University, Jena, Germany YANWEI MIAO, The Radiology Department, First Affiliated Hospital, Dalian Medical University, Dalian, P. R. China SANDEEP MITTAL,

Karmanos Cancer Center, Detroit, MI, USA

STEVEN MUNSON, Department of Interventional Neuroradiology, Loma Linda University Medical Center, Loma Linda, CA, USA JALADHAR NEELAVALLI, The MRI Institute for Biomedical Research, Detroit, MI, USA; Nuffield Department of Surgery, University of Oxford, Oxford, UK; Department of Radiology, Wayne State University, Detroit, MI, USA HELEN NICHOL, Department of Anatomy and Cell Biology, University of Saskatchewan, Saskatoon, Saskatchewan, Canada MICHAEL D. NOSEWORTHY, Electrical and Computer Engineering, and School of Biomedical Engineering, McMaster University, Imaging Research Centre, Brain-Body Institute, St. Joseph’s Healthcare, Department of Medical Physics and Applied Radiation Sciences, McMaster University, Diagnostic Imaging, St. Joseph’s Healthcare, Department of Radiology, McMaster University, Hamilton, Ontario, Canada UDOCHUKWU E. OYOYO, Department of Radiology, Loma Linda University Medical Center, Loma Linda, CA, USA SUNG-HONG PARK, Department of Radiology, Magnetic Resonance Research Center, Department of Bioengineering, University of Pittsburgh, Pittsburgh, PA, USA BOGDAN F. GH. POPESCU,

Department of Neurology, Mayo Clinic, Rochester, MN, USA

KARTHIK PRABHAKARAN, Neuropsychiatry Section, Department of Psychiatry, Brain Behavior Laboratory, University of Pennsylvania, Philadelphia, PA, USA

xvi

CONTRIBUTORS

YANG QI, Department of Radiology, Xuanwu Hospital, Capital Medical University, Beijing, P. R. China ALEXANDER RAUSCHER, Canada

MRI Research Centre, Vancouver, University of British Columbia,

€ R. REICHENBACH, Medical Physics Group, Department of Diagnostic and JURGEN Interventional Radiology, Jena University Hospital, Friedrich Schiller University, Jena, Germany

DANIEL B. ROWE, Center for Imaging Research, Department of Biophysics, Medical College of Wisconsin, Milwaukee, WI, USA MATTHEW SCHRAG, Neurosurgery Center for Research, Training and Education, Loma Linda University, Loma Linda, CA, USA JAN SEDLACIK, Department of Radiological Sciences, St. Jude Children’s Research Hospital, Memphis, TN, USA YIMIN SHEN, MR Research Facility, Departments of Radiology, Wayne State University School of Medicine, Detroit, MI, USA OLIVER SPECK, Institute for Experimental Physics (IEP), Otto-von-Guericke University, Magdeburg, Germany JESSICA TAN, USA JIN TANG,

Department of Internal Medicine, Kettering Medical Center, Dayton, OH,

McMaster University, Hamilton, Ontario, Canada

BEJOY THOMAS, Department of Imaging Sciences and Interventional Radiology, Sree Chitra Tirunal Institute for Medical Sciences and Technology (SCTIMST), Thiruvananthapuram, India KAREN TONG, Department of Neuroradiology, Loma Linda University Medical Center, Loma Linda, CA, USA GUANGBIN WANG, Department of Radiology and Comprehensive Stroke Unit, Tokyo Metropolitan Ebara Hospital, Tokyo, Japan; Shandong Medical Imaging Research Institute, Jinan, Shandong, P. R. China STEPHAN WITOSZYNSKYJ, Austria ZHEN WU,

Department of Radiology, Medical University of Vienna, Wien,

Magnetic Resonance Innovations, Detroit, MI, USA

JOHN WUCHENICH, USA

Department of Radiology, Loma Linda University, Loma Linda, CA,

NATHANIEL WYCLIFFE, Department of Radiology, Loma Linda University, Loma Linda, CA, USA YINGBIAO XU,

The MRI Institute for Biomedical Research, Detroit, MI, USA

FIGURE 1.4 (a) MRA pre-Gd; (b) phase processed SWI post-Gd; (c) high-resolution perfusion weighted imaging (PWI) with the original cerebral blood volume (CBV) map; (See text for full caption.)

FIGURE 8.12 Examples of MRI phase (left) and Perls’ iron stain (right) of line of Gennari (layer 4b) in human V1.

FIGURE 10.2 Cystic high-grade glioma. (See text for full caption.)

SWI and T1-Gd findings on each type of abnormality Number of patients identified

12

P=0.0020

P=0.005

P=0.005

P=0.0078 P=0.0020

10

P=0.0078

8 6 4 2

SWI T1-Gd Enlarg. Transmed Veins

FIGURE 17.1 for full caption.)

Mild Moderate Prominent

SWI

T1-Gd

Enlarg. PeriVentr. Veins

SWI T1-Gd

SWI T1-Gd

SWI T1-Gd

Enlarg.Choroid Leptomeningeal Cortical Plexus Abn. Gyriform Abn.

SWI T1-Gd GM/WM Junct. Abn.

Number of patients with each type of abnormality identified by SWI and T1-Gd. (See text

FIGURE 13.3(b) 59-year-old male, cardioembolic stroke in the left middle cerebral artery, MRI was done 2 h after onset on a 1.5 T scanner. (See text for full caption.)

FIGURE 13.4 46-year-old female, cardioembolic stroke in the left middle cerebral artery, MRI was done 80 min after onset on a 1.5 T scanner. (See text for full caption.)

FIGURE 17.6 T1 pre-contrast image along with corresponding SWI magnitude, SWI phase and the CBV map from PWI sequence are shown. (See text for full caption.)

FIGURE 17.7

The enlarged images of Figure 17.6 showing the correlation between SWI and PWI.

FIGURE 17.8

Coregistered SWI and PET images of a 6-year-old girl with Sturge–Weber syndrome affecting the left hemisphere. (See text for full caption.)

FIGURE 23.1 RS-XRF iron mapping setup. Rapid scanning X-ray fluorescence imaging setup as used to collect image in Figure 23.4. (See text for full caption.)

FIGURE 26.7 In vivo visualization of the BOLD mechanism. Phase images acquired during breathing ambient air, pure oxygen, and carbogen are presented in (a, d), (b, e), and (c, f), respectively. The field inhomogeneity around a single venous vessel is shown in the lower row. Lines in (a) demonstrate the view direction along the vessel axis and indicate the location of the four adjacent phase images that are presented via average projection in (d–f). The location of the vessel is indicated by the dashed circle in (d–f). The magnetic field inhomogeneity decreases with increased blood oxygenation. Reprinted from Ref. 48.

FIGURE 26.8 T1-weighted spin echo scan (TR/TE/FA ¼ 575 ms/14 ms/70  ) before (a) and after application of Magnevist Ò (b) of a patient with glioblastoma multiforme. Corresponding venograms acquired during breathing ambient air are shown in (c) and (d). The heterogeneous overlay in (d) maps signal increases of the tumor signal induced by carbogen inhalation. The active perimeter can be clearly distinguished from the inactive center of the tumor. Reprinted from Ref. 58, with permission from Georg Thieme Verlag KG.

FIGURE 26.11 Minimum intensity projections over 17 mm of SWI data (TE/TR/FA/B0 ¼ 20ms/57 ms/ 20  /3 T) acquired before (a) and 50 min after caffeine ingestion (b). Relative signal changes between preand post-caffeine uptake are shown for signal magnitude (c) and phase (d). The decreased blood oxygenation after caffeine intake increases field inhomogeneities around veins and the phase shifts between spins inside and outside the vessel. Consequently, the venous signal decreases and, hence, improves the contrast between veins and parenchyma.

arterial blood is completely oxygenized. Images were adopted from He and Yablonskiy [19].

FIGURE 28.6 Maps of the venous blood volume fraction (l) and oxygenation extraction fraction (OEF). The OEF can be calculated by Y ¼ (100% OEF) providing that the

FIGURE 29.9 A multiple sclerosis case showing an acute lesion with contrast: (a) FLAIR, (b) postcontrast T1-weighted imaging, (c) SWI magnitude image, (d) SWI filtered phase, and (e) high-resolution PWI-rCBV. FLAIR shows many lesions in this slice but only one lesion (in circle) shows enhancement in the postcontrast T1-weighted imaging. This lesion shows an increase in rCBV of the PWI data.

FIGURE 29.2 Comparison between low- and high-resolution PWI images for a single subject on rCBV maps (left column), rCBF maps (middle column), and rMTT maps (right column). (a–c) High resolution, long TE (1  1  4 mm3, TE ¼ 98 ms); (d–f) low resolution, long TE (2  2  4 mm3, TE ¼ 98 ms); (g–i) high resolution, short TE (1  1  4 mm3, TE ¼ 52 ms, 6/8 partial Fourier); (j–l) low resolution, short TE (2  2  4 mm3, TE ¼ 52 ms). Note the blooming effect in the Sylvian fissures (images d, e and j, k) in the low-resolution PWI image compared with high resolution.

FIGURE 29.10 A multiple sclerosis case showing that some lesions (perhaps chronic) have a reduced CBV and increased iron content. (a) FLAIR, (b) precontrast SWI magnitude, (c) SWI filtered phase precontrast, and (d) PWI-CBV. The bright areas in the FLAIR correspond with the dark gray in the PWI scan indicating reduced CBV. Both the SWI magnitude and phase images show iron deposition in the larger lesion (arrow).

FIGURE 32.2 A simple global threshold can often be used as a means to visualize the major veins. An example of the data produced by this process overlaid on the original mIP is shown here. This can be used as the first step in the more complicated segmentation using statistical local thresholding. Image acquired at 7 T with 0.21  0.21  1 mm3 resolution and mIP over 25 mm. FIGURE 32.3 Statistical segmentation results before size and shape filtering to remove false positives. (See text for full caption.)

FIGURE 32.5 Final segmentation results displayed on the mIP along with the original mIP for comparison. (See text for full caption.)

FIGURE 32.6 Final segmentation results shown for a single slice. The small veins are well marked with only a few being missed. The large number of very small veins identified by this semiautomated process is far more practical than manual segmentation.

FIGURE 32.7 Original mIP (a), segmentation results overlaid on mIP (b), and surface rendered image of the segmented vessels (c). Surface rendering is very fast allowing the user to easily adjust the orientation of the image and fully understand the 3D geometry.

FIGURE 16.3 (a) Coronal view based on unwrapped SWI phase images (acquired in axial orientation and reformatted) of a patient shows a cavernous lesion with the typical paramagnetic pattern. (b) Simulated coronal phase image showing a spherical paramagnetic field distribution. Phase values are decreased at both lobes (dark) and increased at the equator (bright). (c) Isosurface rendering of the lesion shown in (a). (d) Isosurface representation of the field distribution (with B0 parallel to the z axis) induced by a spherical perturber with a different susceptibility than its surroundings. The sign of the two lobes is reversed, compared to that of the equatorial rim. If the perturber is paramagnetic, both lobes possess positive values and the equatorial rim is negative. This effect is reversed for a diamagnetic perturber. Reproduced with permission from Ref. 36.

FIGURE 32.9 (a) MIP over 26 mm of SWI data. (b) Manually marked true microbleeds identified using magnitude, phase, SW, and mIP images. (c) Automatically marked suspected bleeds (80.9% sensitivity, 5–30% specificity). These would be treated as a candidate set of suspected microbleeds and manually reviewed to increase the specificity. The two that were missed here (bottom left, shown in blue in part (b)) were merged with the vein they lie adjacent to causing them to have more vein-like features.

FIGURE 34.5 Reconstructions from a 9.4 T BOLD 3D venographic data set of cat brain. (a) Coronal view reconstructed by averaging pixels across a 1.25 mm thick slab. Red curves are 2.3 mm in length and indicate different cortical depths, within visual cortical area 18. (b) A single-pixel thick (78 mm) reconstruction at the location of the yellow curve in (a). The red square in (b) represents a 2.3  2.3 mm2 region within the visual cortex. (c–f) Expanded views of selected 2.3  2.3  0.078 mm3 regions at shallow, middle, and deep cortex, as indicated by the red curves in (a). Dark spots in expanded images indicate intracortical emerging venous vessels.

FIGURE 34.6

Comparison of high-resolution BOLD fMRI map (a) and BOLD venographic image in a rat brain (b). Activation foci in the somatosensory cortex (a) are correlated with intracortical veins (b), as indicated by arrows, and some activation foci outside the somatosensory cortex (arrowheads) are located around regions of large draining veins, including the superior sagittal sinus. The bar in (b) represents 3 mm.

Part I

Basic Concepts

1 Introduction to Susceptibility Weighted Imaging J€ urgen R. Reichenbach and E. Mark Haacke

Susceptibility weighted imaging (SWI) in its current form has only recently entered the realm of magnetic resonance imaging (MRI) techniques despite the fact that magnetic susceptibility, c , is certainly of central importance in the field of magnetism and magnetic resonance. SWI is an MRI method that takes advantage of signal loss and phase information to reveal important anatomical and physiological information about vessels and tissues. To date, it has been used predominantly in the brain, but is now beginning to find uses in other parts of the body as well. All current applications will be addressed in this book. With the clinical use of SWI now in place at hundreds of sites around the world, it is likely that radiologists and researchers alike will continue to discover new applications throughout the body. Although being relatively young in age, the method already has some history and has changed its name from its infancy to later developments. Originally, it was referred to as high-resolution BOLD venographic (HRBV) imaging to stress the ability for visualizing the venous vasculature in the brain. A little later, an alternate acronym named AVID BOLD was suggested, where AVID stood for the application of venographic imaging to diagnose disease and BOLD for blood oxygenation level dependent imaging. Finally, the term susceptibility weighted imaging, or SWI for short, was introduced. The older acronyms can of course still be used if the goal is just to visualize the veins for vascular or anatomical purposes; however, one should be aware that they refer to a more specific subset of the more general concept of SWI. Historically, the work developed from a focus on BOLD imaging. Due to Seiji Ogawa’s seminal papers on BOLD imaging in 1990 [1–3], the importance of a comprehensive understanding of the BOLD phenomena was soon understood. This led to a publication

Susceptibility Weighted Imaging in MRI, By E. Mark Haacke and J€urgen R. Reichenbach Copyright  2011 by Wiley-Blackwell

3

4

INTRODUCTION TO SUSCEPTIBILITY WEIGHTED IMAGING

expanding on the importance of this concept in 1993 [4], followed by papers on the topics of high-resolution BOLD imaging [5], the size of the expected signal [6], and the role that the venous blood played [7]. The next steps on this historical path included investigations on the consistency of the BOLD effect [8], new ways to reveal its presence through the creation of images showing the susceptibility-affected regions from other tissues [9], and investigations of long echo time effects [10]. All this work with gradient echo imaging culminated in a review of the topic [11]. Much of these efforts on understanding the early BOLD effect led to the great vein/brain debate set off by discussions between Amos Hopkins and Mark Haacke, then at Case Western Reserve University (who proposed that the major source of the BOLD signal came from major veins), and Bruce Rosen and Jacques Belliveau (the early investigators of the BOLD effect with an emphasis on diffusion effects) at Massachusetts General Hospital [12]. The result of the thrust by the CWRU group was a demonstration that veins played a major role in the BOLD effect from both intravascular and extravascular perspectives. This work provided the early roots in identifying the importance of veins in generating the BOLD effect and the concepts laid out in the paper of Lai et al. [4], and eventually led to the focus on a better understanding of the sources of susceptibility and also enhancing the visibility of the veins themselves. Prior to this, and often still mistakenly today, people believed that it was diffusion around these gradients that led to the BOLD effect. At this point in time, it had become clear that the phase of the complex MR signal could reflect a major non-T2* -based beating effect. This was then used to collect high-resolution 3D gradient echo data at the appropriate echo times to enhance the cancellation of the signal of veins with brain parenchyma (see Figure 1.1). Thus was born the high-resolution BOLD venographic, or HRBV, method [13]. During this period, as an improved understanding of the effects of oxygen saturation and blood flow evolved, a new interleaved method was used to measure susceptibility and flow almost simultaneously [14]. In this way, it was shown that venous oxygen saturation (Y) deep in the brain was roughly 0.55 [14, 15]. With these experiments, it became clear that phase could be used to distinguish arteries from veins. This possibility was first examined in the leg (due to the fact that its vessels are almost parallel to the main magnetic field), where, using the high-pass phase information, signal from veins could be separated from arteries, even in the presence of a contrast agent [16]. About the same time, high-resolution capabilities demonstrated convincingly that HRBV shows small veins better as the spatial resolution increases, giving an unprecedented in vivo view of cerebral venous vessels heretofore only available from cadaver brain studies [17]. Then a new direction of evaluating the BOLD effect was pursued where the signal behavior was investigated in greater detail by applying multi-echo methods [18]. Still, the role that other brain tissues played in the signal formation, especially cerebrospinal fluid, was not clear, so some work was done on modeling the BOLD response [19–21]. In parallel to these developments that were more oriented toward basic research, HRBV was also being tested for a number of interesting clinical applications (hence the move to a new acronym AVID BOLD), including occult venous brain diseases [22, 23], arteriovenous malformations [24], multiple sclerosis [25], brain tumors [26, 27], comparisons of activated regions in functional MRI (fMRI) [28], and applications with respect to improved target volume characterization and treatment planning in radiotherapy [29]. Methods were explored to further improve the image quality, such as reducing echo times using a contrast agent [30]. This worked well for T1 shortening agents because it increases the signal from the blood pool and leads to larger cancellation effects. Another possibility

INTRODUCTION TO SUSCEPTIBILITY WEIGHTED IMAGING

5

FIGURE 1.1 Phase images acquired at 3 T with echo times of (a) 12 ms, (b) 20 ms, (c) 40 ms, and (d) 60 ms. Most veins and cortical structures start to become visible even at the 12 ms echo time (equivalent to 24 ms TE at 1.5 T), and become more and more pronounced with longer echo times. However, the signal loss associated with T2* effects due to extravascular field distortions around the veins also increases with echo time, making the apparent venous vessel diameter much larger than it is physically (this is also known as the blooming artifact). Hence, an echo time of 20 ms appears to provide a nice balance of good structural definition in phase with low concomitant T2* loss.

to improve image quality is to utilize the signal gain with higher field strengths and the HRBV concept was successfully extended to 3 T soon after [31]. Around the same time, the Ohio group started to use their 8 T scanner to acquire susceptibility weighted images at this ultrahigh field strength. They demonstrated with post mortem specimens that images with spatial resolutions of 0.25
0.25
2.0 mm3 could depict vessels of less than 100 mm

6

INTRODUCTION TO SUSCEPTIBILITY WEIGHTED IMAGING

FIGURE 1.2 The left image represents a projection over eight 1 mm thick susceptibility weighted (SW) images with an in-plane resolution of 215 mm
215 mm at 7T. The right image is a blowup of part of a single-phase slice to compare with the stained cadaver brain results from Duvernoy et al. [37]. Part of the image reprinted from Ref. [37] with permission from Elsevier Science.

in diameter [32]. It was also shown that phase rather than magnitude reconstruction can further improve these images at 8 T by providing not only improved depiction of the vasculature, but also better GM/WM contrast [33]. The topic of using phase images and employing unwrapping methods to improve the diagnostic value of HRBV was also investigated at lower field strengths (1.5 and 3 T) and resulted in high-quality brain venograms, even in regions where rapid susceptibility changes occur [34, 35]. More recently, SWI has been evaluated at 7 T [36], showing beautiful venograms and revealing even the smallest of veins: the venules (see Figure 1.2), which are similar to in vitro studies by Duvernoy et al. [37]. In 2004, the term susceptibility weighted imaging was coined to better stress the fact that susceptibility differences between tissues, which is different from spin density, T1- or T2weighted imaging, can be utilized as a new type of contrast in MRI [38], and that the method is not necessarily restricted to visualizing veins in the brain. In fact, the areas of applications, to name a few, may range from enhancing gray matter/white matter contrast and water/fat contrast using phase information to identifying brain iron [39] or cerebrovascular malformations. Key to these possibilities is the utilization of magnetic susceptibility differences as they manifest themselves in local phase changes between tissues, and that the SWI high-pass filtered phase image is used either by itself as a new source of contrast and/or as a means of altering the contrast in the magnitude image. A simple example is given in Figure 1.3, although one will find many other examples throughout the book. As it happens many times during the development of a new method or technique, the term introduced to describe the method has already been used before. Not surprisingly, this is also the case with the term susceptibility weighted imaging that has been used in the literature to describe data acquisition by using the magnitude information of conventional, T2* -weighted gradient echo images, which are mostly 2D with relatively long echo times and long repetition times. As an example, Ohnishi et al. applied this technique, which they

INTRODUCTION TO SUSCEPTIBILITY WEIGHTED IMAGING

7

FIGURE 1.3 (Left) A fluid attenuation inversion recovery (FLAIR) magnitude image and (right) a highpass filtered phase image acquired at 3 T. Note the gray matter/white matter contrast in the area of the motor cortex (arrow) on the phase image.

called susceptibility weighted gradient echo MR imaging [40], to investigate whether cerebral vasodilatory capacity can be shown by the acetazolamide challenge in healthy subjects and patients with chronic occlusive cerebrovascular disease. Also commonly known in the literature is the technique of dynamic contrast-enhanced susceptibility weighted imaging, which acquires T2* -weighted images to track the bolus of a contrast agent passing through the brain or any other organ, thereby leading to a signal intensity decrease because of a transient increase in susceptibility. This method has become a widely used tool for perfusion measurements and is usually performed with rapid gradient echo imaging or ultrafast echo planar imaging sequences. Under normal clinical conditions, only magnitude information is used with these sequences and phase information is discarded. Furthermore, acquisition speed is traded off against spatial resolution. However, technology continues to develop and resolution for EPI scans continues to improve (Figure 1.4). Even these methods can be used to obtain phase data that are subsequently processed to create what is referred to in this book as SWI filtered phase and processed SWI magnitude data. Contrasting these developments, SWI, as it has evolved over the years, can now be considered an imaging method that combines the following features in a rather unique combination. It is based on high-resolution 3D gradient echo imaging (usually with full flow compensation in all three directions), where the 3D nature of the sequence allows for the acquisition of thin slices to reduce signal losses from background field inhomogeneities. Filtering the phase images removes unwanted field effects and phase wraps, generating an image contrast distinct from the magnitude image. A phase mask is created that is applied to the magnitude images, inherently combining the magnitude and phase contrast. Finally, a minimum intensity projection (mIP) is taken over adjacent contiguous slices. With this special data acquisition and image processing, it becomes possible to produce magnitude images with enhanced contrast that are exquisitely sensitive to venous blood, hemorrhage, or iron storage, and offer the potential to improve diagnosis of diseases and follow-up for

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INTRODUCTION TO SUSCEPTIBILITY WEIGHTED IMAGING

FIGURE 1.4 (a) MRA pre-Gd; (b) phase processed SWI post-Gd; (c) high-resolution perfusion weighted imaging (PWI) with the original cerebral blood volume (CBV) map; and (d) overlay of SWI data with PWI data in an attempt to remove the macrovessel contamination and reveal pristine gray matter and white matter. Image quality and contrast may not be optimal due to conversion from color to grayscale display. Please see the color plates section for the original version of this figure.

INTRODUCTION TO SUSCEPTIBILITY WEIGHTED IMAGING

9

longitudinal studies. Of course, the SWI processed phase images themselves are of importance for quantifying iron [41] and for susceptibility mapping [39]. The latter is the final step of deconvolving phase into a susceptibility map. Although 3D data is preferred in the brain because of the vessels and small structures of interest, 2D breath-hold approaches are also possible in imaging the liver. The key feature for SWI is to use phase information for enhanced contrast and for local susceptibility information. One frequently asked question concerning susceptibility weighted imaging is: ‘‘How is SWI different from conventional gradient echo imaging?’’ The answer to this lies in the use of the filtered phase as briefly discussed above. Let us therefore diverge a little bit into the physics of why a T2* -weighted sequence shows signal losses in the first place and why, for example as in Figure 1.5a, it does not show the veins as well as they are seen

FIGURE 1.5 (a) Original magnitude gradient echo image, (b) phase mask, and (c) final processed SWI data. Note the enhanced venous contrast obtained by using the phase mask.

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INTRODUCTION TO SUSCEPTIBILITY WEIGHTED IMAGING

on the filtered phase (Figure 1.5b) or on the SWI processed image itself (Figure 1.5c). First, it must be remembered that signal dephasing occurs because a phase spread exists across a voxel. Without phase dispersion, there is no extra T2* effect. Therefore, tissues that have very low and uniform iron distribution, for instance, will show a phase effect, but not a T2* effect. An example of this antithetic effect is shown for the stroke patient in Figure 1.6. Now, performing gradient echo imaging with higher and higher spatial resolution, the phase dispersion across a voxel diminishes, and one sees less and less T2* effects while the phase maintains its integrity. This is just as true at high field strengths, where, as long as the product of B0TE remains constant, the filtered phase images will look the same at all field strengths apart from signal-to-noise effects (see Chapter 20). Therefore, one would expect that the fully processed SWI data should show the veins much better than the original gradient echo magnitude images (see Figure 1.7). An important precursor to the final processed SWI magnitude data is the creation of the filtered phase images. These images directly carry susceptibility information, although they are not yet a direct map of the actual susceptibility. Nevertheless, after processing the phase, the information seen on these images correlates well with veins and iron in the form of ferritin or hemosiderin in the brain. One interesting aspect, which is also covered in the following chapters and anticipated to have a major impact in the field of SWI, is the topic of susceptibility mapping and potentially quantifying magnetic susceptibility. Since the magnetic induction B determines the local precession frequency and is given by B ¼ m0  ðH þ MÞ ¼ m0  ð1 þ xÞ  H, any spatial variation in x is also reflected in the spatial variation of the Larmor frequency (see chapter 2 for more details). Therefore, it should be possible to relate directly the spatial variation of the MR frequency to the spatial variation of susceptibility. This is indeed readily possible for objects with simple geometries, such as cylinders, spheres, or plates. The problem, however, becomes more intricate for more complex susceptibility distributions, for which it is usually necessary to use numerical methods. Quite recently, efforts have been undertaken to calculate magnetic field perturbations via Fourier analysis of heterogeneous magnetic susceptibility distributions [42, 43]. Based on these approaches, it may become possible to calculate tissue susceptibilities from phase images, which, in turn, would be highly beneficial since magnetic susceptibility is an intrinsic tissue property that reflects tissue composition more closely than the phase image. Quantifying magnetic susceptibility of biological tissues in this way would have immediate important clinical implications, such as differentiating a hemorrhagic lesion as acute or chronic, identifying calcifications, or measuring oxygen saturation in the blood (see Figure 1.8). This susceptibility mapping concept will make it possible to quantify iron and even new iron-tagged contrast agents for molecular imaging. The collection of topics in the following chapters demonstrates the plethora of possible applications both from a basic research point of view and from a clinical point 3

FIGURE 1.6 An example SWI study for a stroke patient. (a) FLAIR image showing a hint of some remnant edema in the left globus pallidus in just one single slice. (b) The T1-weighted anatomical scan shows no evidence of the bleed. (c) A long TE gradient echo scan (TE ¼ 40 ms) shows no evidence of the bleed on the magnitude image as far as T2* effects are concerned. (d) The SWI filtered phase image clearly shows the area of stroke in one of the seven slices, where all seven slices revealed a similar effect. (e) A T2 weighted imaging showing no bleed. (f) The SWI image clearly delineating the blood. Reprinted with permission from American Journal of Neuroradiology.

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INTRODUCTION TO SUSCEPTIBILITY WEIGHTED IMAGING

FIGURE 1.7 (a) Pre-caffeine minimum intensity projection (mIP) over 20 slices with 2 mm thickness each. Visualization of the vessels is not particularly good. (b) A maximum intensity projection (MIP) over the high-pass filtered phase images for the same 20 slices. This image shows which parts of the magnitude image will be affected when the SWI data are processed. (c) Post-caffeine mIP over the same 20 slices. The visualization of the vessels has improved compared to (a) due to the vasoconstrictive effect of caffeine, although the image quality is not as good as the SWI processed data shown in (d). (d) The mIP of the fully processed SWI data demonstrating the venous system in great detail with excellent contrast.

of view. Written by experts in their respective fields, these topics comprise issues (among many others) such as the extraction of oxygen saturation, quantification of iron, applications to functional fMRI, and efforts in speeding up data acquisition, followed by a wide range of clinical applications in which SWI has already proven its potential.

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FIGURE 1.8 (a) Conventional SWI image (same as Figure 1.7d), showing the venous vasculature. (b) The corresponding susceptibility map showing the oxygenation levels of the same veins quantitatively.

When taking all these different aspects into consideration, it appears that there will be a bright future for the use of susceptibility weighted imaging in research and clinical applications in the years to come. REFERENCES 1. Ogawa S, Lee TM. Magnetic resonance imaging of blood vessels at high fields: in vivo and in vitro measurements and image simulation. Magn. Reson. Med. 1990;16:9–18. 2. Ogawa S, Lee TM, Nayak AS, Glynn P. Oxygenation-sensitive contrast in magnetic resonance image of rodent brain at high magnetic fields. Magn. Reson. Med. 1990;14:68–78. 3. Ogawa S, Lee TM, Kay AR, Tank DW. Brain magnetic resonance imaging with contrast dependent on blood oxygenation. Proc. Natl. Acad. Sci. USA 1990;87:9868–9872. 4. Lai S, Hopkins AL, Haacke EM, Li D, Wasserman BA, Buckley P, Friedman L, Meltzer H, Hedera P, Friedland R. Identification of vascular structures as a major source of signal contrast in high resolution 2D and 3D functional activation imaging of the motor cortex at 1.5 T: preliminary results. Magn. Reson. Med. 1993;30:387–392. 5. Haacke EM, Hopkins A, Lai S, Buckley P, Friedman L, Meltzer H, Hedera P, Friedland R, Klein S, Thompson L, Detterman D, Tkach J, Lewin JS. 2D and 3D high resolution gradient echo functional imaging of the brain: venous contributions to signal in motor cortex studies. NMR Biomed. 1994;7 (1–2):54–62. Erratum in NMR Biomed. 1994;7:374. 6. Yablonskiy DA, Haacke EM. Theory of NMR signal behavior in magnetically inhomogeneous tissues: the static dephasing regime. Magn. Reson. Med. 1994;32:749–763.

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7. Haacke EM, Lai S, Yablonskiy DA, Lin W. In vivo validation of the BOLD mechanism: a review of signal changes in gradient echo functional MRI in the presence of flow. Int. J. Imaging Syst. Technol. 1995;6:153–163. 8. Moser E, Teichtmeister C, Diemling M. Reproducibility and postprocessing of gradient-echo functional MRI to improve localization of brain activity in the human visual cortex. Magn. Reson. Imaging 1996;14:567–579. 9. Lai S, Reichenbach JR, Haacke EM. Commutator filter: a novel technique for the identification of structures producing significant susceptibility inhomogeneities and its application to functional MRI. Magn. Reson. Med. 1996;36:781–787. 10. Barth M, Diemling M, Moser E. Modulation of signal changes in gradient-recalled echo functional MRI with increasing echo time correlate with model calculations. Magn. Reson. Imaging 1997;15:745–752. 11. Reichenbach JR, Venkatesan R, Yablonskiy DA, Thompson MR, Lai S, Haacke EM. Theory and application of static field inhomogeneity effects in gradient-echo imaging. J. Magn. Reson. Imaging 1997;7:266–279. 12. Belliveau JW, Rosen BR, Kantor HL, Rzedzian RR, Kennedy DN, McKinstry RC, Vevea JM, Cohen MS, Pykett IL, Brady TJ. Functional cerebral imaging by susceptibility-contrast NMR. Magn. Reson. Med. 1990;14:538–546. 13. Reichenbach JR, Venkatesan R, Schillinger DJ, Kido DK, Haacke EM. Small vessels in the human brain: MR venography with deoxyhemoglobin as an intrinsic contrast agent. Radiology 1997;204:272–277. 14. Haacke EM, Lai S, Reichenbach JR, Kuppusamy K, Hoogenraad FGC, Takeichi H, Lin W. In vivo measurement of blood oxygen saturation using magnetic resonance imaging: a direct validation of the blood oxygen level-dependent concept in functional brain imaging. Hum. Brain Mapp. 1997;5:341–346. 15. Hoogenraad FG, Reichenbach JR, Haacke EM, Lai S, Kuppusamy K, Sprenger M. In vivo measurement of changes in venous blood-oxygenation with high resolution functional MRI at 0.95 tesla by measuring changes in susceptibility and velocity. Magn. Reson. Med. 1998;39:97–107. 16. Wang Y, Yu Y, Li D, Bae KT, Brown JJ, Lin W, Haacke EM. Artery and vein separation using susceptibility-dependent phase in contrast-enhanced MRA. J. Magn. Reson. Imaging 2000;12:661–670. 17. Reichenbach JR, Essig M, Haacke EM, Lee BC, Przetak C, Kaiser WA, Schad LR. High-resolution venography of the brain using magnetic resonance imaging. MAGMA 1998;6:62–69. 18. Barth M, Reichenbach JR, Venkatesan R, Moser E, Haacke EM. High-resolution, multiple gradient-echo functional MRI at 1.5 T. Magn. Reson. Imaging 1999;17:321–329. 19. Hoogenraad FG, Hofman MB, Pouwels PJ, Reichenbach JR, Rombouts SA, Haacke EM. Submillimeter fMRI at 1.5 Tesla: correlation of high resolution with low resolution measurements. J. Magn. Reson. Imaging 1999;9:475–482. 20. Hoogenraad FG, Pouwels PJ, Hofman MB, Reichenbach JR, Sprenger M, Haacke EM. Quantitative differentiation between BOLD models in fMRI. Magn. Reson. Med. 2001;45:233–246. 21. Lai S, Glover GH, Haacke EM. Spatial selectivity of BOLD contrasts: effects in and around draining veins. In: Moonen CTW, Bandettini PA, editors. Functional MRI, Springer, Berlin, 1999, pp.221–231. 22. Lee BC, Vo KD, Kido DK, Mukherjee P, Reichenbach J, Lin W, Yoon MS, Haacke M. MR highresolution blood oxygenation level-dependent venography of occult (low-flow) vascular lesions. AJNR Am. J. Neuroradiol. 1999;20:1239–1242.

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23. Reichenbach JR, Jonetz-Mentzel L, Fitzek C, Haacke EM, Kido DK, Lee BC, Kaiser WA. Highresolution blood oxygen-level dependent MR venography (HRBV): a new technique. Neuroradiology 2001;43:364–369. 24. Essig M, Reichenbach JR, Schad LR, Schoenberg SO, Debus J, Kaiser WA. High-resolution MR venography of cerebral arteriovenous malformations. Magn. Reson. Imaging 1999;17: 1417–1425. 25. Tan IL, van Schijndel RA, Pouwels PJ, van Walderveen MA, Reichenbach JR, Manoliu RA, Barkhof F. MR venography of multiple sclerosis. AJNR Am. J. Neuroradiol. 2000;21:1039–1042. 26. Haacke EM, Herigault G, Kido D, Tong K, Obenaus A, Yu Y, Reichenbach JR. Observing tumor vascularity noninvasively using magnetic resonance imaging. Image Anal. Stereol. 2002;21:107–113. 27. Reichenbach JR, Haacke EM. High-resolution BOLD venographic imaging: a window into brain function. NMR Biomed. 2001;14:453–467. 28. Baudendistel KT, Reichenbach JR, Metzner R, Schroeder J, Schad LR. Comparison of functional MR-venography and EPI-BOLD fMRI at 1.5 T. Magn. Reson. Imaging 1998;16:989–991. 29. Schad LR. Improved target volume characterization in stereotactic treatment planning of brain lesions by using high-resolution BOLD MR-venography. NMR Biomed. 2001;14:478–483. 30. Lin W, Mukherjee P, An H, Yu Y, Wang Y, Vo K, Lee B, Kido D, Haacke EM. Improving highresolution MR BOLD venographic imaging using a T1 reducing contrast agent. J. Magn. Reson. Imaging 1999;10:118–123. 31. Reichenbach JR, Barth M, Haacke EM, Klarh€ofer M, Kaiser WA, Moser E. High-resolution MR venography at 3.0 Tesla. J. Comput. Assist. Tomogr. 2000;24:949–957. 32. Dashner RA, Kangarlu A, Clark DL, Chaudhury AR, Chakeres DW. Limits of 8-Tesla magnetic resonance imaging spatial resolution of the deoxygenated cerebral microvasculature. J. Magn. Reson. Imaging 2004;19:303–307. 33. Abduljalil AM, Schmalbrock P, Novak V, Chakeres DW. Enhanced gray and white matter contrast of phase susceptibility weighted images in ultra-high-field magnetic resonance imaging. J. Magn. Reson. Imaging 2003;18:284–290. 34. Rauscher A, Barth M, Reichenbach JR, Stollberger R, Moser E. Automated unwrapping of MR phase images applied to BOLD MR-venography at 3 Tesla. J. Magn. Reson. Imaging 2003;18:175–180. 35. Rauscher A, Sedlacik J, Barth M, Mentzel HJ, Reichenbach JR. Magnetic susceptibility weighted MR phase imaging of the human brain. AJNR Am. J. Neuroradiol. 2005;26:736–742. 36. Deistung A, Rauscher A, Sedlacik J, Stadler J, Witoszynskyj S, Reichenbach JR. Susceptibility weighted imaging at ultra high magnetic field strengths: theoretical considerations and experimental results. Magn. Reson. Med. 2008;60:1155–1168. 37. Duvernoy HM, Delon S, Vannson JL. Cortical blood vessels of the human brain. Brain Res. Bull. 1981;7:519–579. 38. Haacke EM, Xu Y, Cheng YC, Reichenbach JR. Susceptibility weighted imaging (SWI). Magn. Reson. Med. 2004;52:612–618. 39. Haacke EM, Cheng NY, House MJ, Liu Q, Neelavalli J, Ogg RJ, Khan A, Ayaz M, Kirsch W, Obenaus A. Imaging iron stores in the brain using magnetic resonance imaging. Magn. Reson. Imaging 2005;23:1–25. 40. Ohnishi T, Nakano S, Yano T, Hoshi H, Jinnouchi S, Nagamachi S, Flores L, 2nd, Watanabe K, Yokogami K, Ohta H. Susceptibility weighted MR for evaluation of vasodilatory capacity with acetazolamide challenge. AJNR Am. J. Neuroradiol. 1996;17:631–637. 41. Haacke EM, Ayaz M, Khan A, Manova ES, Krishnamurthy B, Gollapalli L, Ciulla C, Kim I, Petersen F, Kirsch W. Establishing a baseline phase behavior in magnetic resonance imaging to

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determine normal vs. abnormal iron content in the brain. J. Magn. Reson. Imaging 2007;26:256–264. 42. Marques JP, Bowtell R. Application of a Fourier-based method for rapid calculation of field inhomogeneity due to spatial variation of magnetic susceptibility. Concepts Magn. Reson. 2005;25B:65–78. 43. Salomir R, de Senneville BD, Moonen CTW. A fast calculation method for magnetic field inhomogeneity due to an arbitrary distribution of susceptibility. Concepts Magn. Reson. 2003;19B:26–34.

2 Magnetic Susceptibility Jaladhar Neelavalli and Yu-Chung Norman Cheng

INTRODUCTION Magnetic susceptibility is a basic material property that measures the ability of a substance to get magnetized when placed in an external magnetic field. It may also be characterized as being the measure of the extent to which a substance modifies the strength of the magnetic field passing through it. Although these qualitative definitions appear very simple and straightforward, the physical explanation of how this property comes into being and what factors affect it requires a bit more elucidation. In this chapter, we briefly look at the physical sources of magnetic susceptibility at the atomic level and discuss how it affects MR signal and image formation. Although electric charge is the basis for all electric fields, it is the motion of electric charges that produces magnetic fields. A simple case is to consider a loop carrying current. The magnetic field produced by the current loop is equivalent to the magnetic field produced by a magnetic dipole (Figure 2.1). A magnetic dipole is a basic physical entity, which acts as the source of the magnetic field and has always two poles associated with it (hence the name dipole). Unlike isolated electric charge, isolated magnetic charges have not yet been observed in nature. A magnetic dipole is characterized by a vector quantity called magnetic moment (for more detailed discussion, see page 20 of Ref. 1). It is measured in A m2 in SI units. In this chapter, unless mentioned otherwise, we use SI units.

MAGNETIC MOMENT OF AN ATOM At the atomic level, the motions of electrons are described by quantum mechanics. In the physics of quantum mechanics, when a magnetic field is imposed on an atom, quantized energy states of electrons, protons, and neutrons will occur. The physical quantity spin is

Susceptibility Weighted Imaging in MRI, By E. Mark Haacke and J€urgen R. Reichenbach Copyright
2011 by Wiley-Blackwell

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FIGURE 2.1 A schematic drawing of a current loop showing the equivalent magnetic dipole of this loop. Note the direction of the current flow and the direction of the magnetic moment m.

used to describe these energy states. Spin is proportional to the magnetic moment of an electron or a nucleon; thus, for our discussion here, these two quantities are interchangeable. In theory, the net magnetic moment of an atom (or by extension of a molecule) can be calculated by vector summation of the individual spins from nucleons and electrons. Since the gyromagnetic ratio of an electron is roughly 680 times larger than the gyromagnetic ratio of a nucleon, the magnetic moment of an atom is dominated by the overall spin of electrons in an atom. The overall spin is calculated from the orbital spin, the spin of each electron itself, and the interactions between them. Hence, the macroscopic magnetic property of a material is predominantly from the electrons. Nonetheless, magnetic moments of nucleons provide the basis for the nuclear magnetic resonance (NMR) phenomenon, thus making MRI possible. The net spin (and therefore net magnetic moment) of nucleons in an atom provides the NMR signal. Since the tissue in most biological samples and living species contains predominantly water molecules, the proton in the hydrogen atom has become the essential nucleon in NMR and MRI. From an energy point of view, electrons within an atom are arranged in different orbitals or shells around the nucleus, each associated with a quantized energy level. In general, the arrangement is such that the total energy of the system is minimized; hence, in most cases, electrons preferentially occupy the lower energy shells first. Furthermore, within a given shell or subshell, electrons are preferentially arranged in pairs with their spin magnetic moments oppositely oriented. This arrangement leads to a cancellation of the spins, making the net magnetic moment contribution from that pair zero [2]. The same is the case with nucleons where protons and neutrons are arranged with their spins oppositely oriented for a minimum energy configuration. However, in elements that have an odd number of electrons or nucleons, usually at least one of the subatomic particles is left unpaired (there could be more than one unpaired electron, depending on the order of the filling of shells and subshells). In such cases, the unpaired electrons and nucleons together contribute to a finite atomic magnetic moment. For molecules, the orbital distribution of the electrons is further modified, because the chemical bond between atoms alters the energy levels of the molecular orbitals and thus affects the number of paired/unpaired electrons in the final molecule. Even if the individual atoms (or molecules) of a substance possess a magnetic moment, corresponding macroscopic objects usually may not exhibit magnetic properties, unless the moments align preferentially in a particular direction as, for example, in iron. Due to thermal energy at room temperature, in many substances, different atomic magnetic dipole moments point randomly in different directions and the net vector sum of these moments ends up

BULK MAGNETIC FIELDS

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being zero or negligible. However, when placed in an external magnetic field, these atomic magnetic moments tend to align preferentially with the external field, thus resulting in a measurable macroscopic magnetic moment.

BULK MAGNETIC FIELDS When an external uniform magnetic field B0 ¼ m0H0 is applied to a substance, the actual field B inside the material is given by B ¼ m0 ðH þ MÞ

ð2:1Þ

where B is measured in Tesla (T), H is measured in Ampere/meter (A/m), M is the permanent magnetization or the induced magnetization (i.e., magnetic moment per unit volume of the substance measured in A/m), and m0 is the absolute permeability of free space (4p  107) with units of T m/A. Outside the material, the field is given by B ¼ m0H. The bold notation signifies that these quantities are vectors. The fields B0 and H in the entire space (inside and outside) are solved through the boundary conditions with the given material geometry, B0, and M [3]. When a material is not permanently magnetized, that is, when M is not a constant, the induced magnetization M inside the material may be related to the H field by a constant susceptibility x through M ¼ xH

ð2:2Þ

In this case, the fields B and H are still solved through the boundary conditions with the applied field B0 and object geometry but with susceptibility x. Note that x is dimensionless. In addition, equation (2.1) can be written as B ¼ m0 ð1 þ xÞH


 1þx or B ¼ m0 M x

ð2:3aÞ

The field distribution outside the material will also be perturbed due the fact that the object has an induced magnetization. The solution for field perturbation outside the object is a vector function of the induced magnetization M and depends on the shape and volume of the object: Bout ðrÞ ¼ B0 þ f ðM; object shape; object size; rÞ

ð2:3bÞ

where f denotes ‘‘function of’’, B0 is the external magnetic field, and Bout is the field at a point r outside the object. Now, why are we interested in magnetic field deviations within and around a sample or tissue? It is because MRI measurements are sensitive to the magnetic field manifested in frequency through the Larmor equation (we assume a right handed system in this chapter). v ¼ g  B ð2:4Þ where v is the precession angular frequency, g is the gyromagnetic ratio of the proton, and B is the actual field experienced by a proton. Equation (2.4) is central to MR imaging

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methodology and this is the reason why susceptibility is key to understanding the signal response in MR images.

DIAMAGNETISM, PARAMAGNETISM, AND FERROMAGNETISM Based on the macroscopic behavior under the influence of an external magnetic field, various substances are broadly classified into diamagnetic, paramagnetic, and ferromagnetic materials. From equation (2.3a), if the susceptibility x is positive, the material or the object is considered as paramagnetic. If x is negative, the material is diamagnetic. For vacuum, x is zero. In the case of permanent magnetic or ferromagnetic substances, equation (2.3a) is not suitable. The original equation (2.1) must then be used. In this case, the magnetization M is a positive constant. Detailed discussion of different magnetic behavior and properties of materials can be found in any of the standard texts on the subject [4–6]. Chapter 25 of the MRI textbook [1] also serves as a good starting point. Diamagnetism Inert gases, crystal salts, such as NaCl, most organic molecules, and water are some examples of diamagnetic substances. Human tissues tend to be mostly water by weight. As a consequence, almost all soft tissues in the body are diamagnetic in nature. Apart from soft tissue, bone is also diamagnetic and is slightly more diamagnetic than most of the soft tissues in the body. In MRI, it is important to realize that the term ‘‘paramagnetic’’ or ‘‘diamagnetic’’ is used relative to the susceptibility of water, rather than that of vacuum, as originally defined in physics. As we will see later in this book, the relative difference between tissue magnetic susceptibilities is still a very fascinating aspect to study. To put things in perspective, Table 2.1 provides magnetic susceptibility values for a few tissues of interest [7]. Paramagnetism Copper (Cu2 þ ), manganese (Mn2 þ ), cobalt (Co2 þ ), chromium (Cr2 þ ), iron (Fe2 þ and Fe3 þ ), dysprosium (Dy3 þ ), and gadolinium (Gd3 þ ) are some examples of paramagnetic ions. Molecular oxygen is also slightly paramagnetic in nature. The most prominent ion among these is Gd3 þ , which combined with a chelating agent, DTPA to reduce its toxicity,

TABLE 2.1 Magnetic Susceptibilities of a few Biological Tissue Tissue Lipids (stearic acid) Cortical bone Hemoglobin protein (without Fe ions) Fully deoxygenated red blood cell Fully deoxygenated whole blood (assuming Hctb ¼ 0.45) Ferritin (completely loaded with 4500 Fe3 þ ions) Pure water a b

From Ref. 7. Hct: Hematocrit.

Magnetic Susceptibilitya 10  106 12.82  106 9.91 106 6.56  106 7.9  106 þ 520  106 9.05  106

THE EFFECT OF MAGNETIC SUSCEPTIBILITY IN MRI

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makes the commonly used T1 reducing paramagnetic contrast agent for MR imaging. Gd3 þ is one of the strongest paramagnetic ions with seven unpaired electrons. The efficiency as a T1 reducing agent primarily comes about due to its large magnetic moment, as the T1 reducing capacity of a paramagnetic ion is proportional to the square of its magnetic moment [8]. Ferromagnetism Ferromagnetism is the magnetic phenomenon that we are most familiar with in our daily lives. From the horseshoe magnets and small permanent magnets we stick on refrigerators to the ones used in stereo speakers or to the metallic cores of the power transformers that help distribute electricity to our homes; all of them are made from ferromagnetic materials. Ferromagnetic materials can achieve saturation magnetization even at room temperature under high external magnetic field. Saturation means that the magnetization is a constant when the magnetic field is higher than a specific field strength. Like paramagnetism, ferromagnetism also arises from the individual atomic magnetic moments but results in much stronger induced magnetization because of their special structural arrangement. Atoms or molecules in ferromagnetic materials are arranged in unique crystalline structures in which neighboring atomic moments preferentially orient themselves parallel to each other as it proves to be actually a state of lower energy. As a result of this cooperative interaction, a large number of neighboring atoms together form a magnetic domain in which all its constituent atomic moments are pointing in one direction. However, the presence of ferromagnetic particles within the human tissue is rare and is often attributable to external sources, rather than biological [7].

THE EFFECT OF MAGNETIC SUSCEPTIBILITY IN MRI We have seen that owing to their magnetic susceptibility, different materials can alter the external applied field within and outside themselves. This change in field has a bearing on the MR image formation process, as is pointed out by the relations in equations (2.1–2.4). In MRI, spatial encoding is done by applying a magnetic gradient field that imparts a unique, known precession frequency at each location along the gradient direction. We can illustrate this concept with a simple one-dimensional magnetic gradient Gx, where the zcomponent of the applied magnetic field changes linearly along the x-direction. So when the gradient field is switched on, the field at a position x is given by: BðxÞ ¼ B0 þ Gx  x

ð2:5Þ

and the corresponding Larmor frequency using equation (2.4) is given by: vðxÞ ¼ gðB0 þ Gx  xÞ

ð2:6Þ

That is, each frequency corresponds to a specific spatial location and the Fourier transform is used to put back the signal amplitudes to their corresponding positions using their frequency information. Now, this process assumes that during the application of the field gradient (i.e., during the spatial encoding), the static field B0 is uniform across the whole volume being imaged and the gradient field is the only well-defined deviation from

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uniformity. However, as seen from equations (2.1) and (2.3a) the magnetic field can be perturbed by the presence of a magnetic substance. In such a case, the net precession frequency of the spins in or around a material is influenced not only by the applied gradient field, but also by the induced field perturbation. Therefore, in the presence of an additional field perturbation at a location x, equations (2.5) and (2.6) can be written as follows: BðxÞ ¼ B0 þ DBðxÞ þ Gx  x

ð2:7Þ

vðxÞ ¼ gðB0 þ DBðxÞ þ Gx  xÞ

ð2:8Þ

and

Equation (2.8) can be rewritten as





DB vðxÞ ¼ g  B0 þ Gx  x þ Gx

 ð2:9Þ

or vðx0 Þ ¼ g  ðB0 þ Gx  x0 Þ

ð2:10Þ

where x0 ¼ x þ

DB Gx

ð2:11Þ

Consequently, because the spins precess now with an angular frequency v(x0 ) and not with v(x), those spins that are experiencing the additional field perturbation DB(x) are mapped to a different (incorrect) location x0 (instead of x) during image reconstruction. This process is schematically illustrated in Figure 2.2a and an example of common image distortion seen near the air–tissue interface is presented in Figure 2.2b and c. This problem is more pronounced in places where there are metallic implants having strongly different magnetic susceptibilities compared to the susceptibility of the surrounding tissue in which they are embedded, as with hip and knee implants. Typically, imaging volumes are placed away from these implants to avoid susceptibility artifacts. In addition to image distortion, local differences in magnetic susceptibility also cause spins in the same neighborhood to precess at different frequencies. As time evolves, these spins start getting out of phase with each other. In a voxel containing a set of spins, the net MR signal is the vector sum of all the spins within that voxel. As these spins start getting out of phase with each other (i.e., phase dispersion within a voxel) due to magnetic susceptibility effects, the net vector sum of the signal from all the spins decreases dramatically, thus decreasing the net signal from the voxel. This leads to what is referred to in general as T2* dephasing, but the extra signal loss over and upon the irreversible T2 effect is referred to as the T 02 loss. This T 02 term is specific to the gradient echo acquisition (see Chapter 20 of Ref. 1 and Chapters 3 and 5 in this book). Although geometric distortion and T 02 signal loss are deleterious effects of magnetic susceptibility phenomena, all is not gloomy with magnetic susceptibility. As will be seen throughout the rest of this book, with proper MR image acquisition and processing, magnetic

THE EFFECT OF MAGNETIC SUSCEPTIBILITY IN MRI

23

FIGURE 2.2 (a) A simplified illustration of image distortion in one dimension. Profile (1) is the actual object spin density profile. (2) A hypothetical magnetic field deviation profile due to a magnetic susceptibility effect (such a profile can be seen in a vessel parallel to the main magnetic field). (3) An applied magnetic field gradient for spatial encoding. The profile, otherwise a straight line (the dashed part is the ideal field gradient), has an overlying additional localized field deviation due to the susceptibility effect, thus distorting the gradient profile. (4) The resultant MR signal profile showing signal distortion (compared to the actual profile in (1)) caused by incorrect mapping of the spins due to this additional magnetic field perturbation. (b) An example of a low-bandwidth, 120 Hz/pixel (i.e., prone to more distortion), transverse brain image showing distortion near the air–tissue interface (arrow) near the paranasal sinuses. (c) The corresponding image acquired with a higher bandwidth (465 Hz/pixel) showing much less distortion. A high bandwidth corresponds to a steeper slope in (a–3).

24

MAGNETIC SUSCEPTIBILITY

FIGURE 2.2 (Continued)

susceptibility differences between tissues can provide a very unique contrast. Furthermore, susceptibility itself can help in quantifying physiological status (Chapters 27 and 28) and in distinguishing lesions from normal tissue (Chapters 10–13 and 15). Another quite important aspect of magnetic susceptibility with respect to MR imaging (although not the focus of this book) is the compatibility of implants or other medical devices used in an MRI environment. The compatibility issue has primarily two aspects to it: (a) compatibility of the implant/instrument in terms of patient safety, that is, referring to bulk magnetic forces acting on the implants and/or heating up of the implants and consequently the surrounding tissues during imaging experiments, and (b) field perturbations around the implant/device, which result in image artifacts. From a safety perspective, implant materials should have minimal conductivity and especially from an imaging perspective, to keep distortion effects minimal, they have to be either weakly paramagnetic or diamagnetic. A more detailed discussion of this topic is given in Ref. 7. Chemical Shift An important physical phenomenon, which is similar to magnetic susceptibility in its electronic nature of origin, but has a different macroscopic manifestation in MRI, is the phenomenon of chemical shift. Chemical shift, unlike bulk magnetic susceptibility, does not induce a bulk magnetization in the material when it is placed inside an external magnetic field. However, being more local and related to the time-averaged interaction of the electrons within a molecule (i.e., intramolecular) and/or between neighboring molecules (intermolecular), it causes a uniform and finite shift in the magnetic field B0 experienced by certain nuclei within the molecule [9]. This shift in the field experienced by certain nuclei is proportional to the applied external magnetic field and is denoted by d. Thus, the actual field shift DB is given by the deviation from the applied field B0, that is,

25

THE ISSUE OF UNITS AND EFFECTIVE SUSCEPTIBILITY CALCULATION

DB ¼ dB0. Similar to magnetic susceptibility, the chemical shift d also is dimensionless, as it is expressed as a relative shift with respect to the external applied field (i.e., DB/Bo). As is the case with tissue susceptibility, chemical shifts are also small numbers, d  1. Usually, they are specified in terms of parts per million (ppm), that is, in units of 106 of the main field. As a result of the field shift DB, the precession angular frequency is shifted by Dv ¼ gðd  Bo Þ

ð2:12Þ

This frequency shift which is similar to frequency shifts from susceptibility effects, can cause both a shift in phase of the signal and image distortions in position (e.g., fat shift). Since chemical shift (as defined here) does not induce any net magnetic dipole moment in the material, there are no external field perturbation effects due to this phenomenon. Due to the difference in resonance field strength, there may be misregistration artifacts, for instance, of water and fat on MR magnitude images. Figure 2.3 shows the finite phase shift of hydrogen protons in fat, with respect to the precession frequency of water protons in the surrounding tissue.

THE ISSUE OF UNITS AND EFFECTIVE SUSCEPTIBILITY CALCULATION Although SI units are the accepted standard for quoting physical quantities, the use of cgs or Gaussian units continues to exist in the literature. Hence, a brief discussion about the different units used to measure/quote magnetic fields and magnetic susceptibilities and their conversion from one to another is beneficial. For the physical quantities discussed in this chapter, cgs units, SI units, and their corresponding conversion factors are summarized in Table 2.2 [7, 10]. The units of magnetic susceptibility of a substance can be measured/ quoted in three different ways: volume susceptibility x, mass susceptibility xg, or molar susceptibility x m. Table 2.3, adapted from Refs 1 and 7, provides the definitions of each of these quantities. As x r and x M are defined in terms of the volume susceptibility x, conversion from one form to the other becomes easy. However, one has to be careful when considering conversion of one susceptibility quantity to the other, especially for composite substances, such as solutions or biological tissues. For example, in a solution, each of its constituents along with the solvent need to be considered for proper conversion. The expression below provides a simple formula for calculating volume susceptibility for a solution from molar susceptibilities of its individual constituents: x¼

X

Ck  x M;k

ð2:13Þ

k

where Ck denotes the concentration of constituent k and x M,k is the molar susceptibility of constituent k. The index k considers all the constituents of the solution, including the solvent. The application of this expression is best seen with an example. If we add 80 mL of 0.5 M Gd-DTPA solution to 4 mL of water, what is the volume susceptibility of the resultant solution? We can calculate this using equation (2.13) as follows. The net solution volume is 4.080 mL (4 mL water þ 0.080 mL Gd-DTPA). Since the density of water is 1 g/mL, 4 mL of water contains 4/18 moles of water molecules. Therefore, the concentration of water is Cw ¼ (4/18)  (1/4.080) mol/mL. We know from

26

MAGNETIC SUSCEPTIBILITY

FIGURE 2.3

Magnitude and phase images of head (a, b) and neck region (c, d). Fat surrounding the optic nerve posterior to the eye (image (b), arrowhead) and subcutaneous fat in the neck (image (d), arrowhead) showing a distinct phase shift with respect to the surrounding brain or muscle tissue. The effective echo time of the phase images is 1 ms.

Ref. 7 that molar susceptibility of water is x M,water ¼ 1.64  1010 m3/mol  1.64  104 mL/mol. Now, 0.080 mL of 0.5 M solution of Gd-DTPA is added, so the number of Gd-DTPA moles in the solution is 0.5  80  106. Hence, the concentration of Gd-DTPA in the final solution is CGd-DTPA ¼ (0.5  80  106)/4.080 mol/mL. From Ref. 11, we know that the molar susceptibility of Gd-DTPA is x M,Gd-DTPA ¼ þ 0.3393

27

THE ISSUE OF UNITS AND EFFECTIVE SUSCEPTIBILITY CALCULATION

TABLE 2.2 Conversion Factors for Physical Quantities from cgs to SI Units Multiply the Number for Quantity

in cgs Unit

by

To obtain the Number in SI Unit

Flux density, B Magnetic field strength, H Magnetizationa, M Volume susceptibility, x Mass susceptibility, x r Molar susceptibility, x M Magnetic dipole moment, m

G Oe erg/G/cm3 or emu/cm3 Dimensionless cm3/g cm3/mol erg/G

104 103/4p 103 4p 4p  103 4p  106 103

T or Wb/m2 A/m A/m Dimensionless m3/kg m3/mol A/m2

a

The designation ‘‘emu‘‘ is not a physical unit and only stands for electromagnetic unit.

TABLE 2.3 Definitions of Volume, Mass, and Molar Magnetic Susceptibilities Symbol Volume susceptibility Mass susceptibility Molar susceptibility

x xr xM

Definition x ¼ M/H x r ¼ x/ra x M ¼ (x  MWb)/r

In the text, the terms volume susceptibility and magnetic susceptibility have been used interchangeably. a b

r is the mass density measured in kg/m3 in SI units and g/cm3 in cgs units. MW is the molecular weight measured in kg/mol in SI units and g/mol in cgs units.

 106 m3/mol  þ 0.3393 mL/mol. So, using equation (2.13), the volume susceptibility of the net solution is xv;solution ¼ Cw  x M;water þ CGd-DTPA  xM;Gd-DTPA ¼ 5:060  106 or 5:060 ppm Now, on the other hand, if volume susceptibilities of substances constituting a composite material, say for example blood, are known, finding out the net volume susceptibility of the composite material is also straightforward using the volume fractions of each of the constituents: X x¼ lk  x k ð2:14Þ k

where lk and xk are the volume fraction and volume susceptibility of the kth constituent, respectively. As mentioned, blood is a good example of such a composite substance, constituting mainly the red blood cells and plasma (they together constitute about 99% of whole blood by volume). However, one caveat is that volume susceptibility of a red blood cell depends on the oxygen saturation of hemoglobin within it. Neglecting the slight paramagnetic susceptibility contribution of dissolved oxygen in plasma, the net volume susceptibility of whole blood can be approximated as xwhole blood ¼ Hct  ðY  x oxy þ ð1YÞ  x deoxy Þ þ ð1HctÞ  xplasma

ð2:15Þ

where Hct stands for hematocrit, which is the volume fraction of red blood cells in whole blood, x plasma is the volume susceptibility of plasma, and x oxy and x deoxy are the volume susceptibilities of a red blood cell with 100% (Y ¼ 1) and 0% (Y ¼ 0) oxygen

28

MAGNETIC SUSCEPTIBILITY

saturation, respectively. So, the susceptibility difference between fully oxygenated whole blood (i.e., xwhole blood at Y ¼ 1) and any other vessel with a Y value between 1 and 0 can be given as x whole blood @ Y¼1 xwhole blood ¼ Hct  ð1YÞ  ðx oxy x deoxy Þ

ð2:16Þ

The susceptibility difference between fully oxygenated blood and fully deoxygenated red blood cell (x deoxy  x oxy) has been measured to be 2.262 ppm per unit hematocrit [11]. Furthermore, if we assume that the susceptibility of fully oxygenated whole blood, xwhole blood @ Y ¼ 1, is approximately equal to the susceptibility of the surrounding parenchyma (which is what we usually observe in MR data, see Chapter 25 of Ref. 1), we can write the expression for susceptibility difference between a blood vessel and surrounding tissue as xblood; relative ¼ x whole blood x tissue ¼ Hct  ð1YÞ  2:62 ppm

ð2:17Þ

The dependence of magnetic susceptibility of blood on its oxygenation state is a very useful physical phenomenon that could help in measuring the oxygenation levels and therefore metabolic state of the underlying tissue. EXPRESSIONS FOR MAGNETIC FIELD PERTURBATIONS OF A SPHERE AND A CYLINDER From equations (2.2) and (2.3), we know that any object within an external magnetic field gets magnetized owing to its magnetic susceptibility property and usually changes the magnetic field within and outside the object (not always though as these changes are geometry dependent). Using the boundary conditions for the induced magnetization distribution (which factors in the object’s shape and size), solutions for the fields inside and outside the object are obtained. Analytically solving these equations for objects with some structural symmetry like a sphere or a cylinder is relatively easy. Solving the field equations for an arbitrarily shaped object is cumbersome and often intractable analytically. Nonetheless, it is instructive to look at field perturbation solutions for uniform materials taken in certain standard symmetric geometries like a sphere or a cylinder to get a feel for the nature of the field distortions/perturbations that we can expect in MR imaging. For example, sinuses might be modeled as spheres and blood vessels as long cylinders. Since the external uniform magnetic field, B0, is applied along the z-direction, the objects primarily get magnetized along the z-direction, Mz, with Mx, and My, being negligible. Furthermore, since x  1 for most biological tissues, from equation (2.3a), we can approximate Mz as (x/m0)B0. Given these conditions, assuming that the objects are in vacuum, solving for B inside and outside by applying the proper boundary conditions [1] then yields the expressions for the magnetic field inside and outside a uniform sphere and an infinitely long cylinder as given in Table 2.4. For the cylindrical case, u is the angle that the long axis of the cylinder makes with the main magnetic field B0, and for the spherical case, u is the angle that the position vector r of the point of observation makes with the main magnetic field B0; f is the polar angle subtended by r on the plane perpendicular to the long axis of the cylinder; r is the position vector of the point of observation; and a is the radius of the sphere or the cylinder. Note that x here refers to volume susceptibility.

EXPRESSIONS FOR MAGNETIC FIELD PERTURBATIONS OF A SPHERE AND A CYLINDER

29

TABLE 2.4 Expressions for Field Inside and Outside a Uniform Sphere and an Infinitely Long Cylinder Internal Field Sphere

B0

Cylinder

B0 þ

xB0  ð3cos2 1Þ 6

External Field B0 þ

xB0 a 3   ð3cos2 1Þ 3 jrj3

B0 þ

xB0 a 2  sin2  cos 2w 2 jrj2

If a cylinder or a spherical geometry is embedded in some external medium or compartment that has a finite shape and susceptibility value (e.g., a microbleed or a long venous vessel inside the brain tissue), these field equations are slightly modified. The term x is replaced by Dx ¼ (xsphere or cylinder  xoutside compartment) and an additional field term that is dependent on the global geometry of the outer compartment is added. We will see in the following chapters that these expressions are of considerable help in understanding the phase variations that we observe around venous vessels and microbleeds and even in studying the effect of a blood vessel network on the T 02 signal decay. Phase at a given point in an MR image is sensitive to the local field perturbation (with respect to the uniform applied field B0), rather than the absolute field. So, phase w is given by w ¼ g  DB  t

ð2:18Þ

where DB is the field perturbation in B0 and t is the time at which signal is acquired. Note that, under the situation of structures with different susceptibilities embedded within each other, it is the difference in their susceptibilities, Dx, that becomes the important parameter determining the field perturbation. Within the human body, small relative susceptibility differences between adjacent tissues do exist and cause a unique phase signature in the MR signal. For example, inside a long blood vessel perpendicular (u ¼ 90 ) to the main magnetic field, with a given hematocrit (Hct) and oxygen saturation (Y), the phase inside the vessel can be given using equations (2.17) and (2.18) and the expression in Table 2.4 as w/

ðHct  ð1YÞ  2:62  106 Þ  gB0 t 6

ð2:19Þ

where t is the time at which signal is sampled. Figures 2.4 and 2.5 show a few example SWI filtered phase images (see Chapters 4 and 6) showing phase inside and outside veins and calcium depositions. Since SWI is sensitive to these phase changes, it provides a unique tissue contrast that is almost invariant at any imaging field strength. In conclusion, slight changes in tissue susceptibility can be visualized with phase imaging in MRI and these phase changes can be used in and of themselves and also as a means to enhance contrast over and above that available in the usual magnitude images. It is amazing that in vivo imaging at 3 T is able to distinguish shifts in the local field of 0.01 ppm with a resolution of 1 mm3 in a 10 min scan covering the entire brain. These small changes may help us better understand not only the disease states in the brain but also the normal brain. The next few chapters in this book provide more details about how gradient echo

30

MAGNETIC SUSCEPTIBILITY

FIGURE 2.4 (a) An axial SWI filtered 3 T phase image showing susceptibility reduced gray matter/ white matter contrast. This image shows clearly the difference in phase between veins and the surrounding tissue. Veins containing deoxyhemoglobin, being slightly more paramagnetic with respect to the surrounding parenchyma (see Table 2.1), show a distinct phase signature (negative phase with respect to parenchyma). (b) Sagittal SWI phase image showing the dipolar phase (arrow) pattern of a venous vessel running almost exactly perpendicular to the main magnetic field B0. (c) Left: Simulated phase from a cylinder with a finite Dx, oriented perpendicular to the field B0. The phase is simulated using the field expressions given in Table 2.4 as phase is linearly proportional to the field perturbation. Right: The result of SWI processing of the left image. We can clearly see that the phase behavior seen in this right image is very similar to the one seen in (b) for a blood vessel perpendicular to B0.

FIGURE 2.5 (a) Phase image showing discrete bright spots with opposite polarity field perturbation with respect to parenchyma (i.e., positive phase) indicating that the source is diamagnetic with respect to the surrounding brain tissue. Note the dark phase ring outside the bright region, a unique signature for a diamagnetic content inside the bright region. (b) A corresponding computed tomography image confirming the discrete sources to be calcium, which is indeed diamagnetic (see Table 2.1) with respect to surrounding tissue. (c) Phase image showing a paramagnetic phase of a microhemorrhage (arrowhead). Note the bright phase ring outside the dark region, a unique signature for a paramagnetic content inside the dark region. We can also see discrete calcium depositions in the putamen and globus pallidus (arrows) above. Reprinted with permission from American Journal of Neuroradiology.

REFERENCES

31

imaging works in general and SWI in particular and will further show how SWI is being used to obtain new clinical and technical insights into the human body.

REFERENCES 1. Haacke EM, Brown RW, Thompson MR, Venkatesan R. Magnetic Resonance Imaging: Physical Principles and Sequence Design, Wiley, New York, 1999. 2. Saini S, Frankel RB, Stark DD, Ferrucci JT Jr. Magnetism: a primer and review. AJR Am. J. Roentgenol. 1988;150:735–743. 3. Jackson JD. Classical Electrodynamics, 3rd edn, Wiley, Hoboken, 1999. 4. Van Vleck JH. The Theory of Electric and Magnetic Susceptibilities, Oxford University Press, London, 1932. 5. Morrish AH. The Physical Principles of Magnetism, Wiley, New York, 1965. 6. Jiles D. Introduction to Magnetism and Magnetic Materials, Chapman and Hall, London, 1991. 7. Schenck JF. The role of magnetic susceptibility in magnetic resonance imaging: MRI magnetic compatibility of the first and second kinds. Med. Phys. 1996;23(6):815–850. 8. Runge VM, Clanton JA, Lukehart CM, Partain CL, James AE, Jr., Paramagnetic agents for contrast-enhanced NMR imaging: a review. AJR Am. J. Roentgenol. 1983;141:1209–1215. 9. Zimmerman JR, Foster MR. Standardization of NMR high resolution spectra. J. Phys. Chem. 1957;61(3):282–289. 10. Lide DR. CRC Handbook of Chemistry and Physics, 90th edn, Taylor & Francis, Boca Raton, FL, 2009. 11. Weisskoff RM, Kiihne S. MRI susceptometry: image-based measurement of absolute susceptibility of MR contrast agents and human blood. Magn. Reson. Med. 1992;24:375–383.

3 Gradient Echo Imaging J€ urgen R. Reichenbach and E. Mark Haacke

INTRODUCTION Gradient echo imaging is one of the most important sequence types used in MRI today. In fact, only with the advent of gradient echo imaging sequences it has become possible to collect MRI data rapidly with high spatial resolution and low radio frequency (rf) power deposition [1, 2]. Prior to the availability of homogeneous magnets and gradient coil systems with large gradient strengths and fast switching times, spin echo-based sequences were the workhorse sequences. Nowadays, gradient echo-based imaging is considered a conventional technique and is routinely used for nearly every medical application in both 2D and 3D data acquisition modes. In this chapter, we will briefly touch on the very basic aspects of gradient echo imaging with particular emphasis on some of the issues that are of relevance to susceptibility weighted imaging (SWI). The topic itself has developed so broadly that it is not possible to cover it in its full complexity in a single chapter. For the interested reader, there exist a number of excellent textbooks and review articles that go beyond these introductory remarks and discuss the field in its full breadth [3–7]. In this chapter, we will consider basic signal formation concepts, sequence design, and single and multiple echo acquisition methods (the latter for calculating T2* maps, as will be described in the next chapter). SIGNAL FORMATION Gradient echo imaging utilizes the ability of time-varying gradient magnetic fields to dephase and rephase the MR signal in such a way that one or multiple echo signals can be created. Figure 3.1 illustrates a generic 2D single-echo gradient echo sequence and Figure 3.2 the corresponding sequential line-by-line filling of k-space.

Susceptibility Weighted Imaging in MRI, By E. Mark Haacke and J€urgen R. Reichenbach Copyright
2011 by Wiley-Blackwell

33

34

GRADIENT ECHO IMAGING

FIGURE 3.1 2D pulse sequence timing of a generic gradient echo sequence. rf ¼ radio frequency, a ¼ tip angle, f is the resonance offset angle between two rf pulses, GS ¼ slice select gradient, GP ¼ phase encoding gradient, GR ¼ readout gradient, ADC ¼ analog to digital converter, TE ¼ echo time, and TR ¼ repetition time. When the ADC is marked on, the data are being sampled.

The gradient echo sequence is relatively simple by design. Within each cycle (each TR), there is a single slice-selective rf excitation that tips some of the magnetization into the transverse plane. After excitation, only gradient activity is present (apart from any background field inhomogeneities). These gradients are designed to create one line of data in k-space (Figure 3.2). Since the Larmor frequency is proportional to the local field strength, the presence of a gradient will cause dephasing of the different spin packets (or isochromats) making up the transverse magnetization at each point in 3D space. In the dephased state, these spin isochromats are distributed in a fan-like fashion in the transverse plane and if left long enough do not induce a measurable signal in the receiver coil. Switching the polarity of the gradient, this dephasing effect is reversed to a rephasing effect. This rephasing gradient will lead to a build up of the signal and (for zero ramp times), at a time interval equal to that of the duration of the dephasing gradient, all the spin isochromats will point again in the same direction, creating the so-called gradient refocused echo. Although creating an echo is important, it is the process of sampling at and around the echo center that is critical in producing an image. Figure 3.3 illustrates the creation of a one-dimensional frequency encoded gradient echo in more detail. Particularly, the sampling of k-space starts some time before the echo and continues up to and past the echo by an almost equal amount. More precisely, following rf excitation, a negative dephasing gradient is applied, during which time the k-space variable kx evolves according to the following equation: g  Gx  t 0  t  Tacq =2 ð3:1Þ kx ¼  2p where t ¼ 0 at the beginning of the dephasing lobe in this discussion. This leads to the following phase development:

SIGNAL FORMATION

35

FIGURE 3.2 An example k-space diagram showing the sequential line-by-line filling of k-space.

wðx; tÞ ¼ 2p  kx  x ¼ g  Gx  x  t

0  t  Tacq =2

ð3:2Þ

which depends on the spin isochromat’s x-position. The time dependence is what causes the increasing phase dispersion between the spin isochromats. If a positive gradient pulse is switched on at t ¼ Tacq/2 with the same amplitude and duration Tacq, the transverse spin

FIGURE 3.3 Schematic drawing of a one-dimensional frequency encoded gradient echo acquisition. Here, field echo, FE, is the time from the beginning of the gradient structure to the echo and TE is the time from the center of the rf pulse to the echo.

36

GRADIENT ECHO IMAGING

isochromats will gradually rephase and the signal will increase again up to the echo and dephase once again after that. The k-space trajectory during the second gradient pulse will be kx ¼  ¼


 g g  Gx  Tacq =2 þ  Gx  tTacq =2 2p 2p

g  Gx  ðtTacq Þ 2p

Tacq =2  t  3=2Tacq

ð3:3Þ

Here, t ¼ Tacq is referred to as the field echo time (FE). If the time origin is shifted back to the center of the rf excitation pulse, then the phase can be expressed as wðx; tÞ ¼ g  Gx  x  ðtTEÞ

jtTEj  Tacq =2

ð3:4Þ

For t ¼ TE, the phase w is zero for all isochromats, independent of the spatial x-position, thus making the formation of an ubiquitous echo signal at every pixel possible. The total trajectory of the kx variable is thus a symmetric line through the origin of k-space, starting at kx ¼ g  Gx  Tacq =2

ð3:5Þ

kx ¼ g  Gx  Tacq =2

ð3:6Þ

and ending at

Of course, at the end of the rephasing gradient, the signal has again diminished. This echo creation process can be repeated by continually reversing the gradient pulse. The switching of the polarity of each subsequent gradient creates another echo that can be sampled and another image can be formed. Figure 3.4 represents the sequence diagram for a multi-echo (three in this case) image acquisition. To reconstruct a 2D or 3D spin density distribution, the measured signal S(t) must be phase encoded along one or both spatial directions that are orthogonal to the frequency encoding gradient. In the case of 2D imaging, two orthogonal gradients are applied to encode the in-plane information after a slice has been selectively excited. With conventional rectilinear Fourier imaging, Nx data points are equidistantly sampled in time along the frequency encoding direction in the presence of a gradient with constant amplitude (e.g., GR in Figure 3.1). The second dimension is encoded by incrementing the phase encoding gradient (GP) stepwise for each acquisition of S(t) as shown by the phase encoding gradient table in Figure 3.1. The number of steps, which corresponds to the number of points required to resolve a sample along this direction Ny, determines the number of rf excitations needed and the number of times the signal S(t) needs to be sampled for a simple single-echo or multi-echo approach. As seen from Figure 3.2, a single line of k-space data (Nx sampled data points) is obtained per rf excitation. The excitation is then repeated as many times as necessary (Ny) to fill the raw data matrix along the GP direction. To proceed along the ky direction, a phase encoding

37

SIGNAL FORMATION

αφ

≈

rf TE3 TE2

TE1

≈

GR

≈

ADC

FIGURE 3.4 Simplified sequence diagram for a multi-echo, gradient echo experiment.

gradient pulse of fixed time duration tP is applied prior to switching on the readout gradient, whose amplitude is varied from step to step by DGP. The k-space trajectory, which is dictated by the timing of the imaging gradients GR and GP, is a series of Ny horizontal lines (see Figure 3.2). With FoVx and FoVy being the field of view along the x- and y-direction in the image domain, respectively, the relationship between the image domain and the k-space domain can be expressed as follows:

Dkx ¼

g 1  GR  Dt ¼ 2p FoVx

ð3:7Þ

Dky ¼

g 1  DGP  tP ¼ 2p FoVy

ð3:8Þ

where Dt is the dwell time, tP the pulse duration of the phase encoding gradient, and DGP ¼ 2GP,max/Ny denotes the step size of the phase encoding gradient. Gp,max here is the maximum magnitude of the phase encoding gradient used in the imaging sequence. With fixed tP and Dt, the field-of-view can be adjusted by changes in the readout gradient amplitude and the increment DGP . For 3D imaging, a second phase encoding gradient orthogonal to the first two encodings has to be applied to resolve partitions (slices) within the larger excited volume. Following the same principles described above, we can extend the k-space relations to Dkz ¼

g 1  DGS  tS ¼ 2p FoVz

ð3:9Þ

38

GRADIENT ECHO IMAGING

where DGS is the increment of the partition encoding gradient and tS the corresponding gradient pulse duration. The most important difference between a spin echo and a gradient echo sequence is the absence of a refocusing rf pulse in the latter (typically a 180 pulse). This absence allows the minimum echo time (TE), and thus also the minimum repetition time (TR), to be reduced compared to the spin echo sequence, opening the door to perform short echo time imaging with high spatial resolution. The tip angle a is reduced to a value below 90 , leading to much reduced specific absorption rates (SAR). Due to fundamental trigonometric properties, even a small tip angle may still create a substantial transverse magnetization, while the longitudinal magnetization is diminished only slightly. For instance, a 20 rf pulse acting on a magnetization M aligned parallel to the static magnetic field creates a transverse component of Msin(20 ) ¼ 0.34M, whereas the longitudinal component has been reduced by only 1  cos(20 ) ¼ 6% leaving behind lots of magnetization to excite for the next rf pulse. Signal formation in gradient echo imaging depends on two important parameters. The first one is the natural microscopic T2 relaxation that leads to an exponential signal decay of the transverse magnetization with a relaxation rate constant R2 ¼ 1/T2. The second parameter describes the additional dephasing arising from an inhomogeneous static magnetic field that is due to magnet imperfections and local magnetic susceptibility variations within the object. Usually, this relaxation rate term is denoted by R02 and is considered as a constant additional contribution to the signal relaxation rate from local field inhomogeneities. However, this common assumption holds true only if the number of magnetized objects or structures within a voxel causing the inhomogeneities is large. In this case, the effects of the local inhomogeneities are not altered by the imaging gradients [8]. On the other hand, if the size of the object is comparable to or larger than the voxel dimensions, then the signal decay will no longer be exponential and will depend on both voxel size and imaging gradients. With gradient refocusing of the MR signal, only phase shifts induced by the readout gradients are corrected at the center of the gradient, but not phase shifts resulting from field inhomogeneities, static tissue susceptibility gradients, and chemical shift effects. Thus, the signal evolution with increasing TE may be affected substantially by several factors in addition to T2 relaxation and leads to more rapid signal decay than that due to T2 relaxation alone. If the local resonance frequencies, which are responsible for the additional dephasing, exhibit a frequency distribution that follows a Lorentzian profile, the transverse signal decay can be described by an exponential function: M? ðtÞ ¼ M0  et=T2

ð3:10Þ

1 1 1 ¼ þ T2* T2 T20

ð3:11Þ

*

with

where T20 (relaxation rate R02 ¼1/T20 ) depends on the strength of the magnetic field inhomogeneity and determines the width of the Lorentzian line shape. Note, however,

SIGNAL FORMATION

39

that equations (3.10) and (3.11) represent an important but quite special case and, as mentioned above, the signal time course will not exhibit an exponential decay for other forms of local resonance frequency distributions (see Chapter 5 for more details).

Spoiled Gradient Echo Imaging In the discussion about gradient echo imaging so far, we have not alluded to any limitations on the sequence design related to the repeat time TR. Certainly, when the TR  T2, the transverse magnetization after the echo vanishes prior to the next rf pulse. However, for TR  T2, there still exists a substantial transverse magnetization prior to the next rf pulse. Depending on how this transverse magnetization is handled, one can divide gradient echo imaging sequences into different types. However, we will consider only steady-state incoherent gradient echo imaging in this chapter. The term spoiling refers to the deliberate destruction of transverse coherences that persist from one rf cycle to the next. There are several methods in use to achieve spoiling, including the application of variable gradients, the so-called spoiler gradients along the slice select direction prior to the application of the next rf pulse (gradient spoiling), or shifts of the rf pulse’s phase from cycle to cycle (rf spoiling) that effectively prevents the buildup of transverse phase coherences [3, 9]. The latter is accomplished by changing the rotation axis of a by an angle f (usually set to 117 ) about which the magnetization is rotated. Both methods are often applied simultaneously in practice. For large flip angles relative to the Ernst angle (see below), the transverse magnetization will reach equilibrium rapidly. For small flip angles relative to the Ernst angle, it could take a few hundred repetitions of the rf pulse to reach within say 5% or 10% of the equilibrium value. This steady-state or equilibrium magnetization Mze is given by the expression [3]

Mze ¼ M0 

1eTR=T1 1cos a  eTR=T1

ð3:12Þ

Equation (3.12) shows that Mze depends on the tip angle a, the pulse repetition time TR, and T1. For the transverse magnetization, which is the crucial quantity in terms of available signal, we obtain

M? ¼ M0  sin a 

1eTR=T1 *  eTE=T2 TR=T 1 1cos a  e

ð3:13Þ

In writing equation (3.13), we have made the assumption that M? represents the steadystate signal from a voxel containing several isochromats (hence the introduction of the effective transverse relaxation time constant T2* ). It can be shown that the maximum signal occurs at the so-called Ernst angle aE, which is given by   aE ¼ cos1 eTR=T1

ð3:14Þ

40

GRADIENT ECHO IMAGING

A simple expression for aE (in radians) when TR/T1  1 is given by rffiffiffiffiffiffiffiffiffi 2TR aE  T1

ð3:15Þ

A simple numerical example may illustrate the achievable gain in signal M? when reducing the tip angle of the excitation pulse (we neglect the decay of the signal due to T2* ). With T1 ¼ 1 s, TR ¼ 50 ms, and a ¼ 90 , M? ¼ 0.049M0, whereas at the Ernst angle (aE  18 ), we obtain M? ¼ 0.16M0. SUSCEPTIBILITY WEIGHTED DATA ACQUISITION There is a simplicity and robustness to 3D gradient echo imaging. The high-resolution imaging aspects combined with the low flip angles used for SWI make this approach very user-friendly across field strengths and across manufacturers. Ideally, if there were no flow, or no pulsatility effects on the phase, then the simple gradient echo sequence of Figure 3.5

FIGURE 3.5 A 3D gradient echo sequence design. After sampling the data points, these gradients are rewound, whereas the readout gradient remains to ensure dephasing of the spins in this direction. RF spoiling is also used to ensure T1-weighted contrast. Usually, this is accomplished by changing the resonance offset angle f between each rf pulse by 117  .

SUSCEPTIBILITY WEIGHTED DATA ACQUISITION

41

FIGURE 3.6 Diagram shows the sequence of events in 3D long TE gradient echo MR imaging with flow compensation in all three directions. In addition to the conventional first-order gradient moment nulling in the read (GR) and section (slice) select (GS) directions, the phase encoding (GP) and partition encoding gradients are also flow compensated with respect to the echo. After sampling the data points, these gradients are rewound, whereas the readout gradient remains to ensure dephasing of the spins in this direction. RF spoiling is also used to ensure T1-weighted contrast.

would have been the perfect source for acquisitions such as SWI. In fact, even this same type of sequence in a 2D mode is enough to provide good phase information. But the rapid and pulsatile flow of blood in some cases makes it necessary to apply flow compensation gradients to the gradient echo sequence. This final form, shown in Figure 3.6, is representative of the original sequence used for SWI data acquisition [12, 18]. Further developments for either multiple echo approaches or faster acquisition have been realized and are also considered in Chapters 7 and 33. The rf pulse excites the volume with a slab thickness of several centimeters, which is then spatially resolved by applying the frequency encoding gradient and phase and partition encoding gradients (see Figure 3.6). Flow compensation of first order is applied in all three spatial directions to reduce signal losses of blood due to flow-induced dephasing and to avoid oblique flow misregistration artifacts [13]. The main reason to flow compensate apart from avoiding motion artifacts is that the phase we are interested in is w ¼ g  DB  TE ¼ g  Dx  B0  TE

ð3:16Þ

42

GRADIENT ECHO IMAGING

TABLE 3.1 Typical Parameters for Single-Echo SWI Sequence Parameter TR TE a Slice thickness Number of partitions Nominal pixel size Typical FoV Matrix

1.5 T

3.0 T

57–80 ms 25–50 ms 15 –35 2 mm 32–64 0.5 0.5 mm2 or 0.5 1.0 mm2 192 240 mm2 to 256 256 mm2 192 512 to 512 512

46–51 ms 17–28 ms 10 –30 1–2 mm 48–64 0.5 0.5 mm2 192 256 mm2 to 256 256 mm2 384 512 to 512 512

where DB is the change in local field caused by changes in local susceptibility Dx. The phase for a spin moving with constant velocity v along the read direction for a dephasing/rephasing bipolar pulse Gx of duration 2t is given by w ¼ g  Gx  v  t2

ð3:17Þ

Consequently, as the velocity changes across a voxel, so does the phase although this phase has nothing to do with susceptibility. When the sequence is flow compensated, this velocityinduced phase vanishes, leaving us with the desired susceptibility-induced phase as given in equation (3.16). The flow compensation must be applied in the x, y, and z directions and to the slice select gradient, so there are a total of four components to remove flow-induced phase successfully from a constant velocity contribution. These motion compensating gradients also remove pulsatility effects caused by variable phase across the cardiac cycle as well as oblique flow artifacts. Pulsation artifacts caused by variable inflow effects or variable effective spin density effects can only be reduced by using small flip angles to reduce T1 dependence on the signal. With a 3D sequence, it is also possible to compensate oblique flow in all directions [13]. The sequence shown in Figure 3.6 is strongly T2* -weighted and has a low bandwidth of typically 80–100 Hz/pixel in the readout direction to improve the signal to noise ratio (SNR). Usually, a symmetric echo is acquired. Table 3.1 summarizes several typical sequence parameters for this single-echo gradient echo imaging sequence at two common field strengths. Some example magnitude and phase images collected using this standard SWI sequence are shown in Figure 3.7. A variety of echo times are chosen to demonstrate how the T2* effects modify the magnitude image and how the phase evolves as the echo time gets longer. These data were acquired at 3 T, and by TE ¼ 20 ms, good phase contrast has already developed. By TE ¼ 60 ms, the phase is somewhat corrupted by uncorrected phase effects and venous dipole effects. In gradient echo imaging, the effects of magnetic field inhomogeneities manifest as signal loss and geometric distortion, the former of which gets worse as TE increases. There have been several approaches to overcome the image artifacts due to local field inhomogeneities. One proposed method is to reduce the influence of the field inhomogeneity by reducing voxel size and thus limiting the affected region [14, 15]. Gradient compensation by use of adjustable slice selection gradient strengths [16] has been suggested, as has been the use of tailored rf pulses [17]. In the latter method, superposition of a quadratic phase rf pulse can recover signal loss, although signal strength is reduced. The former methods are

SUSCEPTIBILITY WEIGHTED DATA ACQUISITION

43

basically limited by the slice thickness. Perhaps the best way to reduce geometric distortion is to use a high bandwidth and then add all the images back together to recover the lost SNR. The problem with this approach is that not all echoes will be flow compensated and this can cause a real problem in using the phase information for both creating SWI data and extracting susceptibility information.

FIGURE 3.7 Images (a)–(h) show the magnitude and phase evolution along increasing echo time (TE).

Images (a, b) are the magnitude and phase images at TE ¼ 12 ms, respectively; similarly, (c, d) magnitude and phase at TE ¼ 20 ms, (e, f) magnitude and phase at TE ¼ 40 ms, and (g, h) magnitude and phase at TE ¼ 60 ms, respectively. The TE ¼ 20 and 40 ms phase images have good CNR without being overwhelmed by phase artifacts from air-tissue interfaces.

44

GRADIENT ECHO IMAGING

FIGURE 3.7 (Continued)

Using high-resolution three-dimensional data acquisition with gradient echo sequences is beneficial in terms of reducing the influence of local static field inhomogeneities on geometrical image distortions and image quality [18]. Not only does high resolution help in retaining image appearance, but it also makes it possible to extract physical and/or physiological parameters when reduction of partial volume effects is essential. Figure 3.8 demonstrates the superiority of high-resolution gradient echo imaging over spin echo imaging for depicting multiple focal hemorrhages. Due to the increased sensitivity of the gradient echo pulse sequence to tissue susceptibility differences, areas of hemorrhage are more prominently shown even though the spin echo image was acquired at a much longer effective echo time.

REFERENCES

45

FIGURE 3.8 A 66-year-old patient with multiple hemorrhagic lesions. Left: T2-weighted turbo spin echo (TSE) sequence with TR ¼ 2474 ms, TE ¼ 102 ms, slice thickness 6 mm, matrix 256, and square FoV of length 210 mm. Right: Single partition of a 3D gradient echo SWI sequence with TR ¼ 67 ms, TE ¼ 40 ms, slice thickness 2 mm, matrix 512 512, and FoV 256 256 mm2. This data set was acquired at 1.5 T.

REFERENCES 1. Edelstein WA, Hutchison JM, Johnson G, Redpath T. Spin warp NMR imaging and applications to human whole-body imaging. Phys. Med. Biol. 1980;25:751–756. 2. Haase A, Frahm J, Mathaei D, Haenicke W, Merboldt KD. FLASH imaging. Rapid imaging using low flip-angle pulses. J. Magn. Reson. 1986;67:258–266. 3. Haacke EM, Brown RW, Thompson MR, Venkatesan R. Magnetic Resonance Imaging: Physical Principles and Sequence Design, Wiley-Liss, 1999. 4. Bernstein MA, King KF, Zhou XJ. Handbook of MRI Pulse Sequences, Elsevier, 2004. 5. Vlaardingerbroek MT, den Boer JA. Magnetic Resonance Imaging, 3rd edn, Springer, 2004. 6. Haacke EM, Tkach JA. Fast MR imaging: techniques and clinical applications. AJR Am. J. Roentgenol. 1990;155(5): 951–964. 7. Elster AD. Gradient-echo MR imaging: techniques and acronyms. Radiology 1993;186(1): 1–8. 8. Yablonskiy DA, Haacke EM. Theory of NMR signal behavior in magnetically inhomogeneous tissues: the static dephasing regime. Magn. Reson. Med. 1994;32(6):749–763. 9. Zur Y, Wood ML, Neuringer LJ. Spoiling of transverse magnetization in steady state sequences. Magn. Reson. Med. 1991;21:251–263. 10. Hinshaw WS. Image formation by magnetic resonance: the sensitive point method. J. Appl. Phys. 1976;47:3709–3721. 11. Nitz WR. Fast and ultrafast non-echo-planar MR imaging techniques. Eur. Radiol. 2002;12(12): 2866–2882. 12. Reichenbach JR, Venkatesan R, Schillinger DJ, Kido DK, Haacke EM. Small vessels in the human brain: MR venography with deoxyhemoglobin as an intrinsic contrast agent. Radiology 1997;204:272–277. 13. Frank LR, Crawley AP, Buxton RB. Elimination of oblique flow artifacts in magnetic resonance imaging. Magn. Reson. Med. 1992;25:299–307.

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14. Haacke EM, Tkach JA, Parrish TB. Reduction of T2* dephasing in gradient field-echo imaging. Radiology 1989;170:457–462. 15. Young IR, Cox IJ, Bryant DJ, Bydder GM. The benefits of increasing spatial resolution as a means of reducing artifacts due to field inhomogeneities. Magn. Reson. Imaging 1988;6:585–590. 16. Frahm J, Merboldt KD, Hanicke W. Direct FLASH MR imaging of magnetic field inhomogeneities by gradient compensation. Magn. Reson. Med. 1988;6:474–480. 17. Cho ZH, Ro YM. Reduction of susceptibility artifact in gradient echo imaging. Magn. Reson. Med. 1992;23:193–200. 18. Reichenbach JR, Venkatesan R, Yablonskiy DA, Thompson MR, Lai S, Haacke EM. Theory and application of static field inhomogeneity effects in gradient-echo imaging. J. Magn. Reson. Imaging 1997;7(2): 266–279.

4 Phase and Its Relationship to Imaging Parameters and Susceptibility Alexander Rauscher, E. Mark Haacke, Jaladhar Neelavalli, and J€ urgen R. Reichenbach

INTRODUCTION Phase is a permeating concept in many areas of science, including physics, signal theory, and linear system theory. It occurs in the description of periodic processes, in particular with respect to harmonic waves and harmonic oscillations, and is useful in many other fields as well. Since magnetic resonance imaging (MRI) has its roots in the periodic motion of the transverse magnetization vector about the static magnetic field, it should not be too surprising that phase plays an important role in MRI. In this chapter, the nature of phase and its relationship to MR imaging and susceptibility weighted imaging (SWI) will be introduced and discussed. Understanding phase is the cornerstone to understanding the fundamental elements of MRI and the key to susceptibility weighted imaging and later susceptibility mapping (Chapter 25). Because phase in MR is a broad topic, only key basic concepts are presented in this chapter with more detailed discussion of further specific applications covered in later chapters. Starting with the definition of phase in the context of the magnetization vector, we first discuss MR phase domain properties, phase aliasing, and thesourceof spatial phasevariation, showing that intravoxel phase variation leads to signal loss. This is followed by a discussion of phase filtering concepts and how information from phase and magnitude can be combined to obtain an SWI image. Finally, key features of MR phase signal, such as its invariance with magnetic field strength, the Fourier shift theorem, and noise properties of phase are introduced. Susceptibility Weighted Imaging in MRI, By E. Mark Haacke and J€urgen R. Reichenbach Copyright
2011 by Wiley-Blackwell

47

48

PHASE AND ITS RELATIONSHIP TO IMAGING PARAMETERS AND SUSCEPTIBILITY

COMPLEX REPRESENTATION As mentioned, much of MRI can be understood if phase is understood. In general terms, phase can be defined as the changing orientation of the magnetization vector in the transverse plane. Quantitatively, it depends on the product of time and the angular velocity of the transverse magnetization vector, as well as on an initial phase constant w0 that defines the value of phase at the time origin. Thus, phase can be defined by the following expression: wðtÞ ¼ v  t þ w0

ð4:1Þ

Assuming xy to represent the coordinates of the transverse plane, the transverse magnetization vector Mxy ðr; tÞ at position r can be written as Mxy ðr; tÞ ¼ Mxy ðr; tÞ  eiwðr;tÞ

ð4:2Þ

Let us take a closer look at this mathematical representation of Mxy . Any 2D vector r can be decomposed in terms of its individual components along the x and y directions, ^ þ jrj  sin w  ^y r ¼ rx þ ry ¼ jrj  cos w  x

ð4:3Þ

^ and ^y denote the unit vector in x and y direction, respectively. where x In complex notation, we can write this as rm  eiw ¼ rm  ðcos w þ i sin wÞ;

ð4:4Þ pffiffiffiffiffiffiffi (i ¼ 1) and rm ¼ jrj is the modulus or magnitude of the vector and w is the phase, that is, the angle between the x axis and the vector r measured counterclockwise and in radians, which is defined up to some multiple of 2p. A common geometrical interpretation can be given by using the complex p (orffiffiffiffiffiffiffiffiffiffiffiffiffiffi Gaussian) plane or Argand diagram (Figure 4.1) [3]. In figure 4.1, the magnitude jrj ¼ x2 þ y2 is the length of the vector r ¼ ðx; yÞ, and the phase w is given by the inverse tangent w ¼ tan1 ðy=xÞ

ð4:5Þ

Thus, equation (4.2) fully describes the magnitude and the phase of the magnetization vector Mxy. PHASE VARIATION AND ALIASING In MR imaging, phase is used to encode spatial information. However, in addition to the position-dependent phase created by the spatial encoding gradients, there are unavoidably other forms of remnant or background phase present. These mostly unwanted spurious phase effects also need to be understood and dealt with before useful information from MR phase images can be extracted. Before delving into the details of these phase effects, a brief understanding of the phase domain is necessary. Let us first consider the presence of a simple change in phase over time (with w0 ¼ 0) wðtÞ ¼ v  t ð4:6Þ

PHASE VARIATION AND ALIASING

49

FIGURE 4.1 Complex representation of a vector r in the x–y plane.

Figure 4.2 shows how this phase evolves with time. As time progresses, phase increases linearly. However, once the phase value lies outside the interval (p to þ p), its true value becomes ambiguous as the operation of equation (4.5) can return only a phase value between (p to þ p). Therefore, the measured phase is only correct to within a multiple of 2p. This process of phase continually wrapping back into the interval (p to þ p) is called aliasing. To complicate matters further, as time progresses, phase aliasing will continue to occur again and again and the number of times the phase wraps back into the interval (p to þ p) continues to increase. From the MR perspective, aliasing is the appearance of the transverse magnetization vector (or any vector for that matter) at a given location when it has in fact been around the circle one or more times. For example, when one looks at the vector ‘‘b’’ in Figure 4.2, there is no way to tell if it is at 90 or 450 , or þ 270 . Mathematically, we can write the actual phase (wact ) in terms of the aliased phase as wact ¼ wmeasured þ 2p  n

ð4:7Þ

where n is an integer (positive or negative). That is, the aliased phase, the phase we measure, can only be determined to within some multiple of 2p of the actual phase.

50

PHASE AND ITS RELATIONSHIP TO IMAGING PARAMETERS AND SUSCEPTIBILITY

FIGURE 4.2 Graphical representation of phase with respect to time, where w ¼ vt ¼ 2p  f  t and

f ¼ 1 cycle/s.

Spatial Phase Variation In an ideal imaging scenario, the static magnetic field is exactly B0 in all parts of the sample and the reconstructed MR phase image of such a sample would not display any phase variation but would be homogeneously flat (we neglect at this point any chemical shift effects). Practically, there are changes in the local magnetic field, DBðrÞ, even with excellent shimming. Such phase variations may be caused by imperfect gradient performance (which leads to an echo center shift and other problems), eddy currents, object motion, or, worst of all, due to susceptibility changes at air/tissue interfaces. Recall that in the rotating reference system, which rotates around the field direction B0 with angular velocity v0 ¼ g  B0, the precession of the transverse magnetization due to B0 is not seen, except when taking into account the field inhomogeneity DBðrÞ (in the context considered here, we neglect any contributions from imaging gradients or the radio frequency magnetic field B1). Phase can then be written as a function of the difference between the uniform field B0 and the local field Bðr; tÞ at position r and time t as follows: wðr; tÞ ¼ g  ðB0 Bðr; tÞÞ  t ¼ g  DBðr; tÞ  t

ð4:8Þ

where w is now a function of both spatial coordinates and time due to the spatial dependence and potential temporal dependence (e.g., due to eddy currents) of the local magnetic field.

PHASE VARIATION AND ALIASING

51

Setting t ¼ TE, which corresponds to the echo time in a gradient echo sequence, and neglecting any time dependence of the local field, we can write wðrÞ ¼ g  DBðrÞ  TE

ð4:9Þ

Thus, equation (4.9) describes the spatial distribution of phase that has evolved during the time interval TE (i.e., the time interval between RF excitation and readout of the maximum gradient echo signal) due to the presence of the static, spatially varying, nonhomogeneous local field distribution DBðrÞ. As in equation (4.7), the actual phase, now as a function of position, can be written as wact ðrÞ ¼ wmeasured ðrÞ þ 2p  nðrÞ

ð4:10Þ

Figure 4.3 illustrates schematically one-dimensional phase aliasing along the spatial coordinate x. It occurs when the phase variation between two samples, or in this case two pixels, exceeds the limit of (p, þ p). A more detailed schematic of the phase changes is illustrated in Figure 4.4, which contains a phase image of a phantom. Phase aliasing occurs along the line connecting the points from a to f, similar to the scheme shown in Figure 4.3. The change from bright to dark and back to bright in Figures 4.4a and b represents the aliasing of the phase running from p to p and back to p. These phase discontinuities or phase jumps are commonly known as phase wraps. To be useful for further processing, phase has to be unwrapped to recover a continuous function, where the 2p discontinuities have been eliminated. Unwrapping consists of adding or subtracting multiples of 2p in the appropriate places to make the phase image as smooth as possible. Phase unwrapping is one of the most active areas of research in digital image processing with many applications in quite distinct areas, such as optics, interferometry,

FIGURE 4.3 Schematic graphical representation of 1D phase aliasing.

52

PHASE AND ITS RELATIONSHIP TO IMAGING PARAMETERS AND SUSCEPTIBILITY

FIGURE 4.4 (a) Example phase image for a phantom. We are interested in examining the spatial dependence of the phase from points a to f to understand the aliasing that leads to the banding in the image. (b) A blowup of the left side image so that all points between a and f can be seen more clearly and ^ with zero phase. From a to e and b labeled. (c) Vector representation of these points with a being along x to f, phase changes by 2p radians (360  ). (d) As the phase increases (the vector rotates counterclockwise in a right-handed system), the vector will eventually approach point c. At c the phase is still positive, (pd), but at c þ the phase is now (p þ d), which in a system that only allows phase from (pp) becomes (p þ d); that is, the phase is aliased.

and MRI. Strategies to unwrap phase images will be introduced in other chapters (see Chapter 24 and also below). PHASE IN SUSCEPTIBILITY WEIGHTED IMAGING Structures with magnetic susceptibilities different from their surroundings produce changes in the local and often in the global (i.e., spatially long ranging) magnetic field. If these field changes consist of high spatial frequency components whose variations are comparable to

PHASE IN SUSCEPTIBILITY WEIGHTED IMAGING

53

the voxel dimensions, then they lead to intravoxel spin phase dispersion. If the field varies slowly over larger spatial distances, then the field within a voxel can still be regarded as being constant, though the precession frequency will be altered. Intravoxel dephasing (or dispersion) of spin isochromats (or spin packets) leads to an attenuation of the signal magnitude of a gradient echo scan, whereas the constant offset in resonance frequency becomes apparent in the signal phase (see also equation (4.9)), or more precisely in the phase difference, Dw, between two regions or two voxels, experiencing different but constant local fields: Dw ¼ g  DB  TE

ð4:11Þ

In equation (4.11), DB is the difference in field between the two voxels (DB ¼ Bvoxel 1 Bvoxel 2 ). The minus sign in equation (4.11) (and also in equation (4.9)) stems from the fact that the Larmor frequency, v0 ¼ g  B0 , has a defined sign that for a righthanded system is negative (i.e., the sign indicates the rotation sense of the spin magnetization precession around the static field). Most nuclei, including protons, have positive g, in which case the Larmor frequency is negative. This means that the precession is in the clockwise direction, as seen when looking against the direction of the magnetic field from top to bottom. Consider now for simplicity a two-dimensional object that consists of two compartments with different but homogeneous magnetic susceptibilities, embedded in a homogeneous (outer) main magnetic field (Figure 4.5). Near the interface between the two compartments the field is inhomogeneous and the signal is reduced due to accelerated intravoxel spin dephasing. In regions far from the interface, the field is homogeneous in both compartments. Since no intravoxel dephasing occurs, these areas have similar signal strength in the magnitude image. The local magnetic field strength, on the other hand, is still different and the spins precess at different rates and accumulate phase offsets compared to neighboring spins. In conventional gradient echo imaging, susceptibility sensitivity is reflected as a T2* signal loss in areas with field inhomogeneities. Such regions are visualized as having hypointense signal.

FIGURE 4.5 Graphical representation of field inhomogeneity and spin dephasing effects observed near the interface of a vein and the gray matter (for the vein 180 out of phase with the gray matter). The direction of the arrows represents the direction of the transverse magnetization vectors and the shaded voxels indicate the level of signal loss in areas with field inhomogeneities (the darker shade corresponds to more signal loss).

54

PHASE AND ITS RELATIONSHIP TO IMAGING PARAMETERS AND SUSCEPTIBILITY

From the magnitude images, one cannot tell what is tissue and what is vessel because often the signal inside the ring is the same as that outside. SWI uses two strategies to avoid this problem. It uses very high spatial resolution and it incorporates the phase into the final image. Due to the high spatial resolution, the background field inside a voxel can be regarded as homogeneous [5]. The magnitude images by themselves show the above described ring effect. The veins accumulate a phase offset in a coherent manner that can be observed in the phase image. Consider the examples in Figures 4.5–4.7. The edge of a vessel (vein) will be affected by partial volume effects with the tissue. The phase difference between them will be Dw ¼ g  DBvt  TE  g  Dxvt  B0  TE

ð4:12Þ

where ‘‘vt’’ stands for vein tissue. The signal from the vein will beat against that from the tissue and at roughly 50 ms at 1.5 T causes maximum cancellation. This effect is shown in Figure 4.6b for a long venous vessel in the interhemispheric tissue and for Figure 4.7a and d. By combining the magnitude and the phase (see Chapter 6), the final SWI data show no ring effects in the ideal case. Figures 4.6d and 4.7c clearly show this effect. However, if aliasing is present, the phase no longer behaves as expected (Figure 4.7e) and the resulting SWI data will show this same ring artifact. To remove this problem, antialiasing or unwrapping is necessary (Chapter 6). SWI AND PHASE AS A FUNCTION OF FIELD STRENGTH One remarkable aspect of the phase is that it does not depend on the magnitude of the magnetization. (This is true as long as the SNR is sufficiently high (see below) and in the absence of partial volume effects.) It is therefore independent of relaxation time effects and depends only on the product DBTE. The changes in DB due to magnetic susceptibility are proportional to the main magnetic field strength B0. Apart from differences in SNR, a phase image acquired at 1.5 T with an echo time of 40 ms looks almost identical to a phase image acquired at 3 T with an echo time of around 20 ms (Figure 4.8). This scaling property allows phase images to be compared across different field strengths. However, when partial volume effects play a role, particularly for small venous vessels, the different spin densities and relaxation times of the surrounding tissue compartments will contribute to the resulting MR signal of such a voxel and will affect its net phase. In such cases, the phase images acquired at different field strengths with the same DB  TE may not necessarily look similar [6]. The T2* relaxation time of venous blood, for instance, is much longer at 1.5 T (on the order of 100 ms [7]) compared to 3 T (on the order of 25 ms) and 7 T (on the order of 10 ms [8]). As discussed above, to keep phase constant, the product of the field strength with echo time must be kept constant. So if we use 50 ms at 1.5 T, we would use 25 ms at 3 T and 10.7 ms at 7 T [9]. If the T2* decay properties were to stay the same, then the ratio of TE/ T2* would have to remain invariant. But this ratio changes from 0.5 at 1.5 T to 1.0 at 3 T and 1.0 at 7 T. This means that there is much more signal loss for the same equivalent echo time to generate phase at higher fields. This reduced venous signal then leads to less cancellation effect, and hence at 7 T one finds it necessary to use longer than expected echo times.

SWI AND PHASE AS A FUNCTION OF FIELD STRENGTH

55

FIGURE 4.6 An example image with an in-plane resolution of 1  1 mm2 (a) versus 2  2 mm2 (b) illustrating the effects of reduced resolution. The phase image in (c) is used to create a mask that suppresses the signal from inside this structure (arrow) to give the uniform dark contrast shown in the susceptibility weighted magnitude data (d).

56

PHASE AND ITS RELATIONSHIP TO IMAGING PARAMETERS AND SUSCEPTIBILITY

FIGURE 4.7 (a) Magnitude, (b) phase, and (c) susceptibility weighted images showing an example of the cancellation and edge artifact effect of a vessel in the human brain. Parts (d), (e), and (f) show a similar example except that the aliasing effect seen in the phase image prevents the phase mask from properly suppressing the central part of the signal in some of the veins.

FIGURE 4.8 Phase images acquired at (a) 1.5 T and (b) 3 T. The echo times have been adjusted to produce nearly the same DBTE product. Note the similarity between the two phase images. Acquisition parameters: B0 ¼ 1.5 T: TE ¼ 40 ms, TR ¼ 57 ms, FA ¼ 25  , voxel size ¼ 0.5  0.5  1.5 mm3; B0 ¼ 3 T: TE ¼ 18 ms, TR ¼ 24 ms, FA ¼ 20  , voxel size ¼ 0.5  0.5  1.5 mm3.

HIGH-PASS FILTER EFFECTS ON PHASE

57

HIGH-PASS FILTER EFFECTS ON PHASE Although this topic is covered in other chapters (see Chapters 6 and 24), we present here some example images to show the positive and negative effects of high-pass or homodyne filtering of phase images. First, it should be understood that any two complex MR images acquired with different echo times can be used to create a new unwrapped phase image. Consider two imaging experiments with echo times TE1 and TE2 ¼ TE1 þ e. The corresponding signals can be written as r1c ðrÞ ¼ r1m ðrÞ  eiw1 ðrÞ ¼ r1m ðrÞ  ei  g  DBðrÞ  TE1

ð4:13Þ

r2c ðrÞ ¼ r2m ðrÞ  eiw2 ðrÞ ¼ r2m ðrÞ  ei  g  DBðrÞ  TE2

ð4:14Þ

and If we divide the complex signal r1c ðrÞ by r2c ðrÞ, referred to as complex division, we obtain (since r2m ðrÞ ¼ r1m ðrÞ  ee=T2 ðrÞ ) r12c ðrÞ ¼ eig  e  DBðrÞ  ee=T2 ðrÞ *

ð4:15Þ

As the echo times TE1 and TE2 are usually long, such that jg  DBðrÞ  TE1 j > p, aliasing will occur. However, since the delay e can be chosen to be small, so that jg  DBðrÞ  ej < p for the whole field of view (FOV), no aliasing will occur in the new complex image r12c ðrÞ (Figure 4.9). This trick is not so dissimilar to what is done with high-pass or homodyne filtering. In that case, we take the same data with the same echo time and reconstruct both the original high-resolution image (say p  p) and a low-resolution image (say q  q). Then, with similar notation, we have r1c ðrÞ ¼ rm1;pp ðrÞ  eiwpp ðrÞ

ð4:16Þ

r2c ðrÞ ¼ rm2;qq ðrÞ  eiwqq ðrÞ

ð4:17Þ

FIGURE 4.9 (a) Original phase image acquired at TE ¼ 7.4 ms. (b) Corresponding phase image acquired at TE ¼ 8.9 ms. Both images (a) and (b) were acquired at 4 T. Multiple phase wraps can be seen in both (a) and (b) due to rapid field changes at air–tissue interface. (c) Result of complex dividing the phase of (a) into (b). Almost no phase aliasing is seen in this resultant phase image that has an effective TE of 1.5 ms.

58

PHASE AND ITS RELATIONSHIP TO IMAGING PARAMETERS AND SUSCEPTIBILITY

and assuming rm1;pp ¼ rm2;qq , it follows that r12c ðrÞ ¼ eiðwpp ðrÞwqq ðrÞÞ

ð4:18Þ

Clearly, if p ¼ q, then. Dw ¼ wpp ðrÞwqq ðrÞ ¼ 0. In the discussion above, q is generally made much less than p where q  q refers to the low pass filter size. To better understand the effects of filtering the phase, consider a one-dimensional example of a phase image profile, as shown in Figure 4.10a. The low spatial frequency q version of this profile, q, will look smooth. For example, an 8  8 filter will turn this profile into the smoothed profile shown in Figure 4.10b. Subtracting Figure 4.10b from Figure 4.10a results in Figure 4.11c, where the low spatial frequency baseline has been removed, leaving the veins as the major information in this image. As a numerical example, consider p ¼ 256 and FOV ¼ 256 mm. Then the resolution of this image will be 1 mm. If we use q ¼ 64, we will tend to filter out objects that are about 4 mm in size or greater. (A filter size of q can be considered to filter out objects or phase variations with dimensions of 256/q or greater.) When we filter SWI data in two dimensions, a similar removal of low spatial frequency will take place along both in-plane directions (usually x and y for a transverse image). To demonstrate the effects of homodyne filtering the images in two dimensions, Figure 4.11 shows an original magnitude and phase image followed by filtered phase

Caudate nucleus Vein 2 32 pixels

Vein 1

2 pixels

4 pixels

(a)

(b)

(c) FIGURE 4.10 (a) A schematic profile through two veins and the caudate nucleus. (b) A corresponding low-pass filtered profile using the central eight points in k-space. (c) Subtracted profile (a minus b) revealing the removal of baseline phase and the remaining high spatial frequency phase information. As can be seen, phase information in the caudate is lost because it is larger than 4 pixels across but phase information from the veins remains almost intact.

HIGH-PASS FILTER EFFECTS ON PHASE

59

FIGURE 4.11 (a) Original unfiltered phase image followed by high-pass filtered output images with filter size (b) 4  4, (c) 8  8, (d) 16  16, (e) 32  32, and (f) 64  64. (g) Original unfiltered magnitude image and (h) high-pass filtered magnitude image with filter size 32  32. High-pass filtering the magnitude image keeps the vessel information intact while removing the variations that exist in the image caused by coil or RF inhomogeneities.

60

PHASE AND ITS RELATIONSHIP TO IMAGING PARAMETERS AND SUSCEPTIBILITY

FIGURE 4.11 (Continued ).

images with 8  8, 16  16, 32  32, and 64  64 filter matrices. Clearly, as the central filter size q  q increases, the aliasing goes away and more and more low spatial frequency information disappears. For the 64  64 case, the small vessels remain clear, but the bulk of the phase information from larger structures vanishes. This is best seen from a plot of Dw versus q for structures, such as the superior sagittal sinus, the head of the caudate nucleus, the putamen, and the globus pallidus (Figure 4.12). The Dw is the difference between phase within the structure and white matter. This same homodyne filter concept can be used to correct the variations in the magnitude images as well (see Figure 4.11g and h).

FIGURE 4.12 Plots of Dw versus q for different brain structures such as superior sagittal sinus (SSS), head of the caudate nucleus (CN), putamen (PUT), and globus pallidus (GP). The Dw is the difference between phase within the structure and white matter. The plots indicated here PUT_GP_L and PUT_GP_R stand for the average phase measured from putamen and globus palidus regions as a whole; the L and R refer to left and right hemispheres.

PHASE MASK AND VOXEL ASPECT RATIO

61

PHASE MASK AND VOXEL ASPECT RATIO The design and application of a phase mask is an integral part of creating a susceptibility weighted magnitude image. Although phase images themselves are quite illustrative (Figure 4.8) in depicting susceptibility-based tissue contrast, they contain both intratissue and extratissue phases due to field perturbations both inside and outside the tissues (see Chapter 2). This can obscure/impair a clear differentiation of adjacent tissues. By selectively modifying voxel signal values in the original magnitude image based on their corresponding phase values in the phase image, that is, using a phase-based mask, phase information can be uniquely combined with magnitude information. Also, combining phase and magnitude information ensures the detectability and enhancement of signal intensity changes coming from both T2 and susceptibility differences between tissues. The existence of a phase difference does not necessarily lead to a T2 effect (a uniform phase causes no T 0 2 decay, see Chapter 5); so, these two sources of information complement each other. The phase mask is typically defined to have values between zero and unity and is multiplied into the original magnitude such that structures with certain phase values are suppressed to give a susceptibility weighted magnitude image [10]. Depending on which phase values are of interest, for example, paramagnetic (Dw < 0 for a right-handed system) or diamagnetic (Dw > 0), the phase mask is defined [11–16]. For example, for a paramagnetic venous vessel where Dw < 0, the mask is defined as ½p þ wðxÞ ; for p < wðxÞ < 0 p ¼ 1 otherwise

f ðxÞ ¼

ð4:19Þ

where w(x) is the phase value at location x (the phase value here typically refers to the high-pass filtered phase or phase image where the background field effects have been removed). This phase mask is then multiplied into the original magnitude image, r(x) according to the following relationship: r^ðxÞ ¼ f n ðxÞ  rðxÞ

ð4:20Þ

to create a new susceptibility weighted magnitude image denoted here by r^ðxÞ. The number of phase mask multiplications, n, is chosen to optimize the contrast-to-noise ratio of the SW image. A simple mathematical model can be built to estimate the optimal value of n, which is discussed in detail in appendix of Ref. 13. The number of mask multiplications required to enhance contrast for voxels with phase values w 0:3  p is n 4 and for phase values w 0:3  p is n 4. So, choosing n ¼ 4 proves to be a good compromise giving a 25% increase in contrast for phase values of 0:1  p and p. This has been demonstrated empirically by Reichenbach et al. [10] in 1998. In principle, one could generate a series of SWI magnitude images with a different number of mask multiplications, each enhancing contrast for specific regions with specific phase values. Figure 4.13 graphically illustrates the mathematical mask generation process, while Figure 4.14 demonstrates the effect of such masking via minimum intensity projected images showing contiguous venous vasculature. Figure 4.15 shows the effect of different number of phase multiplications on the contrast generated in the susceptibility weighted magnitude images.

62

PHASE AND ITS RELATIONSHIP TO IMAGING PARAMETERS AND SUSCEPTIBILITY

FIGURE 4.13

Pictorial illustration of the phase masking process. (a) Phase profile in a filtered-phase image. (b) Corresponding profile of the mask created from (a). Once the mask is raised to the fourth power, the vein that has a phase of p=2 and a mask value of 0.5 will become 1/16, and hence this vein will be almost as well suppressed as the vein with a phase of p and f(x) = 0. GM, WM, CSF here indicate gray matter, white matter, and cerebrospinal fluid, respectively.

Depending on the particular application for deliberately suppressing pixels with certain phase values, different phase masks, f(x), can be defined. Not surprisingly, a few different phase masks have been suggested already, including the counterpart to the above-mentioned mask (equation (4.21)), the so-called positive phase mask, given by f ðxÞ ¼

½pwðxÞ ; p

¼1

for 0 wðxÞ < p

for p < wðxÞ < 0

ð4:21Þ

PHASE MASK AND VOXEL ASPECT RATIO

63

FIGURE 4.14 Depicting the effect of phase mask multiplication. (a) A minimum intensity projection over 8 mm thick imaging volume from the original magnitude images. (b) Corresponding projection over the phase images depicting the venous vasculature. (c) Corresponding projection image from the susceptibility weighted magnitude image (i.e., after phase mask multiplication). The enhancement of contrast for venous vessels as well as for gray matter regions is clearly demonstrated. The number of multiplications used here is n ¼ 4.

as well as the symmetric triangular phase mask [11], f ðxÞ ¼

½p þ wðxÞ p

½pwðxÞ ¼ p

for p < wðxÞ < 0 for 0 wðxÞ < p

ð4:22Þ

More recently, an asymmetric phase mask has been proposed that linearly scales the negative phase values between p and 0 from 0 to 1 and the positive phase values between 0 and p/2 from 1 to 0, while phase values greater than p/2 are set to 0 [15]. Even more complicated mask functions include sigmoid-shaped phase masks [16], given for instance by 1 f ðxÞ ¼ g½wðxÞ ¼ ð4:23Þ 1 þ exp½a  ðwðxÞbÞ which includes two adjustable parameters a and b, that can be freely selected and optimized (e.g., a ¼ 10, b ¼ 0.2). Each of these mask definitions has different performance characteristics as can be seen in Figure 4.16 that illustrates the effects of these different phase masks. All the processing steps involved in the creation of susceptibility weighted magnitude images are schematically summarized in Figure 4.17. As discussed earlier, partial volume effects can not only influence the net magnitude signal of a voxel but also the net phase (see also Chapter 5, equation (5.6)). The phase images shown in Figure 4.18 are a case in point. For a venous vessel (that can be approximated as a long cylinder), the phase inside the vessel is actually positive (equation (4.9) and Table 2.4), see Figure 4.18b; however, practically, for a transverse acquisition with a voxel aspect ratio of 1:1:4 or 1:2:4 (LR:AP:HF), the phase for a voxel containing a vein turns out to be negative (see Figure 4.18c). LR, AP, and HF here denote the

64

PHASE AND ITS RELATIONSHIP TO IMAGING PARAMETERS AND SUSCEPTIBILITY

FIGURE 4.15 Influence of the number of phase mask filter multiplications on the final projected venograms. Each minimum intensity projection (mIP) corresponds to the same targeted volume of 20 mm. Data were acquired at 3 T field strength.

left–right, anterior–posterior, and head–foot directions with respect to the subject being imaged. This change in the sign of the phase comes about due to the asymmetric contribution from the extravascular phase in the slice direction. The phase outside a venous vessel perpendicular to the magnetic field varies as cos2f in the plane perpendicular to the vessel axis where f represents the angle to the main field from the shortest line drawn from the point of interest to the center of the vessel. Since the sign of this phase along the magnetic field direction is negative, the phase of the voxel with an aspect ratio of 1:1:4 (LR:AP:HF), containing a venous vessel, will have a large contribution from the extravascular negative phase. This asymmetric phase contribution is pictorially depicted in Figure 4.18a and mathematically detailed in the appendix of Ref. 14. As one can imagine, for an isotropic voxel size or a sagittal acquisition with an aspect ratio of 1:4:1,

PHASE MASK AND VOXEL ASPECT RATIO

65

FIGURE 4.16 Influence of the type of phase mask definition used on the final projected venograms. Each phase mask was multiplied with n = 4 (except in case of (e)) and the minimum intensity projections (mIP) correspond to the same targeted volume of 20 mm. Data were acquired at 3 T and phase masks were applied to the axially acquired data prior to minimum intensity projection. (a) Negative phase mask. (b) Positive phase mask. (c) Symmetric triangular phase mask. (d) Asymmetric phase mask [15]. (e) sigmoid-type phase mask [16]. Note that the positive (b) or triangular masks (c) and (d) cause blurring with this transverse image orientation. As can be seen, the sigmoid window enhances the presence of susceptibility changes similarly to (a).

this behavior vanishes and the phase inside the vein is indeed positive (Figure 4.18b and d). It is important to note that the phase sign described here is for a right-handed phase system (in contrast to the left-handed system, where the phase equation from Larmor relation is defined as w ¼ v  t ¼ g  B0  t). The phase mask definitions will also change accordingly. For example, in the left-handed phase system, the phase mask definition in equation (4.19) for a paramagnetic substance changes to the positive phase mask defined in equation (4.21).

FIGURE 4.17 Chain of processing steps involved in producing susceptibility weighted magnitude images.

66

PHASE AND ITS RELATIONSHIP TO IMAGING PARAMETERS AND SUSCEPTIBILITY

NOISE IN PHASE IMAGES

67

NOISE IN PHASE IMAGES MR data, as any other experimentally acquired data, is affected by noise. Noise can originate from a multitude of sources, for example, electrical noise in the coil and the receiver, as well as radio frequency transmitter noise [17]. If the coil is heavily loaded (i.e., substantial damping is caused by the sample), noise currents in the sample are the dominant noise source [18] and other sources can be neglected. This is important for the discussion of the noise properties of the real and imaginary parts of the signal. While transmitter and receiver may cause correlated noise in the two channels, randomly fluctuating currents in the sample have a random phase and thus produce uncorrelated noise. Thus, for the following discussion, the noise of the real and imaginary parts of the complex signal will be assumed to be uncorrelated. The noise in each channel can then be treated as an independent random variable. The noise of each channel can be assumed to be white noise and satisfies a Gaussian distribution with zero mean [18, 19]. Since both magnitude and phase images are computed from the complex image data (real and imaginary components) using nonlinear mappings, the noise in the respective images is then no longer Gaussian. It can be shown that in the magnitude image the noise is distributed according to a Rician distribution [20]. In regions where only noise is present, this distribution reduces to the Rayleigh distribution PðI Þ ¼

1 I 2 =2s2 e s2

ð4:24Þ

where I is the modulus of the voxel’s complex value and s2 the variance of the real and imaginary parts under the assumption that both variances are the same. If SNR becomes sufficiently high (SNR > 3), the Rician distribution can be approximated by a Gaussian distribution [18, 19]. The distribution of the phase noise for p(Dw) is more complicated. Nevertheless, for two situations, simple equations can be given [17, 18]. The first occurs in regions where only noise is present. In this case, the phase noise is distributed uniformly: 8 < 1 pðDwÞ ¼ 2p : 0

3 FIGURE 4.18

if

p < Dw < p

ð4:25Þ

else

(a) Schematic illustration of the geometric relationship between nominal voxel, vein, and field distribution. The aspect ratio is determined by the nominal voxel dimensions Dx, Dy, and Dz. (b) Saggital phase image acquired with isotropic resolution (0.5  0.5  0.5 mm3). The phase inside the veins (that are almost perpendicular to the field) is positive as theoretically expected for paramagnetic deoxygenated blood (see Chapter 2, Table 2.4). (c) A phase image acquired in axial orientation with a voxel aspect ratio of 2:1:4 (LR:AP:HF or Dx:Dy:Dz in (a)) and voxel size of 1  0.5  2 mm3. The phase inside the vein is negative now due to partial volume effect and contribution from extravascular phase in the HF direction (i.e., along Dz direction (a)). (d) A sagittal phase image acquired from the same volunteer as in (b) with resolution 1  1  0.5 mm3. Phase inside the veins is again positive as the additional extravascular phase contribution is now coming from Dy direction or along f ¼ 90 direction (see Table 2.4) where the sign of the phase is positive. LR, AP, and HF here refer to left–right, anterior–posterior, and head–foot directions, respectively. Parts (c) and (d) are reprinted from Ref. 14 with permission from Elsevier Science.

68

PHASE AND ITS RELATIONSHIP TO IMAGING PARAMETERS AND SUSCEPTIBILITY

FIGURE 4.19 The relationship between magnitude and variance of the phase. The circle indicates the variances of the real and imaginary parts. The variances are the same in (a), (b), and (c). Despite identical variations of the real and imaginary parts, the variation of the phase is much smaller if the magnitude is large. Parts (d), (e), and (f) show the phase error distribution plots for (a), (b), and (c), respectively.

If the SNR is large (SNR > 3), the phase noise ditribution, p(Dw ), can be approximated by a Gaussian distribution I 2 2 2 pðDwÞ ¼ pffiffiffiffiffiffiffiffiffi eDw =ð4s =I Þ 2ps

ð4:26Þ

FIGURE 4.20 An example showing the zebra striping effect of k-space shifts on the phase image. (a) The original phase image, (b) the effect of a 1-pixel shift in the read direction (horizontal), (c) the effect of a 2-pixel shift in the read direction (horizontal), and (d) the effect of a 3-pixel shift in the read direction (horizontal). By counting the number of phase wraps, one can estimate the pixel shift in k-space. The intensity profiles for (a), (b), (c), and (d) are shown in (e), (f), (g), and (h), respectively.

FOURIER PROPERTIES OF PHASE

69

FIGURE 4.21

The effects of shifts in k-space. The phase image on the left was reconstructed from kspace with the echo at the center. For the image at the center, every readout (horizontal) line in k-space was shifted to the right by 2 pixels, and for the image on the right, the shift was 4 pixels. The phase images are shown including random noise in the background. Correctly centering the data in k-space can be seen to give a more pristine representation of background phase effects.

The standard deviation is given by sDw ¼

s I

ð4:27Þ

and is thus seen to be independent of the phase angle. It is inversely proportional to the magnitude, which is also valid on a pixel by pixel basis [17]. The only condition is that the SNR has to be sufficiently large. Figure 4.19 illustrates the relationship between the variance of phase noise and the magnitude of a complex-valued vector.

FOURIER PROPERTIES OF PHASE Understanding how a shift in the origin in one domain can affect the conjugate domain after Fourier transformation is very useful in MRI. Suppose the Fourier transform of some function (image) F[f(x)] is known and the Fourier transform of F½f ðxx0 Þ (i.e., a shifted image) is to be calculated. This can be done as follows: 1 ð

F½f ðxx0 Þ ¼ 1 1 ð

¼

f ðxx0 Þ  ei  2p  k  x dx

f ðx0 Þ  ei  2p  k  ðx

0

þ x0 Þ

dx0

ð4:28Þ

1

¼e

i  2p  k  x0

¼e

i  2p  k  x0

1 ð



0

f ðx0 Þ  ei  2p  k  x dx0

1

 F½f ðxÞ

where x0 ¼ xx0 . Thus, a position shift in one domain results in a linear phase factor in the other domain and vice versa. The effects of k-space shifts on the phase are shown in Figures 4.20 and 4.21. In Figure 4.20, we show the zebra striping effect of a shift in k-space

70

PHASE AND ITS RELATIONSHIP TO IMAGING PARAMETERS AND SUSCEPTIBILITY

along the read direction. Shifting the echo by one time point leads to a 2p shift along the read direction in the image. A shift of n points of the echo leads to n zebra stripes. One can tell just from the image sometimes how much the echo is off-center in k-space. A more practical example is shown in Figure 4.21 where it is more difficult to make that same determination based just on the phase itself since the background phase is fairly complicated. CONCLUSIONS In summary, phase plays the key role in visualizing changes in local background magnetic field. But as we have seen, there are often other phase modifying effects such as poorly shimmed fields, changes in local susceptibility from air/tissue interfaces, and echo shifts as described above. All these corrupt the phase image. Most of these are removed when we high pass or homodyne filter the phase images leaving behind the local phase or field changes of interest. Once we have these filtered images, we can begin to manipulate the data to create susceptibility weighted images. REFERENCES 1. 2. 3. 4. 5.

6.

7. 8. 9.

10.

11. 12.

Lyons R. Understanding Digital Signal Processing, 1st edn, Addison Wesley Longman, 1997. Considine V. Digital complex sampling. Electron. Lett. 1983;19:608–609. Strang G. Linear Algebra and Its Applications, 3rd edn, Brooks Cole, 1988. Sedlacik J, Rauscher A, Reichenbach JR. Obtaining blood oxygenation levels from MR signal behavior in the presence of single venous vessels. Magn. Reson. Med. 2007;58:1035–1044. Reichenbach JR, Venkatesan R, Yablonskiy DA, Thompson MR, Lai S, Haacke EM. Theory and application of static field inhomogeneity effects in gradient-echo imaging. J. Magn. Reson. Imaging 1997;7:266–279. Deistung A, Rauscher A, Sedlacik J, Stadler J, Witoszynskyj S, Reichenbach JR. Susceptibility weighted imaging at ultra high magnetic field strengths: theoretical considerations and experimental results. Magn. Reson. Med. 2008;60:1155–1168. Rauscher A, Sedlacik J, Barth M, Mentzel HJ, Reichenbach JR. Magnetic susceptibility-weighted MR phase imaging of the human brain. AJNR Am. J. Neuroradiol. 2005;26:736–742. Zhao JM, Clingman CS, Narvainen MJ, Kauppinen RA, van Zijl PC. Oxygenation and hematocrit dependence of transverse relaxation rates of blood at 3 T. Magn. Reson. Med. 2007;58:592–597. Koopmans PJ, Manniesing R, Niessen WJ, Viergever MA, Barth M. MR venography of the human brain using susceptibility-weighted imaging at very high field strength. MAGMA 2008;21:149– 158. Reichenbach JR, Essig M, Haacke EM, Lee BC, Przetak C, Kaiser WA, Schad LR. Highresolution venography of the brain using magnetic resonance imaging. MAGMA 1998;6(1): 62–69. Reichenbach JR, Haacke EM. High-resolution BOLD venographic imaging: a window into brain function. NMR Biomed. 2001;14:453–467. Abduljalil AM, Schmalbrock P, Novak V, Chakeres DW. Enhanced gray and white matter contrast of phase susceptibility weighted images in ultra-high-field magnetic resonance imaging. J. Magn. Reson. Imaging 2003;18:284–290.

REFERENCES

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13. Haacke EM, Xu Y, Cheng Y-CN, Reichenbach JR., Susceptibility weighted imaging (SWI). Magn. Reson. Med. 2004;52:612–618. 14. Xu Y, Haacke EM. The role of voxel aspect ratio in determining apparent vascular phase behavior in susceptibility weighted imaging. Magn. Reson. Imaging 2006;24:155–160. 15. Brainovich V, Sabatini U, Hagberg GE. Advantages of using multiple-echo image combination and asymmetric triangular phase masking in magnetic resonance venography at 3 T. Magn. Reson. Imaging 2009;27:23–37. 16. Martınez-Santiesteban FM, Swanson SD, Noll DC, Anderson DJ. Object orientation independence of susceptibility weighted imaging by using a sigmoid-type phase window. Proc. Int. Soc. Magn. Reson. Med. 2006;14:2399. 17. Conturo T, Smith G. Signal-to-noise in phase angle reconstruction: dynamic range extension using phase reference offsets. Magn. Reson. Med. 1990;15:420–437. 18. Edelstein WA, Glover GH, Hardy CJ, Redington RW. The intrinsic signal-to-noise ratio in NMR imaging. Magn. Reson. Med. 1986;3:604–618. 19. Henkelman RM. Measurement of signal intensities in the presence of noise in MR images. Med. Phys. 1985;12:232–233 Erratum in Med. Phs. 1986;13:544. 20. Gudbjartsson H, Patz S. The Rician distribution of noisy MRI data. Magn. Reson. Med. 1995;34:910–914.

5 Understanding T2*-Related Signal Loss Jan Sedlacik, Alexander Rauscher, J€ urgen R. Reichenbach, and E. Mark Haacke

INTRODUCTION Spin relaxation is of central importance in nuclear magnetic resonance (NMR) and magnetic resonance imaging (MRI). To detect any magnetic resonance signal requires a nonzero transverse magnetization of the spin system that must have been excited previously. Such nonthermal states, however, are subject to relaxation processes. Investigations on spin relaxation have become a major tool not only in physics and physical chemistry to study structure and dynamics in solution and in solid state but also in the medical arena to study relaxation effects in biological tissue both under normal and pathophysiological conditions. This is because these macroscopically measured quantities, mainly the longitudinal relaxation time T1 and the transverse relaxation time T2 , depend in the most common cases, on the local (i.e., microscopic) magnetic field environment that the nucleus sees [1–4]. The focus in this chapter will be an introduction to T2* effects in gradient echo imaging.

T2 RELAXATION Consider a spin ensemble, consisting of many different spin isochromats, in the rotating reference frame. After the magnetization has been tipped into the transverse plane, thus generating the maximum observable coherence in the ensemble, the spin isochromats experience local fields that are combinations of the applied field and the fields of their neighbors. Since variations in the local fields lead to different local precessional Susceptibility Weighted Imaging in MRI, By E. Mark Haacke and J€urgen R. Reichenbach Copyright
2011 by Wiley-Blackwell

73

74



UNDERSTANDING T2 -RELATED SIGNAL LOSS

FIGURE 5.1 An example set of spin vectors showing the effect on the net magnetization vector caused by the variation in local magnetic fields. The dashed arrow represents the signal that would have been present if only T2 decay were to take place. The solid arrows are the remnant signal because of the dephasing caused by local field variations.

frequencies, the spin isochromats tend to fan out in time, as shown in Figure 5.1, reducing the net magnetization vector. The rate at which coherence is lost is characterized by the transverse relaxation time T2 . Transverse relaxation in the simplest approximation leads to an exponential decay of any initial transverse magnetization Mxy via Mxy ðtÞ ¼ Mxy ðt ¼ 0Þet=T2 Basically, T2 is caused by stochastic fluctuations of the magnetic field at a microscopic level that cause a loss of spin coherence. These random fluctuating fields make T2 an irreversible process [2]. 

FROM T2 TO T2

While random field fluctuations are the main cause of irreversible T2 decay, there are other reversible sources of transverse signal loss that need not necessarily be exponential in nature. If the static magnetic field is not homogeneous, as for example with poor shimming, nuclei that should resonate at the same frequency exhibit slight differences in the resonance frequency depending on their location in the magnetic field. This leads to an additional

FROM T2 TO T2

75

dephasing of the transverse magnetization, that is, a fanning out of the transverse magnetization components of the spin isochromats. The spatial extent of the deterministic field inhomogeneities referred to here are typically on the order of the size of the imaging voxel (i.e, a few hundred microns to a few millimeters or more). Some of these isochromats will precess faster, some will move more slowly than the rotating frame, corresponding to their different Larmor frequencies (again see Figure 5.1). In a spin echo experiment, these dephasing spins rephase to form a spin echo after the refocusing 180 pulse has been applied. However, in a gradient echo experiment, which lacks the 180 rf pulse, this unrefocused fanning out of the transverse magnetization causes additional signal loss. Apart from these more macroscopic field inhomogeneities where the scale is at least on the order of the voxel size, there may also exist mesoscopic field inhomogeneities that are induced by the static magnetic field and may cause dephasing of the magnetization too. These inhomogeneities are produced by spatial variations of the magnetic susceptibility within the sample. It is common to write the phenomenological transverse relaxation rate as a sum of the intrinsic rate R2 and the external decay rate due to local reversible field contributions R02 , that is, R*2 ¼ R2 þ R02

ð5:1Þ

where R2 is simply the inverse of the relaxation time T2, so in terms of relaxation times, 1 1 1 ¼ þ 0 * T2 T2 T2

ð5:2Þ

Assuming that the transverse relaxation behaves exponentially, which is only the case if the probability density distribution of the local fields within the sample volume shows a Lorentzian form [5], the actual signal loss for a given experiment and local field can be found from the usual inversion of k-space. It must be remembered that each k-space point represents an integral across all space at a given time point in the sampling window. Ignoring a few proportionality constants, the signal at the echo for a 1D voxel of width Dx centered about x, the magnetization across a voxel can be given as, ð xþDx 2 * 0 * Ms ðtÞ ¼ eTE=T2 M? ðxÞeivðxÞt  eðt þTEÞ=T2 dx xDx 2

¼e

TE=T2*

ð xþDx=2 xDx=2

ð5:3Þ M? ðxÞeivðxÞt  et

0

=T2*

dx

where M? ðxÞ is the magnitude of the transverse magnetization available from the voxel immediately after application of the rf pulse, t0 ¼ tTE and vðxÞ ¼ ðg  Gx  xÞ, with Gx here being the imaging gradient or any other field gradient (for e.g. due to inhomogeneities) ^ direction. Neglecting changes in signal loss caused by T2* during the sampling along the x interval between t0 ¼ TS=2 to t0 ¼ þTS=2, that is, if TS  2  TE, then we can simplify this further to ð xþDx=2 TE=T2* Ms ðtÞ  e M? ðxÞeivðxÞt dx ð5:4Þ xDx=2

76



UNDERSTANDING T2 -RELATED SIGNAL LOSS

Doing the inverse transform of this function returns an estimate for the magnetization as a function of position as Mðx; TE; T2* Þ ¼ eTE=T2 M? ðxÞ *

ð5:5Þ

This situation becomes more complicated if there is a local field shift in the voxel. In that case the signal is given by Ms ðt; DBÞ ¼ e

TE=T2*

ð xþDx=2 xDx=2

M? ðxÞeiðvðxÞþDvðxÞÞt dx

ð5:6Þ

where DvðxÞ ¼ g  DBðxÞ. If we assume that DBðxÞ is constant across the voxel, it becomes independent of position and thus can be taken out of the integral. Thus after Fourier transformation, we get the signal at x as a function of TE, and T2* as: Mðx; TE; T2* Þ ¼ eTE=T2 M? ðxÞeigDBTE *

ð5:7Þ

In general, the signal decay is not exponential at all times. For a small number of dipoles [6, 7], a vascular network [5], or macroscopic background field inhomogeneities [8], the decay becomes nonexponential. For example, in the presence of a single large blood vessel [5, 9–11] the assumption of an exponential decay fails. The reason for this is that the relationship between voxel geometry (spatial resolution, slice orientation, imaging sampling point spread function) and field inhomogeneities plays an important role in gradient echo signal formation [5, 12–15]. Venous vessels produce local field inhomogeneities [9], which depend on the vessel’s orientation and the venous blood oxygenation. For example, for a cylindrical vessel oriented parallel to the magnetic field, there exist two different field strengths inside and outside the vessel. Consequently, spins inside and outside the vessel experience two different resonance frequencies that, when superimposed, lead to a beat in the signal decay [10]. Yablonskiy classified magnetic field inhomogeneities according to their length scales [16]. Within this scheme, macroscopic inhomogeneities are larger than the imaging voxel and are caused, for instance, by imperfect shim and air–tissue and bone–tissue interfaces. Mesoscopic field inhomogeneities are smaller than the voxel size, but larger than the typical diffusion length and larger than the diameters of small blood vessels. Microscopic inhomogeneities have length scales corresponding to the size of molecules or the distance between atoms. In contrast to macroscopic and mesoscopic static inhomogeneities that lead to reversible signal decay, microscopic inhomogeneities lead to irreversible T2 decay. 

T2 DECAY OF PARTICULAR GEOMETRIES As mentioned above, the T2* decay strongly depends on the spatial relationship between field inhomogeneities and voxel geometry of a particular imaging method. SWI partly controls this effect by using small voxels on the order of 0.5–1 mm3. Some research experiments with SWI have pushed the resolution as low as 0.04 mm3 which becomes possible with higher field strengths, optimized sequences, and better radio frequency receiver coils. Other T2* -weighted techniques, blood oxygenation level-dependent (BOLD) fMRI, for instance, optimize image plane orientation and voxel aspect ratio to minimize effects from background field inhomogeneities such as spatial misregistration



T2 DECAY OF PARTICULAR GEOMETRIES

77

of the spin density or signal dephasing. Today, most BOLD imaging is done with a resolution somewhere between 8 and 64 mm3. Analyzing the MR signal decay due to the magnetic field inhomogeneities generated by the presence of some simpler geometric forms are of particular interest because their associated field inhomogeneities can be expressed analytically. Along these lines, we next discuss briefly the effects from a single sphere, a single blood vessel, and a vascular network. Single Sphere To investigate the effects of magnetic dipoles in the form of spheres is particularly interesting for applications including the problem of tracking magnetically labeled cells, such as stem cells or macrophages by MRI [17], to distinguish paramagnetic spherical brain lesions from diamagnetic lesions [18] or to quantify the amount of iron in a small hemorrhage [19]. The offset frequency distribution, dvsph , around such a spherical particle can be calculated from its external dipole field dvsph ðr; uÞ ¼ gB0

 Dx a3  3 cos2 u1 3 r

ð5:8Þ

where Dx denotes the magnetic susceptibility difference between the sphere and its surrounding material, a denotes the radius of the sphere, and r and u are polar coordinates. The temporal evolution of the transverse magnetization within a spherical volume of radius R (i.e, a spherical voxel) around this dipole can be calculated by integrating all transverse contributions over the surrounding volume Msph ðtÞ ¼

ð p ð 2p ð R 0

0

M0 ðrÞ  eidvsph ðr;uÞt  et=T2  r2 sin udrdudf

ð5:9Þ

a

where M0 denotes the transverse magnetization at t ¼ 0, T2 the transverse relaxation time, r, u, and f denote the spherical coordinates. The signal decay induced by the spherical susceptibility inhomogeneity depends on the volume fraction of the sphere within the spherical voxel (voxel radius R, volume fraction ða3=R3 Þ), and its susceptibility difference ðDx Þ (Figure 5.2) [5, 14]. The shape of the distribution of frequencies (dvsph ) within the voxel, which depends on the sampling point spread function of the particular MRI sequence as well as the relative position of the sphere within the voxel, also determines the actual decay curve of the transverse magnetization.

Single Blood Vessel The field inhomogeneity induced by a single cylindrical blood vessel and its impact on the transverse magnetization is particularly important for the understanding and optimization of contrast mechanisms in SWI [13, 14]. The induced offset frequency distribution, dvcyl , around a cylindrical vessel is determined by dvcyl ðr; u; fÞ ¼ gB0 

a2 Dx  sin2 u   cos 2f 2 r

ð5:10Þ

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UNDERSTANDING T2 -RELATED SIGNAL LOSS

 

FIGURE 5.2 Left: Offset frequency densities r dvSph



induced by a spherical dipole with different volume fractions a^3/R^3 ¼ 0.020, 0.025, 0.030 and susceptibility difference of 1 ppm ðB0 ¼ 1:5 T Þ. Right: Corresponding transverse magnetization decay curves (eq. 5.9) for a spherical voxel. The sphere is assumed to be concentric with the spherical voxel.

where Dx denotes the magnetic susceptibility difference between the cylinder and the surrounding material, a denotes the cylinder radius, f the orientation of the cylinder axis with respect to B0 , and r and u are polar coordinates. Of note is the dependence of the extravascular frequency distribution on the orientation of the cylinder. It is zero for a vessel oriented parallel to B0 ðu ¼ 0 Þ and becomes maximal for a perpendicular vessel orientation ðu ¼ 90 Þ. Again, the time course of the magnetization around the cylinder can be calculated by integrating all transverse contributions over the surrounding volume MC ðtÞ ¼

ð 2p ð R

M0 ðrÞ  eidvC ðr;u;fÞ t  et=T2  r dr df

ð5:11Þ

a

0

Here, M0 denotes the transverse magnetization at t ¼ 0, T2 the transverse relaxation time, and r and f denote the polar coordinates with R the radius of the cylindrical volume element, that is, cylindrical voxel (Figure 5.3) [11]. The signal decay induced by the cylindrical

 

FIGURE 5.3 Left: Offset frequency densities r dvCyl



induced by a cylinder oriented perpendicular to B0 with different volume fractions a /R ¼ 0.020, 0.025, 0.030 and susceptibility difference of 1 ppm ðB0 ¼ 1:5 T Þ. Right: Corresponding transverse magnetization decay curves for a cylindrical voxel. The cylindrical voxel and the cylinder are taken to be concentric (eq. 5.11). 3

3

BLOOD VESSEL NETWORK

79

susceptibility inhomogeneity depends on its volume fraction within a cylindrical voxel ða2 =R2 Þ and its susceptibility difference. Again, the shape of the distribution of frequencies (dvsph ) within the voxel, which depends on the point spread function of the MRI sequence as well as the relative position of the vessel within the voxel, determines the actual decay curve of the transverse magnetization.

BLOOD VESSEL NETWORK The blood vessel and capillary network can be described by a network formed by randomly oriented and randomly distributed cylinders. Due to the averaging of all different cylinder orientations, the frequency shift ðdvnet Þ induced by the cylinder network is [5] dvnet ¼ gB0

Dx 3

ð5:12Þ

where Dx denotes the magnetic susceptibility difference between the blood vessels and the background tissue in which they are embedded. The induced frequency shift is independent of voxel shape or positioning as long as the cylinders are uniformly oriented and distributed within the voxel. The magnetization decay of a blood vessel network can be calculated analytically and exhibits an asymptotic behavior that is quadratic exponential in the short term and monoexponentially in the long-term period [5]. The short- and long-term asymptotes are given as 2

Mnet; short ðt  1:5=dvnet Þ ¼ M0  e0:3lðdvnet tÞ  et=T2   1 ldvnet t dv net Mnet; long ðt 1:5=dvnet Þ ¼ M0  e  et=T2

ð5:13Þ ð5:14Þ

where M0 denotes the transverse magnetization at t ¼ 0, T2 the transverse relaxation time, and l the volume fraction occupied by the cylinders within the matrix (Figure 5.4) [5].

FIGURE 5.4 Left: Short- and long-term asymptotes shown for a cylinder network with a volume fraction of l ¼ 0.05 and Dx ¼ 0.5 ppm at B0 ¼ 1:5 T . Right: Transverse magnetization decay curves of cylinder networks with different volume fractions ðlÞ and susceptibility differences ðDxÞ.

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UNDERSTANDING T2 -RELATED SIGNAL LOSS

FIGURE 5.5 Left: Offset frequency density around a cylinder of size 5 mm, Dx ¼ 1 ppm and volume fraction a3/R3¼ 0.02. The diffusion coefficient D changes from D ¼ 0, 1, 2 to 5 mm2/ms. Right: Corresponding transverse magnetization decay curves. The cylinder is assumed to be concentric with the cylindrical voxel.

Effect of Diffusion If the size of the spherical or cylindrical objects is within the diffusion length of the spins, the signal evolution time course is further modified. Diffusing spins experience different local magnetic field strengths over time and the frequency shift induced by the objects changes to a Lorentzian-shaped distribution, which causes the magnetization to decay nearly monoexponentially in the long-term period (Figure 5.5) [20]. With respect to SWI, in most applications (at least for human applications), vessels with diameters down to approximately 100 mm are detected and visualized. Monte Carlo simulations demonstrated that diffusion has no impact on the transverse relaxation for vessel sizes above 100 mm [21]. Thus, the effect of diffusion can be neglected to good approximation for the signal and contrast mechanisms in susceptibility weighted imaging (Table 5.1). Voxel Size and Background Gradients In the presence of background magnetic field gradients caused by air/tissue interfaces or suboptimal shim adjustments, the transverse net magnetization of a voxel is additionally attenuated. This fact has to be taken into account for correct T2* measurements. Assuming a linear field gradient over the voxel, the frequency distribution becomes a box function whose extent depends on the voxel size and the strength of the background field gradient. The resulting magnetization decay caused by a box-shaped frequency distribution is a sinc function where the decay rate is again governed by the extent of the box-shaped frequency distribution (Figure 5.6). Measurement of T2 and T20 Since T2* measurements are both affected by T2 and T20 , and T20 further is affected by voxel size and background field gradient strength, special efforts have to be made to measure reliable and reproducible T2* and T20 times, which ultimately may be used to quantify iron depositions [22] or blood oxygenation saturation [23]. Thus, a good shim adjustment, a reasonably small voxel size, and background field correction are essential for reliable T2* and T20 quantification.

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81

TABLE 5.1 Relaxation Times Obtained from the Literature for Venous Blood, White and Gray Matter for Magnetic Field Strengths from 1.5 to 9.4 T B0 (T) 1.5 T

3T

4.7 T

7T

8T

9.4 T

Tissue

T1 (ms)

T2 (ms)

T2* (ms)

Venous blood White matter Gray matter Venous blood White matter Gray matter

1441 120a 884 50a 1124 50a 1932 85a 1084 45a 1820 114a

122b 72 4a 95 8a 32.2d 69 3a 99 7a

97b 66.2 1.9c 84 0.8c 21.2d, 24.3 2.3p 53.2 1.2c 66 1.4c

Venous blood White matter Gray matter

1833 49e 1080 140f 1520 220f

17.9b 63.8 6f 67.5 6.4f

10.96b 41 6.9g 49.5 6.4g

Venous blood White matter Gray matter Venous blood White matter Gray matter

2212 53e 1220 36h 2132 36h n.a. 1300l 1800l

13.2 0.2i 45.9 1.9j 55.0 4.1j n.a. 39.0 1.6l 44.8l

7.4 1.4k 26.8 1.2c 33.2 1.3c n.a. 20.5l 20.3l

Venous blood White matter Gray matter

2429 49e 1970 21m 2280 23m

4.9n 29.5 4.9m 31.8 4.9m

n.a. 25 3o 34 4o

For all field strengths, the blood oxygenation Y of venous blood was assumed to be about 60%. a

The values were listed in Ref. 26. The values were determined ex vivo for bovine blood with an oxygen saturation Y of about 60% [27]. c The values were measured by Peters et al. [28]. d The values were determined ex vivo for bovine blood by Zhao et al. [29]. e The values were measured ex vivo for bovine blood by Dobre et al. [30]. f The values were measured for the macaque monkey and averaged for gray and white matter [31]. g The values determined for the Macaca mulatta given in Table 3 by Bonny et al. [32] were averaged. h The values were measured by Rooney et al. [33]. i The values were measured ex vivo for human blood at Y ¼ 59% [34]. j The values were taken from Ref. 35. k Human venous blood was measured in the sagittal sinus [36]. l The values are listed in Ref. 37. The T2 values were determined using a single gradient echo sampling of spin echo (GESSE) sequence. m The values were determined in ex vivo measurements of rats [38]. n The values were measured in mice and calculated for Y ¼ 0.6 using the R2(Y) ¼ 478  458Y provided by Lee et al. [39]. o The values were determined for the cat by Zhao et al. [40]. p The values were determined from the leg in human studies [41]. b

Left: Different box-shaped frequency shift densities ðrðdvÞÞ caused by different voxel sizes or background field gradient strengths. Right: Corresponding transverse magnetization decay curves.

FIGURE 5.6

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UNDERSTANDING T2 -RELATED SIGNAL LOSS

FIGURE 5.7 (a–c) Magnitude images from a 3D multi-echo gradient echo sequence with echo times of 12.94 ms, 27.74 ms, and 42.54 ms, respectively. (d) T2* map generated by fitting the signal decay from all the echoes collected. A total of 11 echoes were collected starting from 12.94 ms to 49.94 ms. The long arrow in (d) indicates the reduced T2* in the globus pallidus and the short arrow the longer T2* in the optic radiation.

Multi-Echo Experiment for T2 Measurement Ignoring the role of partial volume effects and voxel size (discussed in the “T2* decay of particular geometries” section), signal decay in gradient echo sequences, for the most part, follows equation (5.7). Thus, if we sample the signal at different echo times through a multi-echo gradient echo sequence,

BLOOD VESSEL NETWORK

83

FIGURE 5.8 (a–c) A different slice of magnitude images from a 3D multi-echo gradient echo sequence with echo times of 12.94 ms, 27.74 ms, and 42.54 ms, respectively. (d) T2* map generated by fitting the signal decay from all the echoes collected. A total of 11 echoes were collected starting from 12.94 ms to 49.94 ms. (e) High-pass filtered phase image at TE ¼ 27.74 ms also depicting good gray-white matter contrast.

we can extract both T2* and the field inhomogeneity information (DB) by fitting the signal curve to equation (5.7) [24]. An example T2 * map calculated from an 11-echo sequence is shown in Figures 5.7d and 5.8d. Although not implemented here, it is possible to account for the macroscopic phase variations that lead to the oscillatory behaviors described above by using the phase information across a voxel and thereby improve the estimates of the intrinsic T2* . Separating T2 and T20 Collecting multiple spin echoes and multiple gradient echoes individually to obtain T2 and T2* and then calculating T20 using equation (5.5) is a straightforward way of obtaining the T20 and T2 contributions. A sequence with gradient echo sampling of spin echo data [16, 25] provides a very useful tool to separate T2 and T20 contributions directly. This sequence samples the signal formation around a spin echo with multiple gradient echoes [16]. The advantage of this sequence isits ability to separate the irreversible signal decay ðT2 Þ from the reversible decay T20 caused by static field inhomogeneities in a single self-consistent fashion. Spins that are dephased due to static field inhomogeneities are rephased after the 180 refocusing pulse and dephased again

84



UNDERSTANDING T2 -RELATED SIGNAL LOSS

FIGURE 5.9 Transverse magnetization formation for a cylinder network with a volume fraction of l ¼ 0.05, Dx ¼ 1 ppm, and B0 ¼ 1:5 T around the spin echo occurring at ttSE ¼ 0 with MSE ¼ 1 and T2 ¼ 100 ms. T20 was found to be 150 ms and therefore T2* is 60 ms.

after the spin echo. Contrary to this, the irreversible spin–spin interaction is always present and dephases the spins before and after the spin echo. This makes it possible to determine both signal dephasing processes independently by an almost symmetrically sampled spin echo. Following these considerations, the signal around a spin echo can be expressed as 0

M ðtÞ ¼ MSE  ejttSE j=T2  eðttSE Þ=T2

ð5:15Þ

where MSE is the transverse magnetization at tSE , which is the time the spin echo occurs. The term exp jttSE j=T20 expresses the time with respect to tSE and is negative before and positive after the spin echo. Therefore, this term will be smaller than 1 on both sides around the echo, whereas the second term expððttSE Þ=T2 Þ will give values greater than 1 before and smaller than 1 after the spin echo. Fitting the above expression to the measured signal around the spin echo makes it possible to determine T2 and T20 separately and not entangled in a single T2* value. Figure 5.9 demonstrates the different decays of the transverse magnetization around a spin echo.

CONCLUSION Field inhomogeneities of any spatial extent and from any source lead to T2* signal loss in gradient echo imaging. If macroscopic inhomogeneities are properly avoided with good shimming, the T2* or T20 effects from mesoscopic field inhomogeneities can provide unique tissue contrast as these effects arise from the local tissue structure and susceptibility differences. This T2* contrast can also be modulated by choosing appropriate experimental parameters like proper echo time or voxel size.

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6 Processing Concepts and SWI Filtered Phase Images Alexander Rauscher and Stephan Witoszynskyj

INTRODUCTION As we have discussed in Chapter 4, applying the phase mask generated from the filtered phase images to the original magnitude image is an integral step in generating susceptibility weighted images. Further, filtered phase images themselves serve to provide distinct phase contrast between tissues (see for example Figures 1.1, 3.7 or 4.8). In SWI, we are typically interested in local phase effects arising from the differences in magnetic susceptibility properties between individual tissues. In order to accomplish this, it is necessary to remove other confounding phase effects such as those due to background static field inhomogeneities (see Chapter 24). Methods for filtering or processing of phase images continues to be an active topic of research in studying susceptibility effects. Phase images, as for any kind of image, possess signal variations on a local and global scale. Digital image processing provides numerous methods to extract, enhance or highlight desired features within an image. Phase images, however, contain quite a different feature compared to magnitude images because of the limited domain of the phase between
p and p. This imposed periodicity leads to aliasing artifacts that pose an obstacle to most of phase imaging techniques. The following chapter will explain some of the typical properties of phase images that hinder image processing and will present several methods for dealing with these issues.

Susceptibility Weighted Imaging in MRI, By E. Mark Haacke and J€urgen R. Reichenbach Copyright  2011 by Wiley-Blackwell

89

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PROCESSING CONCEPTS AND SWI FILTERED PHASE IMAGES

PHASE WRAPS The phase wðrÞ can be seen as a function of a more or less boundless physical quantity. Although theoretically phase can take on any value, practically the domain of phase is limited to [
p, p). This mapping from outside the [
p, p) range to inside is referred to as aliasing. In the literature, this mapping is often described by the so-called wrapping operator W [1] wwrapped ðrÞ ¼ W ½wðrÞ

ð6:1Þ

where w(r) is the “true” unbound phase and wwrapped(r) the wrapped phase limited to [
p, p). While, in general, the “true” phase w(r) is a continuous function, the wrapped phase wwrapped(r) will have discontinuities if the “true” phase exceeds the range [
p, p). The process of determining a continuous function w(r) from a wrapped phase wwrapped(r) is usually called phase unwrapping. It corresponds to determining an integer field m(r), which fulfills wðrÞ ¼ wwrapped ðrÞ þ 2mðrÞp

ð6:2Þ

On phase images, phase wraps appear as sharp borderlines between pixels with low phase values near
p and pixels with high values near p (i.e., in grayscale images where the brightness changes or jumps from black to white). It should be noted that although phase wraps appear as steep edges, the “true” phase topography can actually be rather complicated. For example, a “true” phase that fluctuates only slightly around p would result in a phase image that contains a large number of phase wraps. Figure 6.1a gives an example of a phase image that contains phase wraps. The “true” phase is a twodimensional Gaussian function with a maximum value of 5p and a minimal value of 0. Figure 6.1b illustrates how noise affects the appearance of phase wraps. Because phase images have a discrete support a second type of aliasing can occur. In this situation, the phase topography is steep enough to cause a phase difference of 2p (or greater than 2p) between two adjacent pixels. Such a wrap is not necessarily visible in the image and thus cannot be resolved without additional knowledge [1]. It should, however, be noted that in MRI signal from a pixel does not represent an infinitesimally small point, but corresponds to a summation over a certain volume. Thus, a phase topography as steep as required for this type of aliasing usually results in a significant signal loss due to intravoxel dephasing [2]. In the literature, the two types of aliasing are often distinguished as fringelines (in the first case) and cutlines (in the second case) [3]. Fringelines and cutlines may or may not overlap. In MR images, one can distinguish between two types of fringelines: closed (as in Figure 6.1) and open-ended fringelines (Figure 6.2). In the second case, the image contains singularities. If such poles are present it is impossible to describe the phase by a continuous function (unless the presence of cutlines is assumed). Specifically, this means that if one tries to unwrap the function in a circle around the region of interest the resulting phase at the end will not agree with that at the beginning. However, open-ended fringelines can also be separated into three groups: the first group occurs in areas where either no or only little signal is present. In this case, the reason for open-ended fringelines is that the phase is not defined if the magnitude is zero and that phase noise is distributed uniformly in areas that contain noise only. Phase unwrapping is

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FIGURE 6.1 (a) Schematic illustration of phase wraps. The mapping of a continuous function (a 2D Gaussian with a maximum of 5p) to the limited domain of the phase causes discontinuities that appear as sharp edges between dark and bright pixels. Part (b) demonstrates how noise affects the appearance of phase wraps.

thus possible if areas containing low signal are avoided. Open-ended fringelines that pass through areas of sufficiently high signal, but where the poles are in areas without signal, belong to the second group. Finally, in the third case, the singularities occur in areas with a high signal magnitude. This situation usually does not occur, because cutlines and thus extremely steep phase topography have to be present as well. In most cases where this type of open-ended fringelines are found, the phase images were either preprocessed or occur as a result of an incorrect combination of images of phased array coils. Another reason may be partial volume effects. HOMODYNE DETECTION In SWI, the original approach to handle phase variations with low spatial frequencies was homodyne detection [4, 5]. Until now this is the most commonly employed method. The basic idea of homodyne detection is that one can interpret the measured complex MR image Im(r) as consisting of a desired complex component ID(r) (plus noise) that is modulated with a slowly varying phase j(r) [6]: Im ðrÞ ¼ ID ðrÞeiwðrÞ

ð6:3Þ

This slowly varying phase w(r), superimposed as a background on the desired pristine phase wdes(r), is caused by, for example, inhomogeneities of the static magnetic field or coil sensitivity variations. Extracting the desired component ID and can thus be seen as demodulating the original signal. If the desired signal ID(r) the phase w(r) have distinct spectral components, w(r) and can be derived from the original complex image by a lowpass filter. The demodulated signal is thus given by ID ðrÞ ¼ Im ðrÞe
iwðrÞ ¼ jID ðrÞjeiwdes ðrÞ

ð6:4Þ

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PROCESSING CONCEPTS AND SWI FILTERED PHASE IMAGES

FIGURE 6.2 Schematic illustrations of open-ended fringelines. In all three images, unwrapping is impossible unless the presence of cutlines is assumed. However, without additional knowledge the placement of these cutlines is completely arbitrary.

The low-pass filtered complex image that is required to compute w(r) can be created in various ways. The simplest approach is to apply a 2D boxcar function in image space. However, since the Fourier transform of a boxcar function is the sinc-function it also suppresses high-frequency components as well. Thus, most often, low-pass filtering is achieved by applying a Hamming [5] or Hanning [7] window in k-space. An important issue when using homodyne detection is the width of the window of the low-pass filter. If the window is too narrow, ID(r) might still be affected by lowfrequency phase variations and phase wraps. On the other hand, if the window is too wide, contrast between large structures in ID is lost. Figure 6.3 shows the effect of different widths of the smoothing kernel on the low-pass filtered phase image (top row) and the final homodyne filtered phase image (bottom row). Choosing an optimal window width becomes increasingly difficult with steeper phase topographies. This is often the case in areas close to air tissue boundaries such as those near the paranasal sinuses.

PHASE UNWRAPPING

93

FIGURE 6.3 Effect on the low-pass filter ’s kernel width on the phase images of the low-pass filtered data (top row) and on the corresponding homodyne filtered phase images (bottom row). The data were smoothed with a 2D boxcar function with a width of w ¼ 3 (a, d), w ¼ 7 (b, e), and w ¼ 21 (c, e), respectively.

If phase wraps remain in the homodyne filtered phase image it is, in general, impossible to remove them by a subsequent application of true phase unwrapping. The reason is that homodyne filtering can lead to phase images that contain open-ended fringelines with poles in areas of sufficient signal in the magnitude image. PHASE UNWRAPPING Unwrapping true phase in combination with a sophisticated extraction of local variations of the phase offers a powerful alternative to homodyne detection alone [8]. In addition, information on phase variations with local spatial frequency is conserved. Phase unwrapping and the choice of a filter type and/or size are two distinct problems that have to be discussed separately. In principle, any kind of phase unwrapping aims to determine m(r) in equation (6.2) for all pixels of an image such that the resulting phase image does not contain phase wraps. Usually, determining m(r) is not trivial and is often ambiguous. This is especially true in the presence of noise. The problem becomes even harder if the number of dimensions increases. Since phase unwrapping is a problem that occurs in various fields of science, ranging from optics and radar interferometry to MRI, a number of algorithms have been proposed

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over the years [1]. The approaches range from region growing [8–10], splitting merging [11], and neural networks [12] to methods exploiting properties of the Fourier transform [13]. Because phase unwrapping often requires certain assumptions or a priori knowledge about the data, it is often hard to judge whether a specific algorithm is applicable for data other than what it has been developed for. At the same time, additional knowledge about the properties of the image type and image acquisition can be used to improve the results of phase unwrapping methods. An example for additional knowledge that can be exploited in MRI (compared to, e.g., radar interferometry) is the signal’s magnitude. Two phase unwrapping programs that have been successfully applied to SWI data [7, 14, 15] and are freely available to the scientific community are FUN [16] and PRELUDE [11]. The first is available from one of the authors of this chapter (SW), the second is part of the FSL analysis package (Oxford Centre for Functional Magnetic Resonance Imaging of the Brain, United Kingdom). While FUN offers unwrapping in two dimensions only, PRELUDE provides a hybrid and a 3D mode. However, both the hybrid and the 3D mode are computationally very demanding and (in case of the 3D mode) less robust [16]. There are a few points that have to be considered when phase unwrapping is performed. Great care has to be taken that the phase images are acquired properly. The most common reasons for phase images that cannot be unwrapped properly are 1. Operations such as scaling and rotation that were applied on the phase images. As a result sharp edges that characterize phase wraps can be smeared out. Thus, a phase unwrapping program will not recognize them as phase wraps and phase unwrapping will fail. If the images are to be scaled or rotated prior to unwrapping, these operations have to be done either in k-space (i.e., by zero filling in case of scaling) or on the real and imaginary part of the complex image. 2. Filters that are applied to the data before unwrapping may cause singularities and may thus make phase unwrapping impossible. These include simple data interpolation methods as well. Consider for example two adjacent points with phase
p and p. The interpolation value is zero and no phase unwrapping algorithm can now remove this false, discontinuous phase jump. 3. This can also be true for phase difference maps that were obtained by taking the ratio of two complex images. If a phase difference map is to be calculated, it should be calculated by subtracting two unwrapped phase images from each other. 4. Finally, if data are acquired by phased array coils, great care has to be taken concerning the combination of the phased array’s channels’ data. Incorrectly combined data may not only have wrong values but can also contain singularities that impede phase unwrapping. The issue of combining phased array data is discussed in more detail at the end of the chapter. HIGH-PASS FILTERING In contrast to homodyne filtering, phase unwrapping preserves all spatial frequencies. The low spatial frequencies contain information on macroscopic field inhomogeneities that, for instance, lead to geometric distortions in echo planar imaging [17, 18]. In SWI, on the other hand, one is interested in phase effects due to local changes in tissue magnetic susceptibility. The phase image can then be high-pass filtered to remove contributions from field

PHASE IMAGES OF PHASED ARRAY COILS

95

inhomogeneities with low spatial frequencies. High-pass filtering can be performed by subtracting a low-pass filtered image from the original image. The low-pass filtered phase image can be computed by convolving the phase image with a low-pass filter kernel, such as a Gaussian function, or by fitting a 2D polynomial to the phase image or by just using the same homodyne approach discussed earlier.

PHASE MASK Voxels that are traversed by a venous vessel accumulate a phase difference with respect to the surrounding parenchyma. From the unwrapped, high-pass filtered and scaled phase images, a mask is computed, which is then multiplied with the corresponding magnitude image to further enhance signal attenuation caused by T2* shortening. For the phase mask, negative phase values (e.g., veins or tissue with high iron content) are mapped to a range between 0 and 1 and set to unity elsewhere:

wmasked

8 < 1
jwj ; p ¼ : 1;

if
p < w < 0

ð6:5Þ

else

In a final step, the mask is multiplied several times with the magnitude, usually by a factor of 4 (see Chapter 4). PHASE IMAGES OF PHASED ARRAY COILS Phased array coils have become more and more important over the past years. This is mostly due to the desire to decrease acquisition times by using parallel imaging techniques. Phased array coils are arrays of mutually decoupled surface coils [19]. Because of the decoupling, data can be acquired by all coil elements simultaneously. Just as for ordinary surface coils, the sensitivity of each coil element varies across space. The difference in sensitivities can be used as an additional spatial encoding. In theory, one could design an MR system where spatial encoding is done by using a very large array [20]. The basic idea of parallel imaging is to undersample k-space (which leads to aliasing) and to use the information of several coil elements to reconstruct the missing information. Figures 6.4 and 6.5 show the magnitude and respective phase images of all 12 channels from a Siemens TIM Trio head coil. However, the images do not reflect the images measured with each coil element, but are the result of a linear combination of three coil elements by a so-called mode matrix. Since each coil element of a phased array acts as a surface coil with a distinct sensitivity profile, each measurement leads to N images, where N is the number of coil elements in the phased array. In the case of parallel imaging, it is important to distinguish between the reconstruction of the full k-space and the combination of images of each channel. The SENSE algorithm operates in image space on images that are reconstructed from the incomplete k-space of each coil and results in a single combined image [21]. GRAPPA, on the other hand, reconstructs a full k-space (and an image) for each coil element [22]. For GRAPPA, the problem of combining images has to be dealt with separately.

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FIGURE 6.4 Magnitude images of a phantom corresponding to the 12 channels of a Siemens TIM Trio head coil. The signal of each channel does not correspond to a single coil element but is the result of combining three channels with the mode matrix. The top row shows the so-called primary channels, that is, the channels containing most of the signal.

Roemer et al. [19] showed that an optimal combination (in the sense that magnitude SNR is maximized in each point) is achieved by P ¼ lpT R
1 s

ð6:6Þ

where P is the single combined (complex) pixel value at (x, y, z), p a vector containing the values of this pixel for each coil element, R the noise correlation matrix, and s the coil sensitivities at (x, y, z). l is a position-dependent scaling factor. They showed that by setting 1 l / pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi H s R
1 s

ð6:7Þ

PHASE IMAGES OF PHASED ARRAY COILS

97

FIGURE 6.5 The phase images corresponding to each of the magnitude images shown in Figure 6.4.

the noise is distributed uniformly over the whole image. In this case, the resulting image pT R
1 s P ¼ pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi sH R
1 s

ð6:8Þ

is equivalent to an image obtained with a single surface coil. Setting l/

1 sH R
1 s

ð6:9Þ

leads to an image that corresponds to a uniform sensitivity image. The equation for the image is thus P¼

pT R
1 s sH R
1 s

ð6:10Þ

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PROCESSING CONCEPTS AND SWI FILTERED PHASE IMAGES

It should be noted that the SENSE formula reduces to this equation if the SENSE factor is 1. However, since l is real in both cases, the phase image is the same for both types of images. In general, however, the sensitivity profiles are not known. Moreover, the sensitivity profiles depend on the sample. Thus, simplifications are often made in practice. The most common one is to set the sensitivity s to the conjugate of the pixel value p [19]. This is justified by the argument that the MR signal is proportional to the local rf field. Equation (6.8) can be thus rewritten to pH R
1 p P ¼ pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi pH R
1 p Under the assumption that noise is uncorrelated and has the same variance in all channels this equation reduces to P / pH p ð6:11Þ This formula is known as sum of squares (SoS) and is the most common method for combining images of phased array coils. It is obvious that by combining images using this method, all information on the phase is lost. For phase images, an approach that is used by several manufacturers in situations in which magnitude images are reconstructed by SoS is to sum complex signal from all channels one and compute the phase from the combined image w¼ff

N X

! iwj

Mj e

ð6:12Þ

j¼1

where Mj and wj are the magnitude and phase of the pixel at (x, y, z) measured with coil j. In some cases, the phase images wj are corrected for a global phase offset, which is determined from a region of interest [15]. However, combining multichannel data this way corresponds to assuming constant sensitivities (1 in the simplest case) and neglecting the spatial dependency of the sensitivity’s phase. This becomes intuitively obvious if the vector notation is used. ! N X   iwj w¼ff Mj e ð6:13Þ ¼ ff pT s if si ¼ 1 j¼1

Thus, phase images computed in this way may contain artifacts that hamper phase unwrapping (Figure 6.6a). Another common approach is to compute combined images using an adaptive reconstruction [23]. This method tries to estimate the coil sensitivities using a statistical approach. It is, however, difficult to judge the robustness of this algorithm. The SENSE algorithm, on the other hand, uses sensitivity maps that are determined from separate (low resolution) reference scans. As mentioned before, for a SENSE factor of 1, the SENSE formula reduces to equation (6.6). The algorithm proposed by Pruessmann et al. [21] can thus be applied to recombine data acquired with other parallel imaging schemes (such as GRAPPA). Sensitivity maps are determined in the following way: first, a scan with the phased array and one with the body coil is performed. From those two scans raw sensitivity maps are computed. Smoothing with a weighted polynomial of second order eliminates noise. This smoothing filter is also used for extrapolating the sensitivity map in

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FIGURE 6.6 The combined phase image if the coil sensitivities are not taken into account (a) and if measured coil sensitivities are used (b).

low SNR regions. Finally, the sensitivity map is scaled as required for reconstructing the image. Figure 6.6b shows the phase image of the same data set as used to obtain Figure 6.6a, but this time combined using the SENSE algorithm. It should be noted that the smoothing operation requires that the variations of the coil sensitivities just have low spatial frequencies. In general, this is the case. However, if data are acquired using coil compression [24] schemes such as the mode matrix [25] concept, the higher order modes may have sensitivity maps that are not as smooth as required by the smoothing and extrapolation operation. In this case, it might be necessary to use different smoothing and extrapolation schemes. On the other hand, since most of the signal is available in the lower modes, the SNR loss caused by neglecting higher order modes should be acceptable. Unfortunately not all MR systems are equipped with a body coil. Thus, determining sensitivity maps as described before is not possible. In this case, the best method might be to combine phase images after they were corrected for variations of low spatial frequencies such as those caused by the coil sensitivity profiles. However, in this case, also variations caused by inhomogeneities of the static magnetic field are removed, which might be an undesired effect. Nevertheless, this approach has proven to work well practically. The necessary corrections can be achieved by either applying homodyne detection to each channel or unwrapping the phase image of each coil element. In the latter case, the phase variations with low spatial frequencies have to be subtracted subsequently. Also, it might be necessary to limit phase unwrapping to areas of high SNR, or at least to mask the phase images before combination. The combination can then be done either by computing 0

w ¼ff

N X j¼1

! e

iwcorrected j

ð6:14Þ

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PROCESSING CONCEPTS AND SWI FILTERED PHASE IMAGES

or by a weighted average of the phase images 0

w ¼ff

N X

aj  e

! iwcorrected j

ð6:15Þ

j¼1

qffiffiffiffiffiffiffiffiffiffiffiffi P 2ffi where aj ¼ Mj or in a least squares optimization sense aj ¼ Mj = j Mj . In conclusion, it can be stated that combining phase images of phased array coils is still an open area of research. REFERENCES 1. Ghiglia, DC, Pritt MD. Two-Dimensional Phase Unwrapping, Wiley, 1998. 2. Reichenbach JR, Venkatesan R, Yablonskiy DA, Thompson MR, Lai S, Haacke EM. Theory and application of static field inhomogeneity effects in gradient-echo imaging. J. Magn. Reson. Imaging 1997;7:266–279. 3. Chavez S, Xiang Q S, An L. Understanding phase maps in MRI: a new cutline phase unwrapping method. IEEE Trans. Med. Imaging 2002;21:966–977. 4. Yu Y, Wang Y, Haacke EM, Li D. Static field inhomogeneity correction using a 3D high pass filter. Proc. Int. Soc. Magn. Reson. Med. 1999;180. 5. Reichenbach JR, Barth M, Haacke EM, klaho¨fer M, Kaiser WA, Moser E. High-resolution MR venography at 3.0 Tesla. J. Comput. Assist. Tomogr. 2000;24:949–957. 6. Noll DC, Nishimura DG, Macovski A. Homodyne detection in magnetic resonance imaging. IEEE Trans. Med. Imaging 1991;19:154–163. 7. Deistung A, Rauscher A, Sedlacik J, Witoszynskyj S, Reichenbarh JR. GUIBOLD: a graphical user interface for image reconstruction and data analysis in susceptibility-weighted MR imaging. Radiographics 2008;28:639–651. 8. Rauscher A, Barth M, Reichenbarh JR, Stollberger R, Moser E. Automated unwrapping of MR phase images applied to BOLD MR-venography at 3 Tesla. J. Magn. Reson. Imaging 2003;18:175–180. 9. Xu W, Cumming I. A region-growing algorithm for InSAR phase unwrapping. IEEE Trans. Geosci. Remote Sens. 1999;37:124–134. 10. Witoszynskyj S, Rauscher A, Reichenbarh JR, Barth M. Automated phase unwrapping of MR images at different field strengths using multiple quality maps. Proc. Int. Soc. Magn. Reson. Med. 2005;2249. 11. Jenkinson M. Fast, automated, N-dimensional phase-unwrapping algorithm. Magn. Reson. Med. 2003;49:193–197. 12. Schwartzkopf W. Two-dimensional phase unwrapping using neural networks. In: Proceedings of the IEEE Southwest Symposium on Image Analysis, 2000, pp.274–277. 13. Volkov VV, Zhu Y. Deterministic phase unwrapping in the presence of noise. Opt. Lett. 28:2156– 2158. 14. Koopmans PJ, Manniesing R, Niessen WJ, Viergever MA, Barth M. MR venography of the human brain using susceptibility weighted imaging at very high field strength. Magn. Reson. Mater. Phys. 2008;21:149–158. 15. Hammond KE, Lupo JM, Xu D, Metcalf M, Kelly DA, Pelletier D, Chang SM, Mukherjee P, Vigneron DB, Nelson SJ. Development of a robust method for generating 7.0 T multichannel phase images of the brain with application to normal volunteers and patients with neurological diseases. Neuroimage 2008;39:1682–1692.

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16. Witoszynskyj S, Rauscher A, Reichenbarh JR, Barth M. Phase unwrapping of MR images using UN - a fast and robust region growing algorithm. Med Image Anal 2009;13;257–268. 17. Jezzard P, Balaban RS. Correction for geometric distortion in echo planar images from B0 field variations. Magn. Reson. Med. 1995;34:65–73. 18. Johnson G, Hutchison JMS. The limitations of NMR recalled-echo imaging techniques. J. Magn. Reson. 1985;63:14–30. 19. Roemer PB, Edelstein WA, Hayes CE, Souza SP, Mueller OM. The NMR phased array. Magn. Reson. Med. 1990;16:192–225. 20. Hutchinson M, Raff U. Fast MRI data acquisition using multiple detectors. Magn. Reson. Med. 1988;6:87–91. 21. Pruessmann KP, Weiger M, Scheidegger MB, Boesiger P. SENSE: sensitivity encoding for fast MRI. Magn. Reson. Med. 1999;42:952–962. 22. Griswold MA, Jakob PM, Heidemann RM, Nittka M, Jellus V, Wang J, Kiefer B, Haase A. Generalized autocalibrating partially parallel acquisitions (GRAPPA). Magn. Reson. Med. 2002;47:1202–1210. 23. Walsh DO, Gmitro AF, Marcellin MW. Adaptive reconstruction of phased array MR imagery. Magn. Reson. Med. 2000;43:682–690. 24. Buehrer M, Pruessmann KP, Boesiger P, Kozerke S. Array compression for MRI with large coil arrays. Magn. Reson. Med. 2007;57:1131–1139. 25. Reykowski A, Blasche M. Mode matrix—a generalized signal combiner for parallel imaging arrays. Proc. Int. Soc. Magn. Reson. Med. 2004;1487.

7 MR Angiography and Venography of the Brain Samuel Barnes, Zhaoyang Jin, Yiping P. Du, Andreas Deistung, and Ju¨rgen R. Reichenbach

INTRODUCTION Visualization of the intracranial venous vasculature can be clinically significant in the diagnosis and assessment of several neurovascular lesions and diseases, such as arteriovenous malformation, brain tumors, stroke and hemorrhage, cavernous and venous angioma, and venous sinus thrombosis [1]. Several vascular MRI techniques have been used for the visualization of veins using 2D or 3D time-of-flight (TOF) and 2D or 3D phase-contrast acquisitions with low velocity encoding gradients. These techniques are not able to provide an adequate depiction of small veins because of slow venous flow and contamination from arterial flow. Contrast-enhanced MR venography (MRV) can provide high-quality images of venous vasculature in the steady state or as part of a real-time process, monitoring first the arterial signal and then the venous signal with the use of very fast acquisition to ensure that the filling of contrast media in the venous vasculature can be adequately captured during the scan [2]. While these techniques can provide excellent results for larger veins, they are limited in their ability to image small veins as they depend either on flow (which is very low in small veins) or on a contrast agent that usually requires fast scanning (lower resolution) and risks arterial contamination. MR venography with susceptibility weighted imaging (SWI) utilizes deoxygenated hemoglobin in the veins as an intrinsic contrast medium. The magnetic susceptibility difference between deoxygenated hemoglobin and both oxygenated hemoglobin and parenchyma gives excellent venous contrast with SWI. Since this contrast is not dependent on flow or the arrival of a contrast agent, high-resolution scans can be performed to image

Susceptibility Weighted Imaging in MRI, By E. Mark Haacke and J€urgen R. Reichenbach Copyright
2011 by Wiley-Blackwell

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small veins and even venules. In this way, submillimeter veins not seen with other in vivo techniques can be reliably depicted without arterial contamination [3]. Using the SWI acquisition strategy and postprocessing technique, excellent venous contrast can be obtained [4, 5]. Deoxygenated hemoglobin introduces a slight shift of the Larmor frequency in venous blood and in the nearby surrounding tissue, depending on the orientation of the veins. This frequency shift can be effectively detected in the phase images using a relatively long echo time (TE). The resulting phase shift introduced by the venous blood can provide excellent contrast for the veins. This contrast in the phase image can be visualized directly or used to create susceptibility weighted images as described in detail in Chapters 4 and 6. SWI-BASED MR VENOGRAPHY (MRV) A radio frequency- and gradient-spoiled T2* -weighted gradient-recalled echo (GRE) pulse sequence, such as FLASH, SPGR, and TFE, is commonly used for SWI-based MRV acquisition because of its high sensitivity in detecting susceptibility induced phase shifts. Three-dimensional acquisition is commonly used because of its advantages of higher SNR and thinner slice thickness compared to a 2D acquisition. Full flow compensation along all three directions is desirable in an SWI acquisition so that there are no remnant phase effects from moving blood to confound the desired susceptibility phase information. These effects would be more prominent in larger veins and most arteries in which the flow velocity exceeds a few centimeters per second. Flow along an oblique direction can cause a spatial shift of the blood signal along the phase encoding direction, as well as signal void at the site of a given vessel, especially for a long TE [6, 7], resulting in dark streaks in the SW images. Finally, the pulsation of arterial flow can introduce ghosting along the phase encoding direction as for example near the middle cerebral arteries [8]. Artifacts caused by laminar blood flow can be reduced by full first-order flow compensation in all three directions (see the following section). To visualize the SWI venographic data, a minimum intensity projection (mIP) over the processed SW images is typically used. The effect of a mIP is to better show the connectivity of the veins, while the processed SWI, being a combination of the magnitude and phase images, shows a more complete venous structure than either magnitude or phase alone (Figure 7.1). MR venography with SWI can be performed with good results at field strengths 1.5 to 9.4 T with generally higher quality at the higher field strengths [3, 9, 10]. Contrast in the phase image is generated according to the following formula: Dw
g  Dx  B0  TE

ð7:1Þ

where g is the gyromagnetic ratio (for protons) and is a constant. The phase varies only with the difference in tissue susceptibility Dx and the product B0TE. This product allows much shorter echo times at higher field strengths to generate the same phase contrast as long echo times at lower fields. The improved signal-to-noise ratio (SNR) at higher magnetic fields allows for high spatial resolution, which additionally reduces signal loss caused by intravoxel spin dephasing from background field inhomogeneities [11]. In fact, 7 T venographic data not only provide high spatial resolution (up to 0.21  0.21  0.6 mm3) but also show new structures in the form of venules (which are about 50 mm in

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105

FIGURE 7.1 Minimum intensity projections over 28 mm of magnitude (a), phase (b), and processed SW (c) images. Data were acquired at 4 T with TR/TE/FA/resolution of 30 ms/20 ms/10  /0.25  0.25  1 mm3. Both magnitude and phase show good venous contrast that is complementary allowing the SW images to combine the two for a more complete vascular picture. Notice the small artifact visible in the frontal lobe of the phase and SW image caused by incomplete phase unwrapping (black arrow).

diameter, Figure 7.2) and the arcuate fibers [12]. A more detailed description of magnetic field strengths’ effects on susceptibility weighted imaging can be found in Chapter 20. SIMULTANEOUS ARTERIAL AND VENOUS IMAGING BY USING DOUBLE-ECHO ACQUISITION Three-dimensional MR angiography (MRA) based on time-of-flight (TOF) contrast provides excellent details of arterial vasculature and has been used routinely in clinical brain exams for many years [13, 14]. Acquisition of both MRA and MRV can provide a more comprehensive depiction of cerebrovascular abnormalities for improved assessment of

FIGURE 7.2 Single phase images (a and b) acquired at 7 T show the clear depiction of deep white matter veins and small branching cortical veins. The mIP over 8 mm in (c) reveals the overall vessel continuity. Images were acquired with TE/TR/FA/resolution ¼ 16 ms/30 ms/15  /0.21  0.21  1.0 mm3.

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brain diseases. For example, MRA and MRV can complement one another in tumor characterization, with the former useful for visualizing feeding vessels and the latter for draining vessels. Both 3D TOF-based MRA and SWI-based MRV scans, however, are relatively long, typically ranging from several minutes to 15 min. Recently, a dual-echo technique was developed to incorporate the data acquisition for SWI-based MRV into the 3D TOF-based MRA scan: the first echo of the scan is used for MRA and the second echo is used for MRV. This dual-echo approach is referred to as an MRAV sequence [15] in this chapter. By applying the SWI postprocessing technique to the second echo, the resulting venogram has normal SWI contrast. To implement MRAV sequence [15], a second echo was added to a conventional 3D TOF pulse sequence (Figure 7.3), with flow compensation applied along the frequency encoding direction to reduce the flow artifact. By using a flyback gradient trapezoid, the second readout gradient had the same polarity as the first readout gradient. The flyback gradient was placed in the middle, between two readouts to restore the flow compensation along the readout direction in the second echo, which can be either a partial or a full echo. For

FIGURE 7.3 This figure shows the diagram of the dual-echo MRAV pulse sequence. MRA data are acquired at the first echo. MRV data are acquired at the second longer echo, as indicated by the dashed rectangle. Flow compensation was applied to the slice-selection (Gss) and readout (Gro) directions. A flyback gradient was applied to the readout direction to refocus the second echo. The flyback gradient was located in the middle between both echoes to restore flow compensation in the second echo. The second echo was acquired with partial echo to either reduce TR or increase the second echo time (TE2). Phase rewinders were applied to the slice-selection and phase encoding (PE) directions, followed by a gradient spoiler that destroys residual transverse magnetization.

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FIGURE 7.4 This figure shows the MIP of MRA of the concatenated slabs (a), the mIP of MRV of 16 slices in the inferior slab with a thickness of 25.6 mm (b), and the mIP of MRV of 20 slices in the superior slab with a thickness of 32.0 mm (c). These healthy volunteer data were acquired with the dual-echo MRAV pulse sequence (Figure 7.3) on a 3T GE scanner (Milwaukee, WI) with a standard birdcage head coil using a rectangular field of view (FOV) of 20  16 cm2, a slice thickness of 1.6 mm, and a flip angle of 20  . TE1/TE2/TR ¼ 4.1 ms/24.5 ms/32 ms. The two slabs (32 slices per slab) were acquired with the MOTSA technique with an overlap of four slices, a matrix size of 384  312, and a readout bandwidth of 15.6 kHz (81 Hz/pixel). The scan time was 10 min and 46 s. A 66.7% partial echo was used in the acquisition of the first and second echoes to reduce the repetition time (TR).

example, Figure 7.4 shows the MRA maximum intensity projection (MIP) of the concatenated slabs (a), the MRV mIP in the inferior slab with a thickness of 25.6 mm (b), and the MRV mIP in the superior slab with a thickness of 32.0 mm (c). To concatenate the multiple slabs and to overcome wrap-around artifacts at the slab boundaries along the slice direction induced by imperfect slab selection profiles, we propose to merge the TOF and SWI echo data in image space in two different ways. For the TOFecho (first echo), only the first and last two slices from an overlapping slab are removed. The remaining overlapping magnitude images are then combined by maximum intensity projection. The slabs of the second echo are concatenated by removing a sufficient number of slices in the overlap region. Since the second echo of the MRAV pulse sequence is flow compensated in the readout direction only, signal drop out and spin displacement due to oblique flow (especially in arteries) may occur. Therefore, the need for full 3D flow compensation of the second echo was studied based on a modified MRAV pulse sequence, which is herein referred to as TOF-SWI sequence [16] (Figure 7.5). In contrast to the MRAV sequence, the dual-echo TOF-SWI sequence was additionally equipped with flow compensation pulses in phase and slice encoding directions in front of the second echo to preserve 3D velocity compensation of the SWI echo. To implement complete flow compensation of the second echo in the TOFSWI sequence, an additional bipolar rephasing gradient pulse pair was added in readout direction after the first echo. Furthermore, gradient pulse tables were added in slice select and phase encoding directions to both null zero-order (M0) and first-order gradient moments (M1) at the end of these gradient trains on all axes. Adding mirrored bipolar gradient pulse tables in the two phase encoding directions just before the second echo results in M1 ¼ 0, but finite M0 at TE2, with the effective phase encoding being the same as for the encoding of the first echo. Dual-echo data acquisition with no flow compensation, flow compensation in

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FIGURE 7.5 Scheme of the TOF-SWI pulse sequence showing the rf-pulse (rf), readout gradients (read), phase encoding gradients (PE), and slice-selection gradients (SS). Compensation of the zeroorder and first-order moments of the gradients after the first echo is a prerequisite for variable and independent adjustment of the parameters for the second flow compensated echo.

readout direction only, and full 3D flow compensation of the second echo revealed that 3D flow compensation minimizes signal loss in arteries, thus reducing potential mistaking of arteries as veins in the SWI echo (Figure 7.6). ATOF-SWI example tailored for high spatial resolution and whole brain coverage with 3D flow-compensation of the second echo is presented in transverse and sagittal views in Figure 7.7. The primary advantage of the dual-echo acquisition of MRAV and TOF-SWI is that it provides additional MRV images without significantly increasing the typical scan time for an MRA acquisition and this acquisition time is naturally much less than the total acquisition time of an individual MRA and MRV scans put together. However, there is a trade-off in MRAV and TOF-SWI acquisition between background signal suppression in TOF images and preservation of sufficiently high SNR in SWI. Acquisition with multiple overlapping slabs (MOTSA) improves arterial delineation in TOF-MRA due to reduced flow saturation. However, compared to a single slab [14] acquisition, venous contamination is also increased the TOF images. Another drawback of MOTSA is the reduction of SNR pinffiffiffiffiffiffiffiffiffi ffi 1 by a factor of nslabs . However, using simultaneous acquisition with MRAV or TOFSWI also eliminates possible misregistration between the arterial and venous vasculatures that otherwise could be induced by interscan patient motion, especially considering the relatively long acquisition time of both scans. The elimination of misregistration artifacts makes the simultaneous display of MRA or MRV data sets more precise, which could be of great merit for clinicians to identify the exact spatial relationship between the arterial and venous vasculatures at or near lesions.

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FIGURE 7.6 Influence of flow compensation on vessel depiction for the second echo of TOF-SWI (TE1/TE2/TR/FA/BW1/BW2/TA ¼ 3.42 ms/40 ms/57 ms/25  /100 Hz/pixel/60 Hz/pixel/11:48 min:s, voxel size ¼ 0.54  0.54  1.5 mm3, matrix of 448  368  60, 75% partial Fourier acquisition in both phase encoding directions) at 1.5 T. For reference, the TOF (first) echo is shown in part (a) as a maximum intensity projection over 4.5 mm. Average projections of the same volume were computed from data of the second echo acquired without flow compensation (b), with flow compensation in readout direction only (c) and 3D flow compensation (d), respectively. In part (d), arteries were mapped as hyperintense structures. Signal void in the middle cerebral arteries resulted in hypointense vessel representation in part (b), whereas in part (c) the arterial signal was also spatially displaced and also blurred.

MRA AND MRV WITH SINGLE-ECHO ACQUISITION While the double-echo approaches can produce excellent angiographic and venographic images, the possibility remains open of achieving similar results with a single echo. SWI provides a natural separation of the vasculature, with the arteries being bright from inflow enhancement due to the short TR and the veins dark from the long TE. By using a higher bandwidth and high isotropic resolution to reduce flow dephasing, it is possible to obtain a decent angiogram without significantly degrading the SWI venogram. Generally, by using a long TE and short TR (typically 20 and 30 ms at 3 T, respectively), the veins can be suppressed and the arteries brightened, allowing a very good separation of arteries and veins in a single echo scan. The arteries can be visualized using a standard maximum intensity projection of magnitude information, and the veins visualized with SWI processing and a minimum intensity projection. The choice of flip angle and echo time is very important for determining image quality of both the MRA and MRV. Higher flip angles improve the angiogram due to increased background suppression and better TOF inflow effect, but in turn degrade the venogram by oversuppressing the CSF. Choosing a medium flip angle (15–20 ) and a slightly longer TR appears to be optimal. The longer TR allows more inflow enhancement for the angiography and keeps the CSF from being oversuppressed. Shorter echo times improve the angiography by reducing uncompensated higher order flow losses, but this decreases venous contrast. At 3 T, decreasing the echo time

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FIGURE 7.7 Dual-echo TOF-SWI acquisition of a healthy volunteer (TE1/TE2/TR/FA/BW1/BW2/TA ¼ 3.42 ms/25 ms/42 ms/20 271 Hz/pixel/78 Hz/pixel/24:23 min:s, voxel size ¼ 0.43  0.43 1.2 mm3, matrix ¼ 512  352  44, 3 slabs with distance factor of 20.45%, 75% partial Fourier in phase and slice encoding direction). The maximum intensity projection of the whole volume for the first echo is presented in transverse (a) and sagittal orientation (c). The transverse and sagittal venogram (minimum intensity projection of the susceptibility weighted images over 13.2 mm) is presented in parts (b) and (d), respectively. Note that in contrast to part (b) the sagittal venogram (d) was computed with the positive phase mask to avoid artifacts due to extravascular field inhomogeneities of perpendicular vessels.

below 20 ms substantially degrades venous contrast and is not recommended; an echo time of 20 ms is preferred. For this reason, this technique shows promise at higher fields (>3 T) as shorter echo times can then be used without degrading venous contrast. To reduce uncompensated higher order flow losses, we propose increasing the readout bandwidth and acquiring the data with high isotropic resolution. A high readout bandwidth will reduce the time between spatial encoding and echo sampling. Figure 7.8 shows an example with a readout bandwidth of 50 Hz/pixel versus 160 Hz/pixel. At the lower bandwidth, there is signal loss in the rapidly flowing middle cerebral artery (MCA) and in a smaller artery when it goes through a tight loop, causing

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FIGURE 7.8 50 Hz/pixel (a) shows almost complete loss of the MCA and losses in the middle of smaller vessels while 160 Hz/pixel (b) shows minimal flow losses. Images acquired at 3 T with TE/TR/FA/ resolution ¼ 20 ms/30 ms/15  /0.5  0.5  0.5 mm3.

acceleration effects. These losses are largely eliminated by using the higher bandwidth of 160 Hz/pixel. Often the slower flowing blood at the edge of the vessel does not get dephased and appears as bright bands surrounding a dark center. High isotropic resolution reduces dephasing across a voxel and thus can reduce flow losses. This does reduce the quality of the SWI phase image as an isotropic aspect ratio of 1:1 in-plane to through-plane resolution is not ideal for SWI [9, 17]. The isotropic aspect ratio causes the phase for veins of certain sizes and orientations to have opposite signs (Figure 7.9 or Figure 4.18). This has the potential to confuse clinical interpretation and could reduce contrast in the SWI processed images. This lost contrast can be completely recovered, however, by postprocessing the images and applying a downsampling filter to generate a more ideal aspect ratio of 1:4. A simple k-space crop can be used, which would be equivalent to a lower resolution acquisition with 1:4 aspect ratio. Alternatively, a sliding window complex average can be performed, which takes advantage of the fact that the higher resolution was collected. The sliding window filter takes the average of the complex signal (magnitude and phase) of four slices, advances a single slice, calculates the next average, and repeats until all slices are processed. In this way, the through-plane resolution is reduced but the same number of slices as in the original series is maintained (actually the number of slices will be reduced by a small amount, the collapsing factor minus one or three slices in this case). By reconstructing the thick slabs in an overlapping pattern, optimal partial voluming of small structures is guaranteed, increasing their visibility (Figure 7.10). This reconstruction offers a distinct advantage over the original k-space data in that it uses the high-pass filtered phase in the complex downsampling process, and not the original phase. This reduces the dephasing in areas of rapid phase change (air–tissue interfaces), thereby improving the quality of the phase and magnitude images.

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FIGURE 7.9 Isotropic (0.5 mm) phase image (a) shows veins switching from bright to dark depending on orientation. Downsampled image (b) has higher SNR and shows more homogeneous veins producing a better venogram. The in-plane to through-plane aspect ratio of the original image (a) is 1:1 and of the filtered image (b) 1:4 as in the usual SWI acquisitions. Images acquired at 3 T with TE/TR/FA/BW ¼ 20 ms/ 30 ms/15  /160 Hz/pixel.

FIGURE 7.10 Downsampled phase images comparing k-space crop (a) and complex averaging (b). Note the small vein (arrow) is better depicted in the complex averaging due to increased partial volume effects. The veins that the k-space crop shows slightly better (arrow heads) are equally well depicted in the complex filtering in adjacent slices. Images acquired at 3 T with TE/TR/FA/BW ¼ 20 ms/30 ms/15 /160 Hz/ pixel.

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FIGURE 7.11 Maximum intensity projection (a) over isotropic data showing arteries and minimum intensity projection (b) over SWI processed downsampled image. Images acquired at 3 T without a contrast agent with TE/TR/FA/BW/resolution ¼ 20 ms/30 ms/15  /160 Hz/pixel/0.5  0.5 0.5 mm3.

The SWI contrast and venography, as shown in Figure 7.11, are of good quality with the veins being well depicted. Likewise, nearly all of the arteries are well depicted; however, there is some signal loss in parts of the fast-flowing MCA due to flow dephasing from the long TE. The more distal arteries are well depicted with little to no signal loss. The bright artery/dark vein contrast can be achieved even in the presence of a contrast agent, where the shortened T1 boosts the signal in the arteries and veins but the increased signal from the veins in SWI leads to a larger cancellation effect. This T1/T2* coupling makes it possible to enhance the T2* -like cancellation effect (a more detailed overview of effects induced by contrast agent in SWI can be found in Chapter 26). The use of a contrast agent also helps to partially compensate any flow-related losses thanks to the signal increase in the arteries. In general, Gadolinium based contrast agents will improve results by increasing the contrast in both the arteries and veins, but it is by no means required to get a good MRAV. POSTPROCESSING CONSIDERATIONS Susceptibility weighted images (venograms) are a combination of magnitude and phase information. Thus, venograms can be obscured by incomplete correction of phase wraps in regions with large field inhomogeneities and steep phase topography, for example, close to the paranasal sinuses and the petrous portion of the temporal bone. Another problem in MRV is that venograms are typically visualized via minimum intensity projection over a small stack of adjacent slices in which signal loss in magnitude images can damage the visualization of venous vessels. To overcome this degradation in MRV, several techniques for compensating these artifacts and improving vessel conspicuity are introduced.

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REMOVAL OF INCOMPLETELY CORRECTED PHASE WRAPS (REDUCTION OF OFF-RESONANCE ARTIFACT) Veins in regions with severe field inhomogeneity are obscured in SWI because of the large residual background phase in the phase mask. However, these veins are expected to be conspicuous in the magnitude images. The local field gradient (LFG), i.e. the first-order spatial variation of the B0 magnetic field, can be used to assess the severity of field inhomogeneity. The 3D LFG mapping can be performed by applying the algorithm described below to the same SWI data acquired at a single TE [18]. The spatial variation of phase dws,u caused by the LFG along a direction u in the complex MR signal A(r) can be calculated by * exp½idws;u ðrÞ ¼ exp½iwðr þ DuÞiwðrDuÞ ¼ UDu UDu

ð7:2Þ

where r is the spatial location, w is the phase, and ‘‘exp’’ denotes the exponential function, * UDu ¼ Aðr þ DuÞ=Aðr þ DuÞ; UDu ¼ A* ðrDuÞ=AðrDuÞ; AðrÞ ¼ jAðrÞj

ð7:3Þ

and Du is the voxel size along the direction u (u ¼ x, y, or z). The LFG along u at location r can be calculated by * LFGu ðrÞ ¼ dws;u ðrÞ=ðgTE  2jDujÞ ¼ argðUDu UDu Þ=ð2gTEjDujÞ

ð7:4Þ

where g is the gyromagnetic ratio and arg indicates the operation to take the polar angle of a complex number. A median filter is applied to LFGx(r), LFGy(r), and LFGz(r) to reduce the effect of rapid phase changes that may occur in vessels and other fine structures. The amplitude of the LFG is given by LFGðrÞ ¼

qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi LFG2x ðrÞ þ LFG2y ðrÞ þ LFG2z ðrÞ

ð7:5Þ

The LFG-suppressed phase images are generated by multiplying the HP filtered phase images with a Fermi weighting function, defined by FermiðLFGÞ ¼

1 1 þ eðLFGRÞ=W

ð7:6Þ

where R is the size and W is the transition width of the weighting function. The background phase has a large (positive or negative) value in the HP filtered phase images in the regions with severe field inhomogeneity. The parameter R is selected based on the LFG values in the regions of interest so that FermiðLFGÞ 1 in regions with a large LFG value and FermiðLFGÞ
1 in regions with relatively homogeneous field. A selection of W ¼ 0.1R is usually adequate. After multiplying with FermiðLFGÞ, the background phase in the phase images is nearly unchanged in regions with relatively homogeneous field and is reduced to

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FIGURE 7.12 This figure shows the map of amplitude LFG in units of mT/m (a) at a slice covering the orbitofrontal region (indicated by a thick arrow) after median filtering with a 5  5  5 voxels kernel size. The lateral temporal region (indicated by a thin arrow) and the frontal pole (indicated by a double-lined arrow) also have an increased LFG. The map of Fermi weighting function at the same slice location is shown in part (b), with R ¼ 0.15 mT/m and W ¼ 0.02 mT/m. The mIP display of the original phase masks and LFG-suppressed phase masks are shown in parts (c) and (d), respectively. Two-dimensional homodyne filtering (with Hamming window widths of 192  144) failed in correcting phase wraps in the orbitofrontal region as highlighted by arrows in part (c). With LFG suppression, these remaining phase wraps are suppressed and the septal veins located at the orbitofrontal region become visible in the LFGsuppressed phase mask, as indicated by arrows in part (d). Imaging parameters: matrix ¼ 512  384  64, FOV ¼ 26 cm  19.5 cm, 1 mm thickness, TE ¼ 20 ms, TR ¼ 34 ms, B0 ¼ 3 T.

nearly zero in regions with a large LFG. The resulting phase mask, referred to as the LFGsuppressed phase mask, has a value near unity in regions with severe field inhomogeneity. The venous contrast in the magnitude images is preserved in the resulting SWI, and is referred to as LFG-suppressed SWI or LFG-suppressed MRV, after multiplications of the magnitude images with the LFG-suppressed phase mask. The application of the LFG-suppression technique to homodyne filtered phase data is illustrated in Figure 7.12. LFG suppression clearly diminishes the off-resonance artifact at the orbitofrontal region (Figure 7.12d) compared to Figure 7.12c. Other methods of dealing with this problem are to remove the background phase variations from air/tissue interfaces completely (see Chapter 24).

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VOLUME SEGMENTATION OF SWI DATA (SIGNAL LOSS IN mIP DISPLAY) In conventional mIP implementation, the minimum intensity in voxels along a projection path is selected for the display. Voxels representing air and bone can be in the path of projection in the peripheral regions due to the natural shape of the brain, even in throughplane projection. The low signal intensity in air or bone leads to signal loss from veins and brain tissue in the processed mIP image in these regions. The signal loss due to air and bone can be effectively recovered by applying volume segmentation prior to projection and masking out these regions [18]. Volume segmentation can be performed on SWI data using most popular techniques, such as the brain extraction tool [19], or with techniques designed to take advantage of the additional information in the phase images [20, 21]. The latter techniques, not being dependent on geometry, can also be applied outside of the brain. The volume segmentation generates a 3D binary mask with a value ‘‘1’’ in brain tissue and ‘‘0’’ elsewhere (air, bone, intracranial non-brain tissue). In the subsequent volume-segmented mIP, the projection was only applied to voxels in brain tissue with a value of ‘‘1’’, excluding the voxels with a value of ‘‘0’’. The volume-segmented mIP approach can be applied to the phase mask, magnitude image, or SWI. Any residual voxels missed by the volume segmentation in air, bone, and low-intensity nonvascular voxels after volume segmentation would result in a low-intensity spot or patch in the projection. An erosion algorithm can be used to remove a few layers of voxels in the 3D binary mask prior to volume-segmented mIP to exclude any residual voxels. The conventional mIP of LFG-suppressed MRV is shown in Figure 7.13a. The effect of volume segmentation on the through-plane mIP display of the LFG-suppressed MRV is shown in Figure 7.13b. Several small veins not visible with conventional mIP display become conspicuous in the volume-segmented mIP display, as indicated by the arrows in Figure 7.13b.

FIGURE 7.13 The mIPs of the LFG-suppressed SWI (a) processed with a Hamming filter size of 192  144. With LFG suppression, the veins in the orbitofrontal region are well depicted in part (a). In the volume-segmented mIP of LFG-suppressed SWI, brain tissue and veins in peripheral regions of the brain become more conspicuous, as indicated by the arrows in part (b). Imaging parameters: matrix ¼ 512  384  64, FOV ¼ 26 cm  19.5 cm, 1 mm thickness, TE ¼ 20 ms, TR ¼ 34 ms, B0 ¼ 3 T.

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IMAGE MASKING FOR IMPROVING VESSEL CONTRAST As already pointed out in the previous section, the mIP display of SWI is affected by voxels representing air or bone along the projection path. Apart from a computationally expensive volume segmentation, the representation of veins in an mIP display can also be improved by using an image masking method: fIM ðx; y; zÞ ¼ f ðx; y; zÞ½f ðx; y; zÞ

ð7:7Þ

A mask is produced by applying an arbitrary filter operator, indicated by [ ], to the original volume f(x, y, z) to obtain the image masked volume fIM(x, y, z). If the 3D median filter operator is applied to SWI data with appropriate kernel sizes, venous vessels are suppressed and signal variations of background tissue can be preserved in the mask volume (Figure 7.14b). After subtracting the median filtered SWI volume from the original SWI data, vascular structures are enhanced [22, 23]. The brain volume and veins close to the skull can be recovered in an mIP display. Additionally, local signal variations in SWI volumes resulting from MR imaging (e.g., signal variations in multicoil acquisitions) can be compensated (Figure 7.14). Since the median filter is sensitive to vessel widths that are

FIGURE 7.14 Original cross-sectional SW image (a) and median filtered mask image (b). The subtraction of the mask image from the original SW image (c) preserves small vessel details. Minimum intensity projection of original SW images (projection length ¼ 36 mm) (d) shows a shrinkage of brain volume due to the shape of the head. Furthermore, veins are depicted outside of the brain (see arrows). Applying minimum intensity projection of the corresponding region after 3D median filter enhancement (e), signal loss due to the skull is recovered. Additionally, the visualization of veins is enhanced by reducing signal variations of background tissue.

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less than half of the given kernel width, the optimum kernel width is given by the maximum vessel width, which should be enhanced by the image masking procedure. Note that image masking via 3D median filtering is only useful if the structures of interest are venous vessels. Smallest susceptibility changes resulting from cavernomas, iron or calcium deposits may be suppressed. VESSEL ENHANCEMENT Vessel structures in angiographic data sets can be modeled as small tubes. Line enhancement algorithms can also be tailored to improve vessel visibility [24, 25]. For a closer look to applied vessel enhancement filtering on time of flight and susceptibility weighted images, the reader is referred to Chapter 32. CONCLUSIONS SWI-based MRV can provide excellent contrast of the venous vasculature in the brain without using exogenous contrast media. Using a dual-echo acquisition approach, the acquisition of MRV images can be incorporated in the usual TOF-based MRA sequence without increasing the typical scan time for MRA. Image artifacts in SWI-based MRV can be substantially reduced using appropriate postprocessing algorithms. Single-echo methods for simultaneous acquisition of arteries and veins may also play a role, especially at higher field strengths. REFERENCES 1. Sehgal V, Delproposto Z, Haacke EM, Tong KA, Wycliffe N, Kido DK, Xu Y, Neelavalli J, Haddar D, Reichenbach JR. Clinical applications of neuroimaging with susceptibility-weighted imaging. J. Magn. Reson. Imaging 2005;22(4):439–450. 2. Lovblad KO, Schneider J, Bassetti C, El-Koussy M, Guzman R, Heid O, Remonda L, Schroth G. Fast contrast-enhanced MR whole-brain venography. Neuroradiology 2002;44(8):681–688. 3. Reichenbach JR, Barth M, Haacke EM, Klarhofer M, Kaiser WA, Moser E. High-resolution MR venography at 3.0 Tesla. J. Comput. Assist. Tomogr. 2000;24(6):949–957. 4. Reichenbach JR, Venkatesan R, Schillinger DJ, Kido DK, Haacke EM. Small vessels in the human brain: MR venography with deoxyhemoglobin as an intrinsic contrast agent. Radiology 1997;204 (1):272–277. 5. Haacke EM, Xu Y, Cheng YC, Reichenbach JR. Susceptibility weighted imaging (SWI). Magn. Reson. Med. 2004; 52(3):612–618. 6. Cao G, Parker DL, Sherrill DS, Du YP. Abbreviated moment-compensated phase encoding. Magn. Reson. Med. 1995;34(2):179–185. 7. Nishimura DG, Jackson JI, Pauly JM. On the nature and reduction of the displacement artifact in flow images. Magn. Reson. Med. 1991;22(2):481–492. 8. Parker DL, Goodrich KC, Roberts JA, Chapman BE, Jeong EK, Kim SE, Tsuruda JS, Katzman GL. The need for phase-encoding flow compensation in high-resolution intracranial magnetic resonance angiography. J. Magn. Reson. Imaging 2003;18(1):121–127. 9. Deistung A, Rauscher A, Sedlacik J, Stadler J, Witoszynskyj S, Reichenbach JR. Susceptibility weighted imaging at ultra high magnetic field strengths: theoretical considerations and experimental results. Magn. Reson. Med. 2008;60(5):1155–1168.

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10. Budde JS, Pohmann R, Shajan G, Ugurbil K. Susceptibility weighted imaging of the human brain at 9.4 T. Proc. Int. Soc. Magn. Reson. Med. 2009:43. 11. Reinchenbach JR, Venkatesan R, Yablonskiy DA, Thompson MR, Lai S, Haacke EM. Theory and application of static fuild inhomogeneity effects in graduit-echo imaging. J Magn Reson Imaging 1997; 7; 266–279. 12. Haacke EM, Mittal S, Wu Z, Neelavalli J, Cheng YC. Susceptibility-weighted imaging: technical aspects and clinical applications, part 1. AJNR Am. J. Neuroradiol. 2009;30(1):19–30. 13. Masaryk TJ, Modic MT, Ross JS, Ruggieri PM, Laub GA, Lenz GW, Haacke EM, Selman WR, Wiznitzer M, Harik SI. Intracranial circulation: preliminary clinical results with three-dimensional (volume) MR angiography. Radiology 1989;171(3):793–799. 14. Parker DL, Yuan C, Blatter DD. MR angiography by multiple thin slab 3D acquisition. Magn. Reson. Med. 1991;17(2):434–451. 15. Du YP, Jin Z. Simultaneous acquisition of MR angiography and venography (MRAV). Magn. Reson. Med. 2008;59(5):954–958. 16. Deistung A, Dittrich E, Sedlacik J, Rauscher A, Reichenbach JR. ToF-SWI: simultaneous time of flight and fully flow compensated susceptibility weighted imaging. J. Magn. Reson. Imaging 2009;29(6):1478–1484. 17. Xu Y, Haacke EM. The role of voxel aspect ratio in determining apparent vascular phase behavior in susceptibility weighted imaging. Magn. Reson. Imaging 2006;24(2):155–160. 18. Jin Z, Xia L, Du YP. Reduction of artifacts in susceptibility-weighted MR venography of the brain. J. Magn. Reson. Imaging 2008;28(2):327–333. 19. Smith SM. Fast robust automated brain extraction. Hum. Brain Mapp. 2002;17(3):143–155. 20. Du YP, Jin Z. Robust tissue–air volume segmentation of MRI based on the statistics of phase and magnitude: its applications in the display of susceptibility weighted imaging of the brain. J. Magn. Reson. Imaging 2009;30(4):722–731. 21. Pandian DS, Ciulla C, Haacke EM, Jiang J, Ayaz M. Complex threshold method for identifying pixels that contain predominantly noise in magnetic resonance images. J. Magn. Reson. Imaging 2008;28(3):727–735. 22. Alexander AL, Chapman BE, Tsuruda JS, Parker DL. A median filter for 3D FAST spin echo black blood images of cerebral vessels. Magn. Reson. Med. 2000;43(2):310–313. 23. Kholmovski E, Parker D. High resolution magnetic resonance venography at 3 Tesla: optimized acquisition, reconstruction, and post-processing. In: Proceedings of the 14th Meeting of the International Society for Magnetic Resonance in Medicine, 2006, p. 810. 24. Du YP, Jin Z. SWI-based intracranial MR venography using image-domain high-pass filtering with second-order phase differences. Proc. Int. Soc. Magn. Reson. Med. 2009:90. 25. Jin Z, Xia L, Du YP. Enhancement of venous vasculature in the brain with multi-scale filtering. Proc. Int. Soc. Magn. Reson. Med. 2009:2869.

8 Brain Anatomy with Phase Jeff Duyn and Oliver Speck

INTRODUCTION As we have seen in previous chapters, the MRI signal represents a vector quantity and has both a magnitude and phase component. Although the potential of using phase images for the study of brain anatomy [1, 2] and brain iron content [3–7] has been previously suggested, most applications of gradient echo (GRE) or T2* -weighted MRI have relied on analysis of magnitude data only. Recently, renewed interest in phase contrast has arisen with the improvements in T2* -weighted contrast achieved with high-field MRI [8–10]. With this have come questions regarding the optimal reconstruction techniques to extract image phase and regarding the origin of phase contrast observed in human brain [9]. In this chapter, we will discuss some of these issues and present illustrative examples of phase contrast observed in normal human brain.

MEASUREMENT OF HIGH-RESOLUTION PHASE IMAGES Pulse Sequence and Acquisition Parameters Gradient echo imaging has been mainly applied for fast imaging applications as it allows for short repetition times (TRs). These can be generally realized without the losses that would occur with spin echo (SE) techniques due to saturation of the magnetization and are achieved by lowering the flip angle. The highest signal to noise ratio (SNR) for a given repetition time and T1 in a spoiled GE sequence can be achieved at a flip angle u equal to the Ernst angle uE ¼ arccos(eTR=T1 ) (see Chapter 3). Under this condition, and assuming the full T2* relaxation curve is sampled, SNR of the magnitude GRE signal is independent of TR. This may not be the case, however, for the contrast to noise ratio (CNR). While CNR of the

Susceptibility Weighted Imaging in MRI, By E. Mark Haacke and J€urgen R. Reichenbach Copyright
2011 by Wiley-Blackwell

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FIGURE 8.1 2D (left) and 3D phase data with strongly anisotropic voxel size in the 2D acquisition allowing high in-plane resolution with good contrast and quality at the price of loss of resolution in the slice direction. The 3D acquisitions allow a display of the data in all orientations with identical quality. However, the linear resolution is limited. At very high resolution (right), the signal to noise is compromising the image quality. The upper row is sagittal reformat of the original transversely acquired slices. The middle row shows example transverse slices and the bottom row shows a coronal reformat of the original transverse slices.

phase would be optimal under this condition, this is generally not the case for the magnitude. Since T2* -weighted magnitude images and phase images are reconstructed from the same GRE acquisition, a compromise has to be made. This often means a choice of flip angle somewhat below the Ernst angle. The choice of echo time (TE) is governed by the goal to obtain the highest CNR. For magnitude images, the highest contrast between two tissue types a and b with different T2* is * * reached at T2a < TE < T2b . Similarly, the highest phase CNR can be measured at TE ¼ T2* . For very high-resolution depiction of anatomy, most laboratories use 2D multislice acquisitions with significantly thicker slices than in-plane resolution. For large volume coverage, isotropically resolved 3D acquisitions can offer a signal to noise advantage at the cost of lower in-plane resolution (Figure 8.1). Field Strength and Echo Time Dependence With the introduction of ultrahigh-field human MR systems of 7 Tesla and above, anatomical phase imaging has regained significant interest. In addition to the gain in SNR and susceptibility related T2* contrast at higher magnetic field strength (frequency shifts also increase linearly with field strength). Correspondingly, high-field phase imaging benefits twice, resulting in dramatically improved CNR (Figure 8.2). A quantitative comparison of phase effects at field strengths between 1.5 and 7 T reveals that the phase differences, for example, between gray and white matter are solely a frequency shift between the tissue types. The phase difference increases linearly with echo time and linearly with magnetic field strength (Figures 8.3 and 8.4).

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FIGURE 8.2 T2* -weighted images and phase images acquired at 3T and 7 T with a matrix size of

1024  896. Both data sets have been acquired with 8-channel head coils. TR/TE was 750/28 ms and 750/18 ms for 3T and 7 T, respectively. The significant increase in contrast to noise at 7 T is obvious.

FIGURE 8.3 The echo time dependence of the phase difference between gray and white matter at 7 T shows a linear relation corresponding to a frequency shift between the tissue types.

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FIGURE 8.4 Despite the reduced sensitivity at lower magnetic field strength, the normalized phase and thus frequency differences are very similar at 1.5, 3, and 7 T. For this comparison, the resolution has been reduced in order to allow phase detection with the lower sensitivity available at 1.5 T. Left handed system for phase is used in this image where paramagnetic substances appear with a bright phase. Reprinted from Ref. 16 with permission from Elsevier Science. Reprinted from Ref. 16 with permission from Elsevier Science.

Extracting Phase Information A number of issues have to be considered in the creation of anatomical phase images. The calculation of source phase images from the complex MR data is straightforward and only requires keeping the phase information, which is otherwise discarded in most MR reconstructions. Modern MR systems are equipped with multichannel receive coils and therefore the image information from the different channels has to be combined. For magnitude imaging, a weighted sum of the single element signals, such as the root-sum-ofsquares [11], is efficient and easy. However, corresponding combination of phase data fails especially for measurements at very high-field strength. Partly due to the high frequency and therefore short wavelength in tissue, different coil elements can receive different signal phase from the same source localization (see Figure 8.5). If this phase information or the corresponding complex-valued data are added with realvalued weighting, the resulting phase maps can show significantly reduced sensitivity due to incoherent averaging or even artifactual effects such as 2p phase wraps ending abruptly inside the object (see Figure 8.6; see chapter 6 for more discussion about such phase artifacts). According to Maxwell’s law, such a magnetic field profile (allowing a closed path

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FIGURE 8.5 Single element magnitude (left) and phase (right) source images from a GRE acquisition with an 8-element head coil at 7 T. The localized coil sensitivity can be recognized in the magnitude data. The high sensitivity of the surface coils enables the calculation of phase information in the whole slice from each single coil element. However, the phase between coil elements differs strongly.

along which the path integral is not zero) is indicative of a magnetic monopole and therefore not realistic. Proper combination of the single channel data takes the complex sensitivity profiles of the receiver elements into account. In very high-field MR systems, an absolute reference in form of a body coil data set is usually not available. However, since the absolute phase is not of interest but only the relative differences between tissue types, a filtered version of the single channel data can be used [2, 3, 12].

FIGURE 8.6 The “root-sum-of-squares” magnitude image (left) together with the equally combined phase image (middle) from the single coil data in the previous figure. A local increase in the phase noise can be recognized in the right frontal part of the image due to improper destructive combination. The right image displays another combined phase data set with an unphysical phase wrap ending within the brain.

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FIGURE 8.7 Combined and spatially filtered phase maps. While at small filter width the anatomical information is lost, at large filter widths the anatomy is obscured by global phase variations. For human brain phase imaging, a filter width between 2 and 3 mm combines high local contrast with good homogeneity.

Spatial Filtering of Phase Images In addition to removing phase differences between the single receiver channels, global phase variations have to be removed in order to reveal the local phase differences generated by the tissue microstructure. Even after shimming recognizable phase variations occur across the object. These are caused not only by magnetic field inhomogeneities but also due to eddy current effects. The resulting phase variation will usually be much larger than that generated by the tissue. Therefore, spatial filtering is required in order to visualize the local tissue properties. A proper spatial filter will remove the large-scale inhomogeneities in the phase map while maintaining the contrast between anatomical structures. Apart from air–tissue and tissue–bone interfaces, the shim related inhomogeneities are smooth and of low spatial frequency, whereas the structure of interest is characterized by abrupt local phase variations. Correspondingly, a spatial high-pass filter can be used to highlight the anatomical structures of interest. The choice of the filter width is crucial to the appearance of the resulting phase map (see Figure 8.7). While a larger cutoff width results in uncorrected global phase inhomogeneities, smaller and more restrictive filter widths will remove not only inhomogeneities but also the information of interest by reducing the local phase contrast. Depending on the local shim conditions, the best filter size may vary [7, 13]. Finally, the phase noise outside the object can be masked [14] based on the magnitude data (see Figure 8.8). Large spatial scale field variations can also be removed by fitting multidimensional polynomials to the data [9]. In this case, the polynomial degree determines the spatial scale of the filtering. Image Display Conventions The display of magnitude MR images has been largely agreed upon: stronger MR signal is presented as brighter gray value. For phase contrast images, no convention regarding the presentation exists. Correspondingly, higher frequency is either displayed brighter or darker. In addition to the novel and not fully understood information content in phase images (see next paragraphs), this further complicates interpretation of the data. A common agreement is needed in order to aid data interpretation in the future. Here, we will display higher frequencies darker (as in Figure 8.8, right).

PHASE VERSUS MAGNITUDE CONTRAST Although phase and magnitude GRE data are two aspects of the same signal, they can lead to dramatically different contrast in the human brain. One reason for this is that they are

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FIGURE 8.8 One slice out of 24 phase images obtained with a 24-channel head coil at 7 T. Both images contain identical information. However, the gray scale has been inverted between them. The left image represents phase for a left handed coordinate system (where paramagnetic substances appear with a bright phase) while the right image represents phase for a right handed system.

differently affected by local variation in tissue magnetic susceptibility. While magnitude signal is always reduced by susceptibility variations due to coherence loss in an imaging voxel, phase (and frequency) can both increase and decrease in areas of altered susceptibility. Another reason is that factors other than magnetic susceptibility can affect phase and magnitude differently. In the following, we show some illustrative examples of the different contrast in phase and magnitude data in different brain regions. Gray–White Matter Contrast The CNR for discriminating gray and white matter is generally higher in phase data, as illustrated in Figure 8.9. Often, cortical gray matter shows higher phase than white matter, although this is dependent on tissue geometry and its orientation relative to B0. For planar cortical structures parallel to B0, CNR of phase data can exceed that of magnitude data by up to an order of magnitude [9]. In GRE magnitude data, counteracting effects of T1 (increases WM signal), spin density (lowers WM signal), and T2, T2* (lowers WM signal) can reduce CNR. This sometimes results in a weak or vanishing GM–WM contrast. Intracortical Contrast Similarly, as seen for GM–WM contrast, intracortical contrast is generally superior in phase data. In some regions, such as primary visual (see Figure 8.10) and motor cortices, clear evidence of the laminar structure of the cortex can be observed. The laminar structure seen in V1 resembles the line of Gennari, a structure with increased myelin content associated with

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FIGURE 8.9

Example of GM–WM contrast. CNR of phase data is generally superior to that of

magnitude data.

axonal fibers. The dark phase in the line of Gennari appears to be caused by a higher iron content (see Figure 8.10). The low contrast in the magnitude data is attributed to counteracting effects of T2* and spin density on one hand, and T1 on the other. Contrast Between Fiber Bundles Both magnitude and phase data show substantial contrast between many of the major fiber bundles in white matter [9, 15]. In magnitude data, dense bundles generally have low signal intensity (low PD, short T2, T2* ), e.g. cingulum and optic radiation. Many of the major fiber bundles also stand out in phase images (Figure 8.11). This might offer an opportunity to map the brain’s fiber connections and supplement information available with fiber tracking based on MRI diffusion tensor imaging.

FIGURE 8.10 Example of intracortical contrast in the occipital lobe. Relative strong contrast is seen in the line of Gennari, a cortical layer specific to primary visual cortex.

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FIGURE 8.11 Magnitude and phase contrast in white matter. Many of the major fiber bundles are clearly distinguishable in both images.

CONTRIBUTORS TO PHASE CONTRAST The apparent precession frequency of proton spins can be affected through a number of mechanisms, including tissue magnetic susceptibility, spin, chemical, and diffusional exchange [16], and nuclear shielding (chemical shift), all of which can depend on the temperature and chemical environment. The nature of these effects has been described and is well understood. However, to what extent these mechanisms contribute to the observed phase differences in various tissue types is currently a topic of discussion. In the following, we will review the potential contributions of these mechanisms in more detail. Magnetic Susceptibility Although the effects of magnetic susceptibility variations in tissues on MRI contrast have been recognized for decades, their origin has not been firmly established and may vary from organ to organ. In GM and WM of normal brain tissue, the likely contributors to susceptibility variations are iron and lipid [9] that decrease and possibly increase the diamagnetic susceptibility of pure water, respectively. In human brain tissue, iron is primarily found in hemoglobin in red blood cells and in ferritin, which is distributed throughout the brain. Lipid is most abundant in white matter. Improved understanding of the origin of magnetic susceptibility contrast in T2* -weighted MRI can be gained from tissue samples by correlating MRI and histology. Iron stains of the primary visual cortex have shown a laminar distribution, with a relatively high level of iron in layer 4 [17] (Figure 8.12). The contrast pattern mimics that of MRI obtained in vivo and in vitro, suggesting tissue iron as the main contributor to intracortical contrast. The absence of a frequency shift between WM and CSF, despite their large differences in iron content (see, e.g., Figures 8.8 and 8.11), has been hypothesized to result from the opposing

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FIGURE 8.12 Examples of MRI phase (left) and Perls’ iron stain (right) of line of Gennari (layer 4b) in human V1. Image quality and contrast may not be optimal due to conversion from color to grayscale display. Please see the color plates section for the original version of this figure.

susceptibility shifts related to myelin and iron [9]. Support for this hypothesis is the observation that iron and myelin often colocalize in oligodendrocytes in WM [18], which may relate to the understanding that iron is required for the generation and maintenance of myelin around axons. However, there is evidence in some small sulci that CSF does have the expected phase different from WM [7] suggesting that some of these effects may be related to geometry. This remains an interesting open question for future considerations in modeling the brain. Further evidence for the contribution of iron to susceptibility contrast comes from iron extraction studies [17, 19]. MRI of tissue samples after chemical extraction of iron show a strong increase in T2* and a strong reduction in intracortical T2* and phase contrast. A slight reversal of phase contrast observed in layer 4, after iron extraction, might reflect an opposing susceptibility shift from myelin. Assuming myelin and iron cause opposing and possibly canceling susceptibility shifts, one would expect to see the strongest phase contrast in situations where they do not colocalize or their relative proportions are altered. In a normal brain, this occurs in iron-rich/ myelin-poor regions such as the basal ganglia and cortical gray matter, and in myelin-rich/ iron-poor regions such as the optic radiations [9]. Phase effects have also been observed in neurological diseases that affect the iron–myelin relationship, and therefore are a promising contrast mechanism in pathology such as hemorrhagic infarcts, brain tumors, Alzheimer’s disease and multiple sclerosis. Spin and Chemical Exchange with Macromolecules In conventional MRI, different tissue types, for example, GM and WM, are usually differentiated by their MR relaxation properties. Tissue relaxation is governed by highly diverse and highly dynamic cellular and subcellular processes on a timescale from 1010 s up to seconds. An example of such a process is the exchange of proton spins between sites that have different chemical environments. The exchangeable sites involved can be very diverse, ranging from single amide or hydroxyl protons on small mobile macromolecules to binding sites on complex structures such as organelle membranes. Exchange has been one of the key topics that are investigated extensively in MR exchange studies and magnetization transfer (MT) experiments. MT has been generally applied for subcellular exchange studies to investigate the water proton exchange with exchangeable sites on the surface of macromolecules or other subcellular components. The exchange behavior is usually described by a Bloch equation with a two-site exchange model. Water molecules in the free pool and at an exchangeable site on a macromolecule

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FIGURE 8.13 The water resonance frequency is shifted toward higher frequency with increasing BSA concentration in the solution. This shift is caused by the water–BSA exchange. Here, TMSP is used as a frequency reference in the solution and is not affected by the exchange process.

experience different chemical environments and thus will result in a net frequency shift when the exchange rates are fast (1010–109 s). Such frequency shifts can be considerable compared to the in vivo GM/WM frequency separation (0.01–0.02 ppm). A recent study with bovine serum albumin (BSA) gave the first direct demonstration of this effect and the frequency shift ability of BSA on bulk water is determined to be 0.04 ppm/mM [16] (Figure 8.13). In addition, the temperature dependency coefficient of water–BSA exchange induced shift is determined to be 0.00067 ppm/mM/K (Figure 8.14). The frequency shift was measured against an internal reference substance (TMSP (trimethylsilylpropionate)). Therefore, susceptibility can be excluded to cause the frequency shift since all substances are in a homogeneous solution. The water frequency shift due to macromolecules suggests an alternative source for the in vivo GM/WM phase contrast and therefore an accurate knowledge of macromolecule concentration in brain tissue will help to understand the in vivo GM/WM phase contrast behavior due to water–macromolecule exchange (WME) processes. The macromolecule fraction of brain cytosol in rats and humans and their NMR resonances were previously characterized [6, 20–22] with concentrations from 40 to 60 mg/mL and an average macromolecule molecular weight between 48 and 63 kDa, which results in a protein concentration of about 1 mM. Based on the water–BSA frequency shift, the mobile macromolecule concentration in GM and WM can be estimated from the difference in MR spectroscopy measurements (40%) and the in vivo frequency separation of 0.02 ppm (0.45 mM BSA, 37 C). This results in a WM concentration of 1.1 mM (in BSA equivalent unit) and 1.6 mM for GM and is in good agreement with results from cell culture studies.

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FIGURE 8.14 The temperature dependence of water–BSA exchange for different BSA concentrations.

Analysis of the contrast to noise gain (CNRg), which was systematically discussed in Reference 9 for the in vivo GM/WM phase contrast, is also consistent with the WME model for GM/WM phase contrast. The dependence of the transverse relaxivity R2 on BSA was determined in Reference 23 to be 5.86 s1/mM at 7 T (300 MHz). Assuming that both frequency and R2 differences between GM/WM are induced solely by macromolecules (in BSA equivalent units), CNRg for phase images compared to magnitude images can be derived using the equation given in Reference 9, CNRg  2p  TE  Df/(exp(TE  DR2)  1), where Df is the GM/WM frequency separation and DR2 is the R2 difference between GM/WM. The WME model gives a CNRg value around 13.2 and is close to the in vivo result at 7 T (CNRg ¼ 10.5). This result suggests that the WME process may contribute to the in vivo GM/WM phase contrast. Another important aspect that should be addressed is the relation between WME-induced frequency shift and MT ratio. MT requires spin magnetization transfer and therefore the spin history, and thus phase information, is lost and does not contribute to the frequency shift. MT also depends on the available macromolecule binding sites for spin magnetization transfer (slower process, 109–107 s) while WME frequency shift only requires a water molecule to come in close contact with the macromolecule (fast process, 1010–109 s) to experience a different chemical environment. On the other hand, some WME effect may be caused by the same processes that cause MT. It may be hypothesized that smaller mobile macromolecules contribute to the WME while larger species induce a stronger MT effect. The major difference of the WME model compared to tissue susceptibility is that WME should not result in an orientation dependency due to the fact that spin exchange occurs at a much smaller scale compared to the directional dependent long-range demagnetization field for bulk susceptibility. While the susceptibility effects are related to the presence of

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paramagnetic compounds, the WME model may relate the phase contrast directly to macromolecule alternations, for example, in pathologies. The contributions of WME and susceptibility shift of macromolecules have been studied recently for BSA [24]. The authors used dioxane as the internal frequency reference and found that the BSA WME shift is half of the BSA susceptibility shift with opposite sign. Additionally, they observed broadening of the TMSP resonance peak, which was an indication of interaction between TMSP and BSA. On the other hand, early NMR studies of the water–dioxane system showed a strong water–dioxane hydrogen bonding that shifts the water frequency to lower field [25]. The presence of dioxane therefore creates a competitive binding scenario that reduces the apparent WME shift between water and macromolecule due to the shift of the reference substance frequency. A recent experiment from Zhong et al. showed that for BSA, the WME shift and the susceptibility shift were of similar magnitude with opposite signs. This can be demonstrated by measurements with chloroform as external reference for different BSA concentrations without dioxane nor TMSP as internal references (Figure 8.15). Therefore, caution must be taken when either dioxane or TMSP are applied as internal reference to study the WME shift. Another recent study [26] has also applied TMSP as internal reference to study the WME shift in fixed human and fresh pig brain tissue, showing that the WME effects are larger in WM and generally oppose the susceptibility induced frequency shift. Nevertheless, given the nature of TMSP interaction with mostly hydrophobic binding sites on macromolecules or membranes, some caution should be taken to exclude the potential effect of TMSP interaction with brain tissues for reliable quantitation of GM and WM exchange induced frequency shift.

FIGURE 8.15 The frequency shift of water for different BSA concentrations at 303 K, using chloroform as external reference in a coaxial NMR tube. The frequency shift was determined by the separation between water and chloroform. No concentration-dependent frequency shift was observed, suggesting that the WME shift of BSA and the susceptibility shift are similar with opposite sign.

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ORIENTATION DEPENDENCE OF PHASE CONTRAST The magnetic field changes introduced by magnetic susceptibility variations are orientation and geometry dependent, and often extend beyond the area of altered susceptibility [6, 27]. This can occur at various spatial scales including microscopic (subvoxel) and macroscopic (supra-voxel) scales. For this reason, it is difficult to translate the phase (and to a lesser extent magnitude) into a local tissue susceptibility. Recently, a number of groups have proposed ways to translate phase distributions into susceptibility maps [6, 28–30]. They rely on k-space filtering methods, and generally assume that all of the phase effects originate from macroscopic susceptibility variations, which may not always be accurate. Nevertheless, this work is important and needed to accurately localize and quantify local tissue characteristics, which is often required for disease diagnosis and management (see Chapters 24 and 25). Much work needs to be done to make these approaches robust and practical. POTENTIAL APPLICATION OF PHASE IMAGES IN DISEASE The high spatial resolution and CNR available with GRE phase imaging at high magnetic field strengths make it a great potential candidate for clinical application, in particular for diseases that affect tissue susceptibility and macromolecule distributions. Examples are diseases that affect the brain’s vasculature such as tumors [31] and stroke [32], and diseases that alter tissue iron content, including Alzheimer’s disease [19, 33], multiple sclerosis [34–36], and Parkinson’s disease.

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Part II

Current Efforts in Clinical Translational Research Using SWI

9 SWI Venographic Anatomy of the Cerebrum Daniel K. Kido, Jessica Tan, Steven Munson, Udochukwu E. Oyoyo, and J. Paul Jacobson

INTRODUCTION SWI is almost synonymous with venous anatomy, since the susceptibility changes are associated with the deoxyhemoglobin profiling of the venous system. This book contains several chapters that demonstrate findings associated with the venous system or that occur on a background of veins. However, it is understood that the arterial system is the genesis of most of these venous abnormalities. If there is a severe arterial stenosis, an increased amount of oxygen is extracted from the blood as it passes through the capillaries and there is subsequent venous prominence (see Chapter 13). Tumors can cause venous prominence as a result of increased blood volume (see Chapter 10). Similarly, venous prominence is also seen in several vascular abnormalities, such as venous angiomas, capillary telangiectasias, and Sturge–Weber disease (see Chapters 16 and 17). If desaturated blood is delivered to the brain, as occurs in a variety of congenital heart diseases, venous prominence will reflect the severity of the underlying shunt [1]. In some chronically diseased tissues that have become metabolically less active or inactive, there will be decreased prominence of the veins, as occurs in patients with severe chronic multiple sclerosis (see Chapter 15). To help understand the contribution of the arterial system to venous findings, a brief description of the cerebral arterial system, illustrated by MRA, is given at the end of this chapter. SWI venography differs from conventional invasive and noninvasive contrast-based methods of examining the intracranial venous system for the following three reasons: (1) SWI venography consistently visualizes deep medullary veins while conventional techniques rarely do even when they are pathologically enlarged; (2) SWI images reveal both the amount of oxygen that has been removed from the blood as it passes through Susceptibility Weighted Imaging in MRI, By E. Mark Haacke and J€urgen R. Reichenbach Copyright Ó 2011 by Wiley-Blackwell

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capillaries and the transit time of the blood through the venous system that conventional techniques cannot do; (3) SWI venography of the larger venous structures such as the superior sagittal sinus is not as reliably demonstrated as other conventional techniques because of the susceptibility artifact caused by the adjacent calvarium and air. An exhaustive description of the cerebral venous system can be found in Ref. 2. SWI venography differs from contrast-enhanced MRI venography in that the latter is based on the velocity of venous blood flow while SWI venography is primarily based on susceptibility changes associated with the amount of deoxygenated blood, which in turn reflects the metabolic activity of the brain. Thus, SWI venography indirectly visualizes the metabolic activity in the brain giving some insight into the general and/or local metabolic stress that the brain is experiencing and in some diseases may actually help predict future outcomes (see Chapter 14). SUPRATENTORIAL VENOUS ANATOMY The supratentorial venous system can be broken into two divisions: superficial and deep systems [3]. The anatomy of the deep venous system is more consistent and is made up of the deep medullary veins, the subependymal veins, the internal cerebral veins, the great vein of Galen, the inferior sagittal sinus, and the straight sinus (Figures 9.1–9.3 and 9.5). Special emphasis is given to the deep medullary veins since they are located directly within the white matter and should represent the amount of oxygen being extracted in that area. The infratentorial venous anatomy, although less important than the deep venous anatomy, needs to be understood if one is to avoid diagnosing normal anatomic variations as lesions. Deep Venous Anatomy Deep Medullary Veins Anatomy and Variations The deep medullary veins drain the deep white matter of the brain. Other terms that have been used to describe these veins include transcerebral

FIGURE 9.1 Sagittal midline veins demonstrated by 3 T SWI venography. (a) The deep supratentorial veins consist of the anterior septal (AS) vein, internal cerebral (IC) vein, the great vein of Galen (G), inferior sagittal sinus (IS), and the straight sinus (S). The superficial system consists of the superior sagittal sinus (SSS) and torcular herophili (LTH). (b) Axial lines have been drawn on (a) to demonstrate where the corresponding axial images in Figure 9.2 occur. Letters A–E correspond to Figure 9.2a–e. The sagittal images of (a, b) are a minimum intensity projection over 16 mm.

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FIGURE 9.2 Axial venous images demonstrated by 3 T SWI venography. (a, b) Images through the lower and upper midbrain demonstrate the course of the basal veins of Rosenthal (R) that receive drainage from the deep middle cerebral (DM) veins and hippocampal veins (H); straight sinus (S). Superficial veins that are labeled include the temporal (T) vein, occipital (O) vein, and the superior sagittal sinus (SSS). (c–e) Veins located at or above the lateral ventricles. The deep medullary (MV) veins drain into the thalamostriate (TS) veins in (d). Other components of the deep system include the anterior septal (AS) veins, caudate (C) veins, and internal cerebral (IC) vein (c, d). Superficial veins that are labeled include the anterior frontal (AF) veins, posterior frontal (PF) veins, parietal (P) veins, and the superior sagittal sinus (SSS). The axial images (a–e) are minimum intensity projections over 16 mm that overlap by 8 mm.

veins [4], transcerebral anastomotic veins [5], and veins of the white matter of the cerebral hemisphere [6]. The deep medullary veins increase slightly in size as they converge toward the lateral ventricles where they drain into the subependymal veins (Figures 9.2e, Figures 9.3 and 9.5). We propose a subjective classification of deep medullary veins based on the concentration of deoxyhemoglobin that they contain (Figure 9.3). This classification is based on stratifying the amount of deoxyhemoglobin visualized into three categories: low, normal, and high. This will roughly correspond to hypo-, normal, and hypermetabolic brain activity. A seven-category classification that includes other venous structures in both the deep and the superficial venous system is as follows:(1) absent (no visible deep medullary veins, absent or nearly absent low signal in the subependymal veins, and few nonprominent cortical veins); (2) faint (equivocal low signal in the medullary veins, some low signal in the subependymal veins, and few nonprominent cortical veins); (3) minimal (several definite, fine, light gray deep medullary veins are visible and limited to the deep white matter, the

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FIGURE 9.3

Prominence of vein categories 1–4, with emphasis on the deep medullary veins, is demonstrated by data acquired at 3 T. SWI images (a–d) correspond to categories 1–4 that are described in the text. The images of the upper row are 2 mm thick while that of the lower row are projected over 16 mm. The lower row of images better demonstrate the connectivity of the deep medullary veins.

subependymal veins are present but not prominent, and cortical veins are occasionally prominent); (4) mildly prominent (many dark, distinct deep medullary veins are visible, either diffusely or regionally. The deep medullary veins are wider and better demarcated, but do not extend to the most superficial layers of the deep white matter. The subependymal veins are usually prominent and a few cortical veins may be prominent); (5) moderately prominent (the deep medullary veins are dark, numerous, wider and extend into the superficial white matter, either diffusely or regionally. The subependymal veins are prominent and more cortical veins may be prominent); (6) significantly prominent (the numerous deep medullary veins are very dark and extend through the superficial white matter to nearly the cortex, either diffusely or regionally. Subependymal veins and cortical veins are very prominent. There may be a dark background blush in the white matter); (7) severely prominent (numerous thick, dark medullary veins extend to the cortex. They may be irregular. The subependymal and cortical veins are prominent). Images of this classification in newborns and young infants are shown in Chapter 14. Images of this classification in adults have been previously reported [1]. Factors That Cause Variations in the Prominence of Deep Medullary Veins Patient age is an important factor to be aware of when evaluating deep medullary veins (see Chapter 14). Two hundred and sixty adult patients with normal appearing scans were sorted by decade: 20–29 years (n ¼ 31), 30–39 years (n ¼ 31), 40–49 years (n ¼ 51), 50–59 years (n ¼ 45), 60–69 years (n ¼ 57), 70–79 years (n ¼ 26), 80–89 years (n ¼ 14), and 90–99 years (n ¼ 5). These patients were evaluated for prominence of the deep medullary veins (POV) and given a score between 1 and 7. The median POV observed across all age decades was POV 2, with the exception of patients in the 9th decade (median POV 3). The interquartile range (IQR) spanned one POV unit for all decades, except for the 3rd and 9th (Figure 9.4).

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FIGURE 9.4 Distribution of prominence of veins (POV) by age (decades).

The 25th and 75th percentile positions of the IQR ranged between POV 2 and POV 3 for all decades, except for the 3rd, 6th, and 9th (Figure 9.4). The minimum, maximum, and median were all POV 2 for all patients in the 10th decade. Other situations to be aware of when interpreting deep medullary veins is that increased blood carbon dioxide levels will increase cerebral blood flow, thus making the veins less prominent [1, 7]. Drugs such as diamox will also increase cerebral blood flow and thus have the same effect [8]. In contrast, nitrous oxide will cause venous dilation and the veins will be more prominent. Substances such as caffeine will cause vasoconstriction, increase oxygen extraction, and also darken the deep medullary veins [9, 10]. MR contrast agents that shorten T1 will also make the veins more prominent [7]. Increasing field strength will also make the veins more prominent (Figure 9.5) due to decreased T2* for veins (see Chapter 20). Venous prominence may also appear in the presence of a variety of abnormal systematic metabolites such as lactate. Subependymal Veins/Internal Cerebral Veins The deep medullary veins located around the frontal horn and body of the lateral ventricles drain into the medial and lateral subependymal veins. The thalamostriate veins, the largest lateral subependymal veins, usually join the internal cerebral veins at the foramen of Monro (Figure 9.2c and d). The anterior septal veins are subependymal veins that appear to be an anterior extension of the internal cerebral veins and they drain the white matter around the frontal horns and genu of the corpus callosum (Figures 9.1a and 9.2c and d). The internal cerebral vein drains posteriorly into the great vein of Galen (Figure 9.1a). The subependymal veins can be especially helpful in differentiating POV categories 1 and 2. Subependymal veins are not

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FIGURE 9.5 7 T SWI images. (a) The deep medullary (MV) and subependymal veins (SEV) show sharper borders and better image contrast when compared to the 3 T image in Figure 9.3. The image is a minimum intensity projection over 8.4 mm that overlap by 4.2 mm. (b) Magnified view of the cortex demonstrates pial veins (arrows) and cortical veins (arrowhead) that drain the gray matter and the underlying white matter. Images courtesy of Dr. Yulin Ge and Dr. Samuel Barnes.

seen or are very faint in category 1, while in category 2 they should be more prominent (Figure 9.3). Basal Vein of Rosenthal The basal veins of Rosenthal are formed in the lateral cerebral fissures by lateral branches from the insula (deep middle cerebral veins), superior branches from the anterior perforated substance, anterior branches from the posterior inferior frontal lobes, and medial branches from the anterior interhemispheric fissure (Figure 9.2a and b). After leaving the lateral fissures, the basal vein of Rosenthal passes around the midbrain to drain into the great vein of Galen. While passing around the midbrain, they may receive draining veins from the inferior body of the lateral ventricles and the hippocampus (Figure 9.2a and b). The Great Vein of Galen The internal cerebral vein, the basal vein of Rosenthal, and some of the veins that drain the superior portion of the vermis and cerebellar hemispheres drain into the great vein of Galen (Figure 9.1a). The great vein of Galen courses posteriorly under the splenium of the corpus callosum and then drains into the straight sinus that in turn drains into a region where it joins the superior sagittal sinus before dividing into a left and a right transverse sinus. This region is called the confluence of sinuses or the torcular herophili (TH) (Figure 9.1a).

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Superficial Venous System Small pial veins drain the cortical gray matter [11]. Larger pial veins drain the cortex, as well as a small portion of underlying white matter (Figure 9.5b). These pial veins drain into the cortical veins. The lateral cerebral gray matter above the Sylvian fissures are drained by the frontal and parietal cortical veins (9.2d and e). These superficial veins drain superiorly toward the vertex and may also receive branches from the medial surface of the brain before draining into the triangular-shaped superior sagittal sinus. The superior sagittal sinus, which is located in the midline, drains posteriorly and inferiorly into the torcular herophili, which also receives blood from the straight sinus before dividing into the transverse sinuses (Figures 9.1a and 9.2a–e). The largest superficial vein above the Sylvian fissure is designated as the vein of Trolard and is usually located in the parietal lobe. The region around the Sylvian fissure is drained by the superficial middle cerebral vein that in turns drains into the transverse sinuses. The lateral surface of the cerebrum below the Sylvian fissure and the inferior surface of the temporal and occipital lobes also drain directly into the transverse sinuses. The largest superficial vein beneath the Sylvian fissure is called the vein of Labbe. Posterior Fossa Veins The veins of the posterior fossa have lost their clinical importance since they are no longer useful in classifying posterior fossa masses. However, awareness of at least two groups of veins may prevent misdiagnosis of normal anatomy for lesions. Sometimes the petrosal vein is located in the cerebellopontine angles close to the medial end of the internal auditory canal. They may receive medial branches from the pons (transverse pontine veins), lateral branches from the cerebellar hemispheres (superior hemispheric veins, veins of the greater horizontal fissure, and inferior hemispheric veins), superomedial branches from the wings of the precentral cerebellar fissure (brachial veins), and inferomedial branches from the cerebellar pontine fissure (inferior branches from the hemisphere and veins of the lateral recess). If all these vessels drain into the petrosal vein, it may occasionally be prominent enough to be confused with a vascular tumor, especially following the administration of contrast agent. This region is poorly visualized by SWI venography because of its proximity to bone and air in the adjacent temporal bone. A small midline plexus of veins in the pons can occasionally be confused with lesions such as telangiectasias, cavernous angiomas, or even infarcts (Figure 9.5). Occasionally, these pontine plexuses can be confused with vascular tumors, especially when they are partially calcified (Figure 9.6). Arterial Anatomy The cerebrum is supplied by four large arteries: two internal carotid arteries that supply arterial blood to the anterior circulation and two vertebral arteries that deliver blood to the posterior circulation (Figure 9.7). The internal carotid arteries supply the cerebrum minus the occipital lobes and the thalamus. The external carotid artery supplies the face and the scalp (Figures 9.7 and 9.8). The vertebral arteries supply the basilar artery and its branches that in turn supply the structures of the posterior fossa (brain stem and cerebellar hemispheres). The basilar artery terminates into two symmetric branches, the posterior cerebral arteries, that supply the occipital lobes and the thalamus (Figure 9.7).

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FIGURE 9.6 Pontine venous plexuses. (a) An 80-year-old male was sent to an outside facility where he obtained CT scans suggestive of a pontine stroke. T2 image demonstrates a region of increased signal in the pons (arrow). (b) Corresponding 1.5 T SWI image shows a low-density region in the midline of the pons (arrow). Minimum intensity projection image over 4 mm. (c) 1.5 T SWI image of a patient suspected of shunt malformation that shows small veins radiating from the midline region of low signal. Minimum intensity projection image over 4 mm. (d) Corresponding CT of Figure 9.5c demonstrating calcification in the region of low signal.

Internal Carotid Artery There are three intracranial branches of the internal carotid artery after it emerges from cavernous sinus: the ophthalmic, posterior communicating, and anterior choroidal arteries (in that order) (Figures 9.7 and 9.8a and b). The posterior communicating artery is the most important anastomotic connection between the anterior

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FIGURE 9.7 Coronal and sagittal MRA 3 T images of the cerebrum. (a) The anterior and posterior arterial circulations are superimposed on this coronal image. The anterior circulation consists of the internal carotid artery (IC), the M1 segment (M1) of the middle cerebral artery, the A1 segment (A1) of the anterior cerebral artery, the anterior communicating (AC) artery, and the superimposed pericallosal (P) and callosomarginal (CM) arteries; TE: temporal branches of the external carotid artery. The posterior circulation consists of the vertebral (V) artery, basilar (B) artery, superior cerebellar (SC) artery, and the posterior cerebral artery (PCA). (b) Midline sagittal MRA image of the cerebrum. The anterior circulation consists of the internal carotid (IC) arteries, posterior communicating (PC) artery, pericallosal (P) artery, and the callosomarginal (CM) artery. The posterior circulation consists of the vertebral (V) artery, the posterior inferior cerebellar artery (PICA), the basilar (B) artery, and the posterior cerebral arteries (PCA). This is a maximum intensity projection image over 64 mm. (c) Axial lines drawn on Figure 9.7c demonstrate where the corresponding axial images in Figure 9.8a–d occur.

and posterior circulations. Aneurysms may occur at the origin of these three vessels, as well as at the bifurcation of the internal carotid artery as it divides into the anterior and middle cerebral arteries. Anterior Cerebral Artery Initially, the anterior cerebral artery courses horizontally in an anteromedial direction to the interhemispheric fissure (A1 segment) where it communicates with the opposite anterior cerebral artery via the anterior communicating artery, and afterward it continues anteriorly and superiorly as the pericallosal artery (Figures 9.7a and 9.8a and b). The pericallosal artery courses in the midline around the genu of the corpus callosum and then onto the surface of the body of the corpus callosum where it takes a horizontal and posterior course before anastomosing with the pericallosal branches of the posterior cerebral artery (Figures 9.7b and 9.8c and d). The largest branch of the pericallosal artery is the callosomarginal artery that runs posteriorly parallel to the pericallosal artery in the cingulate sulcus (Figures 9.7b and 9.8c and d).

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FIGURE 9.8 Axial MRA images of the cerebrum and posterior fossa acquired at 3 T. (a) Axial image of the posterior fossa and the circle of Willis. Anterior circulation arteries consist of the internal carotid (IC) arteries, M1 segment (M1) of the middle cerebral artery, the A1 segment (A1) of the anterior cerebral artery, and the posterior communicating (PC) branch of the internal carotid artery; TE: the temporal branch of the external carotid artery. Posterior circulation branches consist of the vertebral (V) artery and the posterior cerebral artery (PCA). (b) Axial image of the circle of Willis. The circle of Willis consists of the A1 segment (A1) of the anterior cerebral artery, the posterior communicating (PC) artery, and the proximal portion of the posterior cerebral artery (PCA). Not visualized is the anterior communicating artery; P: pericallosal artery. Middle (M) cerebral branches in the Sylvian fissure. (c, d) Axial image just above the lateral ventricles; pericallosal (P) and callosomarginal (CM) arteries. Middle (M) cerebral artery branches in the Sylvian fissure. Axial images are maximum intensity projections over 64 mm that overlay by 32 mm.

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Middle Cerebral Artery The middle cerebral artery is larger than the anterior cerebral artery. It extends laterally and horizontally in the lateral cerebral fissure (M1 segment) to the Sylvian fissure, where it usually bifurcates into a superior and an inferior division (Figure 9.7a and b). Small lateral lenticulostriate arteries arise from the superior surface of the M1 segment to supply the putamen, the globus pallidus, and the superior half of the caudate nucleus located above it. Additionally, a small branch from the anterior communicating artery (recurrent artery of Hubner) supplies the anterior limb of internal capsule, and small branches from the superior surface of the A1 segment of the anterior cerebral artery supply the inferior half of the head of caudate nucleus. The middle cerebral artery bifurcates in the anterior portion of the Sylvian fissure in approximately 80% of individuals [12]. When the superior division is dominant, it supplies most of the surface of the brain and has four major divisions. The most anterior division supplies the inferior and middle frontal gyri. The next branch is usually small and supplies the precentral and postcentral gyri, and the last two branches supply the parietal lobe. The inferior division of the middle cerebral artery is smaller than the superior division and usually supplies the lateral surface of the superior and middle temporal gyri. When the superior division is not dominant, the parietal branches come off the inferior division. When there is a trifurcation of the middle cerebral artery, the third division supplies the parietal lobe. Posterior Arterial Circulation The major suppliers of the posterior circulation are the two vertebral arteries that join to form the basilar artery (Figure 9.7a). The last major artery to originate from the vertebral artery is the posterior inferior cerebellar artery (PICA) that supplies the medulla, tonsils, and inferior half of the vermis and cerebellar hemispheres (Figure 9.7b). The first major branch to originate from the basilar artery is the anterior inferior cerebellar arteries (AICA) that supplies the anterior inferior surface of the cerebellum and the internal auditory canals. The size of the AICA is usually inversely related to the size of the ipsilateral PICA. The other major branch of the basilar artery is the superior cerebellar arteries that supply the superior half of the vermis and cerebellar hemispheres (Figure 9.7a). The posterior cerebral arteries are formed when the basilar artery bifurcates in the interpeduncular fossa (Figures 9.7a and 9.8a and b). As they course posteriorly around the midbrain, they send superior branches to the thalamus above it and choroidal branches to the choroid plexus in the temporal horns of the lateral and third ventricles that are lateral and medial to it. The cortical branches can be divided into a lateral and a medial group. The lateral group supplies the medial temporal lobes including the hippocampus as well as the inferior surface of the temporal lobe. The medial group supplies the medial surface of the occipital lobes and a small portion of the posterior parietal lobe. REFERENCES 1. Newbern MS, Jacobson JP, Oyoyo U, Kuhn M, Kido DK. Cyanotic heart disease is associated with increased prominence of cerebral deep medullary veins on susceptibility-weighted imaging in children undergoing evaluation for heart transplantation. Proceedings ASNR, 2009, pp. 400–401. 2. Newton TH, Potts DG. Angiography (book 3 Veins), C.V. Mosby Company, St. Louis, 1974.

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3. Kido DK, Baker RA, Rumbough CL. Normal cerebral vascular anatomy. In: Abrams HL, editor. Abrams Angiography, Little Brown and Co., Boston, 1983, pp. 219–270. 4. Kaplan HA. The transcerebral venous system: an anatomical study. Arch. Neurol. 1959;1:148–152. 5. Schlesinger B. The venous drainage of the brain with special reference to the Galenic system. Brain 1939;62:274–291. 6. Huang YP, Wolf BB. Veins of the white matter of the cerebral hemispheres (the medullary veins): diagnostic importance in carotid angiography. Am. J. Roentgenol. 1964;95:739–755. 7. Lin W, Mukherjee P, Hongyu A, Yingling Y, Wang Y, Vo K, Lee B, Kido D, Haacke EM. Improving high-resolution MR bold venographic imaging using a T1 reducing contrast agent. J. Magn. Reson. Imaging. 1999;10:118–123. 8. Vorstrup S, Henriksen L, Paulson OP. Effect of acetazolamide on cerebral blood flow and cerebral metabolic rate for oxygen. J. Clin. Invest. 1984;74:1634–1639. 9. Haacke EM, Hu C, Parrish TB, Xu Y. Whole brain stress using caffeine: effects of fMRI and SWI at 3T. Proc. Int. Soc. Magn. Reson. Med. 2003;11:348. 10. Sedlacik J, Helm K, Rauscher A, Stadler J, Mentzel HJ, Reichenbach JR. Investigations on the effect of caffeine on cerebral venous vessel contrast by using susceptibility-weighted imaging (SWI) at 1.5, 3 and 7 T. Neuroimage 2008;40:11–18. 11. Duvernoy HM. Cortical blood vessels of the human brain. In: Yasagil MG, editor. Microneurosurgery: AVM of the Brain, History, Embryology, Pathological Considerations, Hemodynamics, Diagnostic Studies, Microsurgical Anatomy, Vol IIIA,Thieme, Stuttgart, 1987, pp. 338–349. 12. Althemus LR, Roberson GH, Fisher CM, Pessin M. Embolic occlusion of the superior and inferior divisions of the middle cerebral artery with angiographic-clinical correlation. Am. J. Roentgenol. 1976;126: 576–581.

10 Novel Approaches to Imaging Brain Tumors Sandeep Mittal, Bejoy Thomas, Zhen Wu, and E. Mark Haacke

INTRODUCTION Recent advances in MR have transformed imaging of brain tumors from a morphological stage to a metabolic and functional level. Anatomic MRI has helped clinicians and researchers to diagnose, grade, and monitor therapeutic response with greater accuracy. MR spectroscopy, diffusion imaging, and perfusion studies have also made significant contributions in this respect. Susceptibility weighted imaging (SWI) is another novel MR technique that exploits the magnetic susceptibility differences of various tissues such as blood, iron, and calcium [1]. SWI consists of using both magnitude and phase images from a high-resolution three-dimensional full velocity compensated gradient echo sequence. A phase mask is created from the MR phase images and multiplying this mask with the magnitude image increases the conspicuity of the smaller veins and other sources of susceptibility effects. These images are often best visualized by using minimum intensity projection (minIP) over two or more contiguous slices [1]. In this chapter, we discuss the use of SWI as a complement to conventional neuroimaging techniques in the evaluation of neoplasms of the central nervous system. SWI is much more than just another gradient echo sequence in that it detects blood products and calcium with greater sensitivity. What makes it particularly relevant in brain tumor imaging are the many contrasts available with this unique sequence such as spin density, T1, T2* , CSF suppression, and susceptibility sensitivity. For example, we have shown that SWI demonstrates perilesional edema similar to that shown by a fluid-attenuated inversion recovery (FLAIR) sequence because TR is short and TE is long enough to mildly suppress other tissues [2]. However, CSF signal is not low but close to that of the surrounding neural tissue because a low flip angle is used to keep the CSF signal high enough so that it can Susceptibility Weighted Imaging in MRI, By E. Mark Haacke and J€urgen R. Reichenbach Copyright Ó 2011 by Wiley-Blackwell

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be on the same order as or overcome the signal from surrounding veins. SWI’s exquisite sensitivity to blood products makes it possible to visualize slow flowing blood in small cerebral veins. Calcium and blood products, which can easily be differentiated using the phase images, help in further characterizing various brain tumors. In addition, contrastenhanced SWI may be used to better define the tumor matrix [3]. Thus, SWI may effectively complement other advanced MR sequences and may provide additional help in characterizing and grading cerebral neoplasms.

PRIMARY BRAIN TUMORS Gliomas are tumors of neuroepithelial origin and account for almost half of all primary brain tumors [4]. The World Health Organization categorizes gliomas as either low grade (WHO grade I and II, for example, pilocytic astrocytoma and diffuse astrocytoma, respectively) or high grade (WHO grade III and IV, for example, anaplastic astrocytoma and glioblastoma, respectively) [5]. Gliomas are named according to the specific type of cell they most resemble. Thus, astrocytomas are derived from astrocytes, oligodendrogliomas develop from oligodendrocytes, and ependymomas originate from ependymal cells. True benign intracranial tumors mainly arise from the meninges (meningiomas), the pituitary gland (pituitary adenomas), and the myelin sheath of cranial nerves (neuromas or schwannomas). Other types of primary brain tumors include choroid plexus tumors, primitive neuroectodermal tumors (e.g., medulloblastoma, neuroblastoma, retinoblastoma, pineoblastoma), tumors originating from neuronal cells (gangliocytoma, central neurocytoma), and mixed glioneuronal tumors (tumors displaying both a neuronal and a glial component, such as ganglioglioma and dysembryoplastic neuroepithelial tumor) [5].

METASTATIC BRAIN TUMORS In contrast to primary tumors, brain metastases are malignant neoplasms that migrate to the brain from elsewhere in the body. They represent the most common neurological manifestation of cancer, occurring in 20–40% of patients with systemic malignancies [6]. In fact, brain metastases are the most common intracranial tumor in adults, accounting for approximately 40% of all intracranial neoplasms. With improved survival of cancer patients, the incidence of brain metastases has been rising. In order of decreasing frequency, lung, breast, melanoma, renal, and colon cancers are the most common primary tumors to metastasize to the brain.

BRAIN TUMOR CHARACTERISTICS The focus of this chapter is predominantly on gliomas, but we will touch upon a variety of other primary and metastatic brain tumors as well. The pathological characteristics of brain tumors (i.e., vascularity, edema, necrosis, hemorrhage, local invasion) are indirectly related to the tumor vasculature and neoangiogenesis. Therefore, the ability to visualize tumoral and peritumoral blood vessels and to differentiate vascular sources of signal change in tumors is a key component in diagnosing their presence, determining the extent of disease, and assessing their level of activity and aggressiveness. Various neuroimaging

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FIGURE 10.1 Left temporo-occipital high-grade glioma. Contrast-enhanced SWI (c) shows similar boundary information and considerably more detail of the internal architecture of the tumor compared to the T1-weighted precontrast (a) or postcontrast image (b). Reprinted from Ref. 14, with permission from American Journal of Neuroradiology.

characteristics that have been suggested as predictors of glioma grade in humans include heterogeneity, contrast enhancement, mass effect, surrounding vasogenic edema, necrosis, metabolic activity, and cerebral blood volume [7, 8]. In human glioma cells, the levels of ferritin and transferrin receptors detected by immunohistochemistry have been shown to correlate with histological grading of the tumor. Bagley et al. [9] noted that T2* -weighted gradient echo MR images were valuable in the preoperative grading of gliomas due to the increased susceptibility artifacts caused by hemorrhages. The development of SWI allows improved contrast and detection of both venous vasculature and hemorrhagic products within tumors that cannot be readily seen with conventional imaging methods [2, 3, 10–14]. There is ample evidence that the growth of solid tumors, such as gliomas, depends on angiogenesis of pathological vessels [15]. High-grade tumors such as glioblastoma often have a hemorrhagic component that may have clinical relevance (Figure 10.1). Christoforidis et al. [16] observed accurate identification of intratumoral and peritumoral microvascularity in glioblastoma using high-resolution T2* gradient echo imaging at 8 T. Moreover, we have noted that high relative cerebral blood volume (rCBV) values on perfusion imaging and elevated choline:creatine ratios on MR spectroscopy in brain tumors correlate with the presence of blood products within the tumor matrix on SWI. Internal Vascular Architecture and Hemorrhage The purpose of this chapter is to demonstrate the advantages of using SWI in the detection and characterization of cerebral tumors compared to conventional MR sequences. As noted above, tumor characterization is partly reliant on understanding angiogenesis and microhemorrhage; this is particularly important for infiltrating glial tumors [9, 17]. Aggressive tumors tend to have a rapidly growing vasculature and commonly demonstrate extensive microhemorrhages. Intratumoral blood vessels are often more tortuous and disorganized compared to normal brain vessels. For example, in astrocytomas the degree of microvascularity increases from low-grade to high-grade gliomas. It has been demonstrated that SWI can delineate the inner structure and the boundary of tumors more accurately. Furthermore, SWI can effectively identify both the venous vasculature and presence of

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hemorrhage within tumors [3, 14]. Detecting these characteristics within tumors could lead to improved determination of tumor status and better therapeutic monitoring. A recent study by Li et al. [17] examined the intratumoral vessels and microhemorrhages in patients with histologically proven astrocytomas using SWI in addition to conventional neuroimaging modalities. They found a strong correlation between SWI findings and histopathology and noted that SW imaging was superior to conventional imaging at showing the small vessels and intratumoral hemorrhages. These findings are not surprising as it has previously been shown that gradient recalled echo (GRE) sequences are more suitable than spin echo (SE) based sequences for evaluating tumor vascularity using a contrast agent [18]. Techniques with increased sensitivity to blood products, such as SWI, therefore provide additional clinically useful information when evaluating brain tumors [17, 19, 20]. The ability to image the tumor vasculature is necessary for detection, developmental characterization, and assessment of tumor activity (Figure 10.2). Moreover, novel antiangiogenic therapies currently used to treat malignant gliomas underscore the importance of studying the tumor vasculature [21]. SWI is especially sensitive to venous vasculature, even to vessels smaller than a voxel, due to the blood oxygen level-dependent (BOLD) effect [22]. BOLD effects are independent of integrity alterations of the blood–brain barrier. Therefore, the venous blood pool can be visualized in a resting state without the use of a contrast agent or pharmaceutical agents [23, 24]. One point of caution is that blood products can mimic intratumoral or peritumoral venous structures due to the similar paramagnetic susceptibility effect produced by them [14]. Nevertheless, hemorrhage can be easily distinguished from veins if SWI is performed both before and after administration of a contrast agent. Blood vessels will change their signal intensity, whereas regions of tumoral hemorrhage will appear unchanged. As discussed earlier, microhemorrhages, which occur most often in high-grade tumors, may be helpful for tumor grading (Figures 10.3 and 10.4) [9]. The evolution of intratumoral and peritumoral hemorrhages can be tracked effectively with SWI (Figure 10.5). Deoxyhemoglobin present in cerebral tissues following hemorrhage, has a marked hypointense signal and decreased T2* [25]. With the destruction of red blood cells, the susceptibility effect of both deoxyhemoglobin and methemoglobin disappears, increasing signal on susceptibility weighted images. In later stages, when ferritin and hemosiderin are formed, strong signal cancellation occurs and high susceptibility effects, which are manifested as reduced signal, return. This well known T2* sensitivity to hemorrhage is further enhanced with SWI [1]. Postcontrast T1-weighted imaging is a fundamental sequence in the evaluation of brain tumors. However, extravasation of the contrast agent can often lead to diffuse enhancement of a tumor, thereby resulting in imprecise visualization of the inner structure and vascular components of the tumor. We found SWI to be equivalent to T1 contrast-enhanced images in a majority of cases and it showed lesions better than T1 CE images in some cases [11]. Contrast agent extravasation within the tumor does not normally lead to a major problem when SWI data are interpreted. However, if the contrast agent concentration is high enough, the phase may alias and consequently the phase mask processing may not lead to the expected enhancement of the contrast. The internal architecture of tumors varies significantly between SWI and contrast-enhanced T1 imaging. The internal architecture in postcontrast T1 images is in large part dependent on the presence of necrosis, cysts, and tumor boundaries. In contrast, the internal architecture in SWI is determined mostly by blood products, either from spontaneous bleeding, as commonly seen in high-grade tumors, or from surgical trauma. This difference in image appearance can allow recurrent

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FIGURE 10.2 Cystic high-grade glioma. (a) Axial contrast-enhanced T1 images shows rim of peripheral enhancement that is also clearly depicted on SWI phase image (b). T2* perfusion with rCBV map showing high perfusion in the margins of the cystic lesion (c). SWI mIP images through the inferior aspect of the lesion show tortuous (venous) vasculature. The phase in (b) is from a left-handed system (LHS) where increases in field (for example, in paramagnetic substances like blood- or Gadolinium-based contrast agents) causes an increase in phase. Image quality and contrast may not be optimal due to conversion from color to grayscale display. Please see the color plates section for the original version of this figure.

tumor to be distinguished from postsurgical changes. On SWI images, necrotic regions become high in signal compared to the low signal tumor parenchyma (Figure 10.6). Pinker et al. found that high-resolution contrast-enhanced SWI at 3 T showed better susceptibility effects not visible with standard contrast-enhanced studies [26]. Furthermore, the

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FIGURE 10.3 Right peritrigonal glioblastoma. (a) Axial contrast-enhanced T1 fat saturation image, (b) 2D gradient echo, and (c) SWI. The blood products and the intratumoral vascularity are better visualized on SWI imaging.

presence of intratumoral hemorrhages correlated with tumor grade as determined by PET and histopathology. Overall, SWI represents a very useful noninvasive tool for determining the grading of gliomas and may help to reduce sampling error by helping to identify optimal sites for biopsy. In some cases, because of its high sensitivity to blood products, tumors not detected by conventional sequences can be indirectly identified by SWI. SWI also appears to be useful in identifying the hemorrhagic changes that can be seen following radiation therapy and for assessing response to antiangiogenic therapies for patients with brain tumors [14]. Intratumoral Calcification Many tumors also contain microcalcifications, which are very important indicators in the diagnosis and differential diagnosis of brain tumors. Calcification cannot be definitively identified by conventional MRI because its signals are variable on conventional spin echo T1- or T2-weighted images [27–29], and it cannot be easily differentiated from hemorrhage by gradient echo images because both will cause local magnetic field changes and appear as hypointensities. However, phase images can help differentiate calcification from hemorrhage because calcification is diamagnetic, whereas hemorrhage is paramagnetic, resulting in opposite signal intensities on SWI phase images (Figures 10.7 and 10.8) [30, 31]. Figure 10.9 is a case of a histologically confirmed oligodendroglioma with intratumoral calcification identified by CT. The hypointensity shown on SWI magnitude images cannot be identified as either calcification or hemorrhage. On SWI filtered phase images, the veins along the lateral ventricle and sulci appear dark, which means the hyperintensities inside the tumor are diamagnetic, that is, they are calcifications, rather than hemorrhage. These properties make SWI comparable to CT in terms of imaging intracranial calcium. However, one has to be careful in inferring magnetic properties from visual image information since the phase patterns going along with the lesions depend not only on the susceptibility difference between tissues but also on the geometry of the lesion [31]. Accurate detection of intratumoral calcium can also be very helpful in the differential diagnosis and grading of brain tumors. It is worth mentioning that for a right-handed system, veins will look dark on the phase image (because the deoxygenated blood is paramagnetic relative to its surrounding tissue) and calcium will look bright (because calcium is diamagnetic relative to the brain tissue).

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FIGURE 10.4 Primary CNS lymphoma: (a) Axial 2D FLAIR, shows iso/hypointense peritrigonal lesion, with significant perilesional edema. (b) On contrast-enhanced T1 fat saturation image there is intense enhancement of the tumor (b) noted. (c) SWI mIP shows hemorrhage within the tumor matrix as well as edema around it with the characteristic ‘‘FLAIR-like’’ contrast. (d) The phase image (from a left handed system) confirms the presence of blood products (appearing with a bright signal) within the lesion. Both presence of hemorrhage and extensive peritumoral edema are atypical features of primary CNS lymphoma. Reprinted with permission from Ref. 11 (permission from Springer).

Calcifications appear as hypointense signal on the magnitude images. On the SWI filtered phase images, veins and blood products are shown as hypointense (negative phase) and calcifications are shown as hyperintense (positive phase) for a right-handed system. This dichotomy makes distinguishing the two very simple.

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FIGURE 10.5 Ill-defined right temporal tumor histologically proven to be a glioblastoma. Compared to contrast-enhanced T1 (a), precontrast T1 (b) images, and fast spin echo T2 (d) images, SWI (c) and phase images (e, f ) are more sensitive in outlining areas of both hemorrhage and venous structures and thus can be a useful adjunct in defining the tumor characteristics. The phase images are shown for a left-handed (e) and right-handed system (f ). Reprinted from Ref. 14, with permission from American Journal of Neuroradiology.

Peritumoral Edema Edema on SWI has FLAIR-like contrast (CSF appears with a low signal, while tissue edema appears with a high signal). While the apparent edema signal is not as high as in a FLAIR sequence, the combination of T2* and edema effects within a single image improves lesion detection even without a contrast agent (Figure 10.10). In the future, with higher field strengths and better signal to noise ratio, it will be possible to lengthen the echo time so that the peritumoral edema will be even better visualized than is possible at current echo times. After contrast injection, areas with blood–brain barrier breakdown show enhancement and appear brighter, similar to a T1-weighted sequence. In a few cases, the deposition of high concentration of gadolinium leads to a paradoxical small loss of signal again because of T2* effects (Figure 10.11). This could partly be seen in Figure 10.11c and d and in the phase images (Figure 10.11e and f). Further details on this effect have been described elsewhere [2, 32]. Postoperative and Radiation-Induced Changes As previously described, SWI will be very useful in detecting postsurgical changes in brain tumors (Figure 10.12). The microhemorrhages along the surgical tracts could be detected

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FIGURE 10.6 Left frontoparietal metastasis from primary lung adenocarcinoma. The contrastenhanced T1 (b) compared to the precontrast T1 (a) shows two areas that do not enhance and that likely correspond to necrosis (black arrows). The same areas appear bright on T2 (not shown), enforcing this hypothesis. Postcontrast T1 (b) applied, immediately after contrast administration, does not show the enhancement, whereas contrast-enhanced SWI (d) compared to precontrast SWI (c) shows an increase in signal in the same areas, suggesting late enhancement due a leakage of contrast agent (the postcontrast SWI was performed more than 7 min after the contrast administration). Reprinted with permission from Ref. 2.

even after many years following surgery (Figure 10.13). SWI also appears to be useful in identifying the hemorrhagic changes that can be seen following radiation therapy. When the blood–brain barrier remains intact, postcontrast T1-weighted images fail to clearly demarcate the site of the tumor, since there is no contrast agent leaking out from the vessels and thus the treated lesion will not enhance [33–37]. In this case, SWI can help to detect the existence of postradiation changes by demonstrating the presence of microhemorrhages at the treatment sites. In addition to postradiation cerebral microbleeds, pial siderosis can be detected better by SWI.

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FIGURE 10.7 Right frontal oligodendroglioma: (a) Axial 2D gradient echo sequence shows the hypointense focus within the lesion but does not give any further clue to its nature, which is proved to be calcification on the CT section through the same level (b). However SWI mIP (c) shows the calcification both within the tumor and the venous vasculature around it. The phase image (d ), from a left handed system, confirms the phase difference between calcification within and the venous blood around the tumor. Note that in the left handed system for phase (d ), while calcifications appear with a hypointense phase signal and veins appear with a hyperintense signal (also in Figure 10.8). This contrast is reversed in the right handed system for phase as seen in Figure 10.9. Reprinted with permission from Ref. 11 (permission from Springer).

METASTATIC BRAIN TUMORS SWI can detect edema surrounding metastases and hemorrhage within metastatic lesions. Many cerebral parenchymal metastatic lesions, including those from renal cell carcinoma, melanoma, and bronchogenic carcinoma, frequently show intratumoral hemorrhage (Figures 10.14–10.16) [20].

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FIGURE 10.8 Left frontal meningioma: (a) Axial postcontrast T1 fat saturation, shows the intensely enhancing extraaxial mass lesion with a nonenhancing focus within the lesion that is proved to be calcification on axial CT section through the lesion (b). SWI (c) and phase (d) images, shown for a left handed system, confirm the presence of calcification within the tumor.

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FIGURE 10.9 An oligodendroglioma in the right frontoinsular region. CT (a) shows patchy calcification inside the tumor. SWI magnitude image (b) shows hypointense signal inside the tumor but cannot identify whether the hypointensity is hemorrhage or calcification. On the SWI phase image (c), calcification is identified and matches the CT results well.

Differentiating Intraaxial and Extraaxial Mass Lesions Conventional MR imaging features can differentiate between intraaxial and extraaxial mass lesions of the brain in most cases. SWI can also help differentiate them by demonstrating the shift of venous vessels around the mass [11]. Menon et al. recently described a case of a large well circumscribed lesion in the basal frontal area consistent with an olfactory groove meningioma on conventional MR imaging [38]. The authors noted that SWI showed multiple areas of intratumoral susceptibility signals suggestive of a glial neoplasm. In fact, final histopathology confirmed a gangliocytoma.

Differentiating Cerebellopontine Angle Schwannomas and Meningiomas SWI can also be used to differentiate acoustic schwannomas from cerebellopontine angle meningiomas with the improved detection of microhemorrhages within schwannomas, which are not observed in meningiomas [11, 39] (Figure 10.17). However, meningiomas can show calcification that can be differentiated from microhemorrhages with the help of phase images (Figure 10.8). Schwannomas in other locations also show microhemorrhages [39]. It appears that SWI could be used as an important sequence in differentiating between these two slow growing tumors.

SWI in Differentiating Tumor Mimics SWI can show the perivenular distribution of the demyelinating lesions in multiple sclerosis [14, 40, 41]. This may be especially useful in large tumefactive demyelinating lesions that mimic tumors [41]. Chronic lesions may show evidence of iron deposition within them, which may be better picked up by SWI than by conventional gradient echo sequences. Also, SWI may be useful in understanding the pathophysiology in various tumor-like lesions such as dysplastic cerebellar gangliocytoma (Lhermitte–Duclos disease) [42].

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FIGURE 10.10 Melanoma metastasis. (a) Axial T1 precontrast image: The lesion is barely visible and is without a hint of hemorrhage. (b) Postcontrast T1 image: The lesion shows an intense enhancement, except in a small area that is probably necrotic. (c) PDWI (Protein Density Weighted Image) also showing the same area of probable necrosis with high signal. (d ) SWI postcontrast: Scattered low signal foci are visible that were interpreted to be hemorrhage. The surrounding edema is clearly visible with a FLAIR-like contrast. Both necrosis and blood products were confirmed by pathological examination.

FUTURE APPLICATIONS SWI at higher field strengths is better in detecting blood products due to the increased sensitivity to susceptibility changes. However, one has to be aware of the possible pitfalls due to susceptibility artifacts that can also theoretically be exaggerated at higher field strengths. SWI-based fMRI may be used in the presurgical evaluation of various brain tumors. But the greatest potential of this sequence may be in molecular imaging or in the

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FIGURE 10.11 Acute necrotizing cerebritis (abscess). (a) T1 Precontrast. (b) T1 postcontrast: Strong enhancement sharply delineates the margins of the lesion. (c) SWI precontrast: A marked hypointense rim delineates a part of the lesion suggesting an increased venous vasculature. (d) SWI postcontrast shows a marked hypointense rim on the periphery of the left portion of the lesion, suggesting an increased vasculature (black arrow). The margins of the right portion of the lesion (white arrow) show an internal increase of the signal (relative to that in (c )) that is supposedly due to aliasing (preventing the mask from suppressing the signal properly) and this is confirmed by the phase images pre- (e) and postcontrast (f ) where the aliasing appears bright (white arrow).

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FIGURE 10.12 WHO grade II astrocytoma following surgery. Compared to the T1-weighted image (a), the SWI image (b) shows much more blood products both in the tumor and in the surrounding tissue, the etiology of which may be postsurgical or tumor induced. Note the visibility of the basal ganglia (thick arrow) and even the red nuclei (thin arrow) because of their high iron content.

FIGURE 10.13

WHO grade III mixed anaplastic glioma with previous surgery. Contrast-enhanced T1 (a) and postcontrast SWI (b) do not display the same pattern of internal architecture. SWI clearly shows a hemorrhagic area (large arrow) that likely represents surgical changes, anterior to enhancing tumor. Both sequences show clearly the recurrent, pathologically proven, tumor (small arrows).

FIGURE 10.14 Right occipital renal cell carcinoma metastasis. Contrast-enhanced SWI (c) shows considerably more detail of the internal architecture than T1 postcontrast (a) or Proton Density (PD) (b). Some linear hypointense signals (arrow) suggest radiating veins.

FIGURE 10.15 Solitary brain metastasis from primary lung adenocarcinoma. (a) T1 precontrast: the lesion is barely visible. (b) T1 postcontrast: The lesion shows a strong enhancement especially in its margins. (c) SWI precontrast: The margins of the lesion are clearly visible due to a thin hypointense rim (which supposedly represents veins) and well-visualized edema. (d) SWI postcontrast: The hypointense rim is even darker, surrounded by clear enhancement suggesting a breakdown of the blood–brain barrier in the surrounding white matter. The conspicuity of the lesion is thus markedly increased. Note that contrast-enhanced SWI compared to contrast-enhanced T1 shows more details of the internal architecture of the lesion.

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FIGURE 10.16 Solitary brain metastasis from bronchogenic carcinoma: (a) Axial unenhanced T1 shows left frontal hyperintense lesion, with significant perilesional edema as seen on axial 2D FLAIR (b). SWI (c) confirms the presence of hemorrhage within the tumor. A chest radiograph PA view (d ) demonstrates the source of the metastatic brain lesion to be left upper lobe bronchogenic carcinoma.

MR-based tracking of labeled stem cells. This might have implications in the early diagnosis and further the development of image guided therapy of brain tumors. We anticipate that SWI will lead to improved characterization of brain tumors and one day perhaps using SWI and susceptibility mapping (SWIM) may lead to the quantification of oxygen saturation in blood vessels associated with brain tumors (see Chapter 25). As we gain increasing experience using SWI across multiple centers throughout the world, the optimal role of SWI in brain tumor imaging will be further exploited to its full potential.

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FIGURE 10.17 Right acoustic schwannoma. (a) Axial 2D GRE and (b) SWI minIP. Both show the microhemorrhages within the tumor, but SWI shows them better. Note also the widened right internal auditory meatus (arrow). Reprinted with permission from Ref. 11 (permission from Springer).

CONCLUSION SWI appears to be a useful adjunct to the available MR sequences in characterizing and grading brain tumors. It also helps to differentiate some of the tumor mimics. Future applications of SWI in imaging tumors appear to be quite promising.

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11 Traumatic Brain Injury Karen Tong, Barbara Holshouser, and Zhen Wu

INTRODUCTION In the past 10 years, MR has undergone tremendous advances and demonstrated an unprecedented ability to obtain structural, metabolic, and physiological information of the brain. One of the newest techniques, susceptibility weighted imaging (SWI), has emerged as a promising technique that has immense potential to more accurately assess the severity and regional distribution of injury after traumatic brain injury (TBI). In particular, SWI appears useful for the assessment of diffuse axonal injury (DAI) that is responsible for a wide range of motor and cognitive impairments. TBI continues to be a leading cause of death and disability in the United States. Researchers have referred to TBI as ‘‘a silent epidemic’’ [1], although recently there is greater public awareness of TBI, partly due to returning injured military personnel. The Center for Disease Control (CDC) reports that over 1.4 million people sustain TBI in the United States each year [2, 3]. Although mortality has decreased to 50,000 per year, another 80,000 people annually experience the onset of long-term disabilities following TBI. Currently, 5.3 million Americans (2% of the population) live with long-term disability as a result of TBI. Although a significant proportion of patients with TBI regain ambulatory and self-care skills, many have long-term neuropsychological and behavioral deficits including impaired intellectual abilities (verbal and nonverbal), academic performance, attention, memory, learning, problem solving, processing speed, language, visual perception, and visual motor skills. In 2000, direct and indirect costs of TBI totaled an estimated $60 billion/year [4]. Clinical and neuroimaging assessment of TBI is more difficult than it seems. TBI is a heterogeneous pathology, and clinical variables, including Glasgow Coma Scale (GCS), are inconsistent predictors of clinical outcome. Although neuroimaging has traditionally been used to triage patients, conventional imaging continues to underdiagnose injury. Computed

Susceptibility Weighted Imaging in MRI, By E. Mark Haacke and J€urgen R. Reichenbach Copyright Ó 2011 by Wiley-Blackwell

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tomography (CT) is useful to screen patients for large hemorrhages or other lesions that require emergent surgical intervention [5]. However, CT assessment remains insensitive to many other primary and secondary injuries, some of which can be detected with conventional MRI [6]. Of particular importance, for most diffuse axonal injuries and many mild to moderate injuries, the patients’ neurological symptoms cannot be explained even with conventional MRI and inconsistently correlate with clinical measures such as GCS. In this chapter, we will discuss how SWI has given us the capability to better detect and evaluate primary and secondary injuries. There are two main types of primary brain injury: focal and diffuse injuries [7]. Focal brain injuries are usually caused by direct blows to the head and often result in contusions, brain lacerations, and larger hemorrhages. Many moderate to severe focal injuries result in obvious intracranial bleeding, including epidural hematoma (EDH), subdural hematoma (SDH), subarachnoid hemorrhage (SAH), or focal intracerebral hemorrhage (ICH). Clinical diagnosis of focal brain injuries usually corresponds to the presence of lesions with mass effect in neuroimaging [8, 9]. Similar to CT or conventional MRI, SWI can show focal hemorrhages, but its strength is in its ability to detect microhemorrhages that are not visible by other techniques, particularly those associated with diffuse injuries [10, 11]. Diffuse brain injuries, usually referred to as DAI, are typically caused by a sudden inertial movement of the head, often resulting in strains at the gray–white matter (WM) junction, and are usually manifest by brief cerebral concussions or more prolonged posttraumatic coma, [7]. DAI is a significant and increasingly recognized pathology of brain injury, possibly occurring in 50% of TBI cases. Autopsy studies have shown that DAI has a characteristic injury pattern of diffuse damage to axons in cerebral hemispheres, corpus callosum, brain stem, and cerebellum [12]. Motor vehicle accidents (MVAs) are the major cause of DAI, and a component of DAI is believed to be present in all MVAs where the patient has lost consciousness [13–15]. DAI accounts for 30% of fatal head injuries in patients who survive long enough to reach the hospital [12, 16, 17], but recent reports showed that up to 30% of mild TBI patients can also have DAI lesions on MRI. A significant portion of DAI cases manifest hemorrhagic lesions, although usually much smaller than extraaxial hematomas and hemorrhagic contusions. Pathological data show microhemorrhages that reflect tissue tears accompanying axonal shearing at the boundaries of GM/WM, in the corpus callosum, internal capsule, and brain stem [15]. Despite significant improvement in detecting both hemorrhagic and nonhemorrhagic lesions [18–20], DAI still remains a ‘‘stealth pathology’’ because there are few findings in conventional imaging [21]. Our own data demonstrate that SWI identifies significantly more hemorrhages than conventional GRE sequences in patients suspected of DAI [22, 23], detecting up to six times more hemorrhagic lesions and approximately twice the volume of hemorrhage. This technique, which can be implemented on standard clinical MR scanners and greatly improves the ability to more accurately assess injury after TBI in both adults and children, the latter being a population that frequently is overlooked for study but in whom permanent injury is associated with a lifetime of hardship and disability.

IMPROVED ABILITY OF SWI TO DETECT HEMORRHAGE IN TBI At Loma Linda University Medical Center, we had the unique opportunity and experience to be the alpha test site for SWI in its applications to trauma. During the past 8 years, we have imaged over 400 trauma cases with SWI. In the material to follow, we report on pediatric and

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173

adult studies. SWI has also been implemented in TBI evaluation at Wayne State University for several years. At LLUMC, we initially compared the ability of SWI (1.5 T, Siemens Magnetom Vision) to detect hemorrhage with conventional 2D T2* weighted GRE (gradient recalled echo with steady-state precession; TR/TE ¼ 500/18 ms, flip angle ¼ 15 ) by retrospectively studying seven children and adolescents (mean age 14  4 years) with TBI and presumed DAI admitted to our pediatric or adult intensive care unit (ICU) [24]. Five patients had GCS 8, while two patients had GCS >8. MRI was obtained at a mean of 5  3 (range 3–11) days after injury. Conventional GRE and SWI images were evaluated for hemorrhagic lesions. Mean admission GCS score was 7  4 (range 3–14). In all cases, SWI images showed more hemorrhage than conventional T2* GRE images. There was up to a sixfold increase in lesions and a twofold increase in the total apparent volume of hemorrhagic DAI lesions compared to conventional GRE images. The mean number of lesions for all patients was significantly higher on SWI images (p ¼ 0.004), and the mean apparent hemorrhage volume load for all patients was also significantly greater on SWI images (p ¼ 0.014). All regions showed a greater number of hemorrhagic DAI lesions using SWI compared to GRE. However, absolute difference in lesion count was greatest in the brain stem/cerebellum, corpus callosum, and to a lesser extent in frontal and parietotemporo-occipital GM and WM. The SWI method also revealed much smaller hemorrhagic lesions than the GRE sequence. In most cases, very small lesions were only visible on SWI. On each axial image, the majority of SWI lesions measured 10 mm2 in area, whereas the majority of GRE lesions were in the range of 11–20 mm2 or larger. Lesions that were visible on GRE were often more hypointense on the SWI sequence and therefore more noticeable. This is a result of the 3D acquisition and postprocessing techniques for SWI as described in Chapters 3 and 6. In short, SWI is a high-resolution, 3D gradient echo imaging technique. SWI’s sensitivity to hemosiderin, a by-product of bleeding, has made it possible for us to detect microhemorrhages as small as 0.5 mm3 (1 voxel). SWI is more sensitive to the detection of microhemorrhages compared to conventional GRE and GRE-EPI because of its high resolution and its use of phase information. The local fields produced by hemosiderin lead not only to T2* signal loss but also to changes in phase. The greater visibility of lesions was particularly important when evaluating the brain stem (Figure 11.1). Most lesions in the posterior fossa were small and often nearly invisible on GRE images. However, most hypointense lesions that were visible on both sequences appeared only slightly larger with SWI.

SPECTRUM OF TBI FINDINGS ON SWI Traumatic brain injuries range from focal contusions to diffuse injuries. The manifestations of these various pathologies have different appearances on imaging, including SWI. Figure 11.2 shows examples of the various imaging findings that can be seen in TBIrelated injuries on SWI, each of which is discussed separately. Contusions Contusions typically occur along the periphery of the brain, most commonly along the frontal and temporal lobes (Figure 11.2c, d, f—black arrows). They can range in size

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FIGURE 11.1 Images from a comatose TBI patient. Conventional GRE (a) and SWI (b) images at the level of the midbrain, where small hemorrhages are best seen on the SWI images (long white arrows). These hemorrhages were thought to explain the prolonged impairment of consciousness. Small hemorrhages in the temporal lobes are also more visible on the SWI images (small white arrows). Hemorrhages are poorly demonstrated on the GRE images (black arrows). Reprinted from Ref. 11, with permission from Elsevier Science.

from several millimeters to several centimeters and are often heterogeneous in signal. The dark areas are representative of hemorrhage, whereas surrounding or adjacent bright signal reflects associated edema. Contusions can be due to direct injury, often found deep to a focal area of scalp swelling. Contrecoup contusions are often found contralateral to the side of the scalp swelling. Gliding contusions can also occur at the inferior surface of the frontal lobes or anterior surface of the temporal lobes (Figure 11.2f; black arrow), as the brain can impact the adjacent skull, which is more irregular in these regions. Some small contusions near the skull may be difficult to delineate on SWI due to bone artifact. However, in many cases, SWI can demonstrate hemorrhagic contusions that are not visible on CT or conventional MRI sequences.

Microhemorrhages Associated with DAI DAI can be associated with hemorrhages, due to tearing of capillaries, and are typically found at the junction of the gray and white matter (Figure 11.2a; black arrows) of the cerebral hemispheres or within the corpus callosum (Figure 11.2b; black arrow). They can also occur in the brain stem, usually within the midbrain (Figure 11.1). The hemorrhages are typically very small and punctate in size (microhemorrhage) but can occasionally be large, especially if located in the deeper gray matter (GM) regions (see below). SWI is particularly helpful in detecting these traumatic microhemorrhages, often showing a multitude of more lesions than suspected (Figure 11.3).

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175

FIGURE 11.2 SWI images from a severe TBI patient. High-resolution SWI allows better detection of lesions, even in brain regions close to the skull and regions such as the brain stem that are not normally possible with conventional MRI.

Deep Gray Matter Hemorrhages Although less common, hemorrhages can occur in the deep gray nuclear regions (Figure 11.2c; within ellipsoid) of the cerebral hemispheres. These may be due to tears of the perforating arteries, associated with DAI, as white matter tracts inevitably traverse these structures, or the hemorrhages may be due to secondary stroke mechanisms. These hemorrhages tend to be larger than traumatic microhemorrhages at the gray–white matter junction. SWI can also be helpful to delineate these larger hemorrhages, as well as increased oxygen extraction at the margins of ischemic areas (Figure 11.4d). Subarachnoid Hemorrhage Traumatic subarachnoid hemorrhage (tSAH) is common in TBI, occurring in 39–41% of TBI patients [25, 26]. Traumatic injury to the head results in stretching, tearing, and laceration of the blood vessels coursing within the subarachnoid space. As a result, blood enters the subarachnoid space and mixes with the CSF. Subarachnoid hemorrhage mostly accumulates in the brain cisterns, but it can appear in the sulci and fissures of the brain. Intraventricular hemorrhage can also be seen with the presence of subarachnoid

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FIGURE 11.3 Hemorrhagic lesions in a 16-year-old TBI patient. CT (a), T1 (b), T2 (c), GRE (d) images easily demonstrate the large lesions in the bilateral frontal lobes and some of the small lesions in the parietal lobes. However, SWI images at the same level (e) and at a lower level (f) clearly demonstrate numerous microhemorrhages that are not visible on the other images.

hemorrhage, as the CSF spaces are communicating compartments. The extent and amount of subarachnoid hemorrhage have significant correlation with the clinical severity at presentation and outcome. Diffuse tSAH has been shown to strongly correlate with poor outcome [26–29]. Different CT grading scales have been proposed to grade tSAH [29–31]. The ability of CT to detect SAH depends on the amount of hemorrhage, the interval after trauma, the resolution of the scanner, and the skills of the radiologist [32]. A multicenter assessment of the accuracy of CT detection of tSAH showed a high interobserver variability [33]. We recently collected both MRI and CT data at Huan Hu Hospital, Tianjin, China, of 24 acute TBI patients (ranging in age from 8 to 74 years) with SAH detected by CT. The initial CTwas obtained within the first 4 days after trauma and MRI was obtained within 15 days of the trauma. We compared the SWI and CT data and found that SWI is also very sensitive in identifying SAH. We focused on regions such as cerebral convexity, basilar cisterns, interhemispheric fissure, Sylvian fissure, and intraventricular hemorrhage. We determined that SWI is more sensitive than CT in demonstrating very small amounts of SAH, especially intraventricular hemorrhage. As shown in Figure 11.5, SWI showed excellent contrast between dark intraventricular hemorrhage and less dark CSF or bright surrounding

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177

FIGURE 11.4 Prominent veins associated with traumatic infarct in a 3-year-old boy ejected in a motor vehicle accident. GRE (a) shows large hemorrhage in the right basal ganglia. SWI (b) better demonstrates smaller hemorrhages within the left basal ganglia and thalamus. FLAIR (c) shows edema (black arrows) in the upper periphery of the right hemisphere. SWI at this level (d) shows prominent ipsilateral deep medullary veins (arrows), suggestive of increased oxygen extraction resulting in higher levels of deoxyhemoglobin. DWI (e) and ADC map (f) confirm infarction associated with diffusion restriction (white arrows). Part of the figure reprinted from Ref. 10, with permission from American Journal of Neuroradiology.

parenchyma. When SAH insinuates into the depths of sulci, it can be difficult to distinguish from normal small veins. However, we found that in this group of patients SAH tended to be thicker and have a rougher boundary than normal veins, sometimes even showing a characteristic triangular pattern (which we have named the ‘‘triangle sign’’) (Figure 11.6), which indicates hemorrhage filling the subarachnoid space [34]. Because of artifact around the air–tissue interfaces on SWI, we assumed that SWI would have difficulty demonstrating SAH in the basilar cistern. However, as shown in Figure 11.7, hemorrhage accumulating in the prepontine cistern was seen very clearly. The signal from CSF surrounding hemorrhage helps to delineate SAH from bone or artifact created by air–tissue interfaces. SWI has some limitations in the inferior frontal regions, where susceptibility artifact occurs. However tSAH can be easily seen in cerebellar sulci (Figure 11.2; e - circle, f - ellipsoid). In summary, SWI is complementary to CT in detection of tSAH and can improve the accuracy of outcome prediction, given that tSAH is strongly correlated with a poor prognosis. Subdural Hemorrhage Subdural hemorrhage is more difficult to visualize due to the difficulty in distinguishing this from the adjacent skull, unless the hemorrhage is large or has heterogeneous signal. This is

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FIGURE 11.5

Examples of intraventricular hemorrhage better delineated by SWI. In the first case (a: CT, b: SWI), CT only showed hemorrhage in the left occipital horn but missed the hemorrhage in the right occipital horn. In the second case (c: CT, d: SWI), CT missed the intraventricular hemorrhage in both occipital horns. Reprinted from Ref. 34, with permission from American Journal of Neuroradiology.

a disadvantage of the SWI sequence in trauma evaluation, although subdural hemorrhages are usually easily seen on other sequences, particularly FLAIR. However, sometimes SWI (or SWI phase) can visualize SDH. Sometimes SDH will appear bright in both T1 weighted and SWI images. Cerebral Ischemia Cerebral ischemia can occur in the setting of trauma, such as from global hypoxic injury or focal infarction due to emboli or dissection. Diffuse brain edema from increased intracranial

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179

FIGURE 11.6 The SWI features of SAH over the cerebral convexity that appears as a triangle of hypointense signal, as indicated by the arrows. (a, b are CT and SWI of the same patient; c, d are SWI of two other patients). Figure (d) also shows SDH on the right frontal area (dark arrow head). Adapted from Ref. 34, with permission from American Journal of Neuroradiology.

FIGURE 11.7 Hemorrhage in the prepontine cistern in a TBI patient (a: CT, b: SWI). SWI from a normal subject (c) shows the normal cistern without SAH. Part of the figure reprinted with permission from Lippincott Williams & Wilkins.

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FIGURE 11.8 Images from a child with severe TBI and severe cerebral edema prior to brain death. Axial T2 (a) shows diffuse cortical edema and sulcal effacement. Axial SWI (b, c) shows scattered hemorrhagic shearing injuries in the frontal white matter and the corpus callosum. In addition, there are prominent deep medullary veins throughout the bilateral hemispheres (thin white arrows), suggesting increased oxygen extraction. Sagittal T1 image (d) shows diffuse sulcal and cisternal effacement and tonsillar herniation (wide white arrow). AP view of nuclear medicine brain scan (e) shows blood flow in the face, minimal blood flow in the superior sagittal sinus (black arrow), and absence of blood flow in the brain. Axial CT perfusion CBV map (f) shows absence of identifiable blood in the brain, and only noise. Part of the figure reprinted from Ref. 10, with permission from American Journal of Neuroradiology.

pressure can also result in decreased cerebral perfusion and secondary global ischemia. In these cases, decreased oxygenation of the brain can result in a greater ratio of deoxyhemoglobin to oxyhemoglobin in the venous vasculature, either directly or secondary to increased extraction of oxygen by the brain tissue. As a result, the veins may become even more prominent in these areas (Figure 11.8). SWI AND CORRELATION WITH TBI CLINICAL VARIABLES We evaluated 40 children and adolescents with TBI and clinically suspected DAI (mean age 12 years; MRI obtained 7  4 days after injury) with SWI and compared hemorrhagic lesions to clinical variables. Children with lower Glasgow Coma Scale scores (8, n ¼ 30) or prolonged coma (>4 days, n ¼ 20) had a greater average number (p ¼ 0.007) and volume (p ¼ 0.008) of hemorrhagic lesions [35]. At Wayne State University, SWI images were also collected on a group of wellcharacterized, (n ¼ 16) nonpenetrating TBI patients who ranged in chronicity (from

COMPARISON OF SWI TO OTHER IMAGING METHODS

181

lesion volume versus PTA Yt = 62.446307254 + 21.47687924611 xt 3018

lesion volume

2518

2018

1518

1018

518

18

0

10

20

30

40

50

60

70

80

90 PTA

FIGURE 11.9 Relationship between SWI lesion volume (mm3) and PTA (days).

3 days to 15 years post-TBI) and severity (mild to severe by admission GCS). A semiautomated method of lesion segmentation was used that involved statistical comparison (Z-score) of TBI images to an SWI atlas that was an averaged image from 14 normal controls, each spatially normalized into MNI305 space. A variance map was also created from the 14 controls. Correlations between SWI lesion burden with GCS and number of days of posttraumatic amnesia (PTA) were found (Figure 11.9). Spearman correlation with PTA was r ¼ 0.54 and with GCS was r ¼ 0.39.

COMPARISON OF SWI TO OTHER IMAGING METHODS In our study group of 40 children and adolescents, we also compared SWI with other conventional imaging methods (CT, T2WI, and FLAIR) [11]. Although each imaging technique used in this study has unique detection capabilities, many more lesions (of any form of parenchymal injury) were demonstrated on SWI (Figures 11.10 and 11.11) compared to CT, T2WI, and FLAIR. The least sensitive study, CT, showed no significant differences in mean lesion number and volume between outcome groups, whereas the mean number and the volume of lesions of any type seen with MRI techniques could differentiate between good and poor outcome groups. Contrary to previous observations that CT was comparable to MRI for detection of hemorrhage, in this study we found that the number of hemorrhagic lesions seen on SWI could better differentiate patient outcomes compared to the number of hemorrhagic lesions detected on CT. This is due to the increased sensitivity of SWI for detecting small hemorrhagic lesions.

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FIGURE 11.10 17-year-old male, 1 day after a motorcycle accident. CT (a) was normal. Focal edema in the corpus callosum (open arrow) is best seen on T2WI (b) and FLAIR (c). A small hemorrhagic shearing injury is also seen in the left frontal WM (white arrow), although better seen on GRE (d) and SWI (e). Many more small hemorrhagic lesions (solid black arrows) are seen only on SWI. Reproduced from Ref. 37. (Permission from American Journal of Neuroradiology).

ABILITY OF SWI TO PREDICT LONG-TERM NEUROLOGICAL OUTCOME IN TBI Pediatric Studies In this same group of 40 pediatric patients, the number and volume of hemorrhagic lesions were compared to long-term neurological outcome assessed using the Pediatric Cerebral Performance Category Scale (PCPCS) score [35]. The PCPCS score is a 6-point outcome scoring system modified from the Glasgow Outcome Scale (GOS) score that quantifies overall functional neurological morbidity and cognitive impairment of infants and children. Children with normal outcomes or mild neurological disability (n ¼ 30) at 6–12 months after injury had significantly fewer number (p ¼ 0.003) and volume (p ¼ 0.003) of hemorrhagic DAI lesions than those who were moderately or severely disabled or in a vegetative state. We also determined that there were regional differences in DAI injury. Over 90% of patients had lesions in parietotemporal-occipital GM, parietotemporal-occipital WM, and frontal WM. Four regions were less commonly affected (i.e., 2 on any one reading (Table 12.3). The trend of MCI cases with elevated CMB counts on entry (7 cases) was for progressively increasing counts over the study period that correlated with a progressive dementing clinical course. The majority of all subjects classified at baseline as MCI (90.6%), or ‘‘normal’’ (100%), had no significant CMB on entry into the study (n  1). This finding may reflect the bias in our selection process of excluding subjects with potential CMB confounders, for example, diabetes, ischemic cerebrovascular or cardiac disease, head trauma, poorly controlled hypertension, iron metabolic disorders, and smoking. Ethnicity, Asian versus non-Asian, is not reported to be a risk factor for CMB prevalence in ‘‘healthy’’ adults, but is a risk factor for Asians in hypertension clinics [6]. The prevalence (n > 1) of CMBs in the elderly normal group on entry was 0%, whereas the baseline MCI group had a prevalence of 9.3% (7/75). The prevalence of CMB in the progressively dementing MCI (PMCI) group is 33.3% (6/18), which is consistent with previous reports using GE-T2* at 1.0–1.5 T. The enhanced sensitivity of SWI for CMB detection may account for the observed CMB prevalence (33%) in the demented cohort over that reported in previous studies of AD 26.8% (95% CI 19.0–36.4%) [19, 20] (Table 12.4). CMBs were found to be clustered principally in subcortical positions in posterior parietal, temporal, and occipital lobes in the progressively demented cases with a size distribution that is mainly 1–3 mm O.D. (95% of CMB). 3% of the CMB are 4–5 mm O.D., 2% >5 but 1 on either the first or last evaluation, and disease as progression to dementia (PMCI). In the cohort classified as MCI at baseline (those considered to be at risk), the unadjusted risk of

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TABLE 12.2 Demographics and Neuropsychological Profile of MCI and Control Participants at Entry

Sex Female Male Age at enrollment (years) Education (years) Ethnicity Non-Hispanic White African American Hispanic American Indian Other

MCI (n ¼ 75)

Normal (n ¼ 28)

31 (41.3) 44 (58.7)

17 (64.3) 11 (35.7)

0.06

75.8 (54–88) 14.2 (6–20)

72.4 (54–84) 14.3 (9–20)

0.03 0.83

67 (89.3) 2 (2.7) 5 (6.7) 1 (1.3) 0

21 (75.0) 1 (3.6) 4 (14.3) 1 (3.6) 1 (3.6)

NA

Normal Borderline MCI

27.22 (22–30) 18 (24.0) 5 (6.67) 52 (69.3)

29.11 (26–30) 27 (96.4) 1 (3.6) 0

Normal MCI

0 75 (100)

27 (98.7) 1 (0.30)

> > > 0 13 > > > >   > 1 Ri > 2 > < ðwi we Þ  B0  3 cos u3D 1  @ A ; 3 r Bz ðrÞ ¼ > > > 0 13 0 13 3 2 > > >1 >   R > i > 4ðwi we Þ  @ A þ we  @Re A 5  B0  3 cos2 u3D 1 ; > > :3 r r

when r < Ri when Ri < r < Re

when Re < r ð24:18Þ

where wi is the susceptibility of the inner sphere (the hollow region), we is the susceptibility of the shell region, and u is the angle between the main magnetic field B0 and the position vector of the point under consideration. We take wi ¼ 0 and we ¼ 9.5 ppm, and the analytic field due to the spherical shell was evaluated using equation (24.18) from which the consequent phase at echo time 1 ms and field strength 1.0 T was then calculated. To simulate the sresidual_phase minimization process for estimating actual effective Dw for the given geometry, phase due to the shell geometry was calculated, using equation (24.17), with Dw varied from 4 to 16 ppm in steps of 1 ppm. Between 9 and 11 ppm, the step size was reduced to 0.1 ppm to improve the accuracy of the determination of Dw. The calculated phase, for each value of Dw, was subtracted from the analytic phase (calculated using equation (24.18)) through complex division to obtain 31 sets of residual phase map volumes. Standard deviation of the residual phase, sresidual_phase, from roughly 7000 (and a smaller subset of 1000) voxels close to the inner sphere in each phase set, was evaluated and plotted as a function of Dw. The value corresponding to minimum sresidual_phase was the estimate of the desired Dw value. Two regions were evaluated to see the effect of VOI size on sresidual_phase minimization process. The 1000 voxel VOI is a subset of the 7000 voxel VOI. Simulation Results A volume of interest of 6728 voxels around the sphere in the simulation was used to mimic roughly how many voxels would be available in human studies near the sinuses/cavities. The results of the sresidual_phase minimization, within this

APPLYING THE INDUCED FIELD CALCULATION FOR CORRECTING SWI PHASE DATA

435

0.12 0.025 0.02

0.1

0.015

0.08

0.01 –11.1

–10.3

–9.5

–8.9

0.06

0.04

0.02

0

VOI-6700 VOI-1024 –16

–14

–12

–10

–8

–6

–4

FIGURE 24.9 Simulation Result: Plot of the residual phase vs. corresponding values. Results of analysis from two volumes of interest (VOIs), one containing 6700 voxels and another containing only 1024 voxels (a subset of the former VOI) are plotted. The inlet shows a zoomed version of the plot between w ¼ 8.9 ppm and w ¼ 11 ppm. Both plots predict a minimum at w ¼ 9.8 ppm (actual value w ¼ 9.5 ppm).

VOI, for finding the susceptibility difference between the shell and the surrounding region are shown in Figure 24.9. The Dw value corresponding to the minimum sresidual_phase value is at 9.8 ppm. The precision of this result is limited by the step size of Dw used in the minimization process, which was 0.1 ppm. This simulation does not consider the effect of noise. However, since noise is additive in nature, it will influence only the minimum attainable sresidual_phase value and does not affect the Dw at which this minimum occurs (assuming we have an SNR of at least 5:1). Figure 24.9 also shows the result from a subset of the former VOI, containing only 1024 voxels to point out the reduced chi-square error achieved from a smaller VOI. Results in Phantom Figure 24.10a shows the plots of sresidual_phase as a function of Dw value, for both Ggre and Gswi geometries. The Dwair_gel corresponding to minimum sresidual_phase for Ggre is 9 ppm, whereas for Gswi it is 6 ppm. This difference clearly shows the influence of the echo time on the estimated effective Dwair_gel that is to be used with the corresponding geometry for correct phase calculations. Figure 24.10c and d shows the two GDAC phase images generated by subtracting the phase predicted using Dwair_gel ¼ 9 ppm with Ggre and Dwair_gel ¼ 6 ppm with Gswi from SWI phase images. Although the result from Dw ¼ 6 ppm still contains some remnant aliasing, the result from Dw ¼ 9 ppm has removed almost all the aliasing in the vicinity of the sphere arising due to air–gel interface. The corresponding HP filtered phase images demonstrate the dramatic improvement in the GDAC phase images. Moreover, Figure 24.10i shows that even a mild filter can be employed to remove most of the remaining rapid phase aliasing. Figure 24.11 illustrates the effect of using the GDAC phase as opposed to the original phase in generating pSWI images.

436

RAPID CALCULATION OF MAGNETIC FIELD PERTURBATIONS

FIGURE 24.10 a) sresidual_phase vs. Dw plot for Ggre and Gswi showing the values with minimum error, i.e., effective Dwair_gel, are at 6 ppm for Gswi and at 9 ppm for Ggre; b) Original SWI phase image (TE 40ms); c) GDAC phase image obtained after subtracting the phase predicted using 9 ppm and Ggre from (b); d) GDAC phase image obtained after subtracting the phase predicted using 6 ppm and Gswi from (b); e) corresponding magnitude image; f) result of HP filtering (b); g) result of HP filtering (c); h) result of HP filtering (d); i) result of high pass filtering (c) using filter size 32  32. In all other cases a filter size of 64  64 was used.

The strong aliasing from the original SWI phase images causes terrible phase artifacts in the HP filtered images, leading to a concomitant artifact in the pSWI images (see Figure 24.11b). However, the pSWI image generated using GDAC phase (using Dwair_gel ¼ 9 ppm with Ggre) is devoid of such artifact (Figure 24.11c). Nevertheless, errors in the definition of the object at the boundary at different locations (typically single voxel errors) cause erroneous local dipolar field and hence erroneous additional local phase at these locations. When this predicted phase is subtracted from SWI phase images, this extra phase gets introduced in the resultant GDAC phase images. This eventually leads to erroneous ‘‘signal loss artifact’’ on the boundary of the object when these HP

PHASE CORRECTION IN HUMAN DATA

437

FIGURE 24.11 Comparison of the minimum intensity projections over 4 slices of; a) original SWI magnitude; b) processed SWI magnitude (phase mask multiplication) using high pass filtered original phase images with filter size 64x64; c) processed SWI magnitude using high pass filtered GDAC phase images (calculated using Dw ¼ 9 ppm with Ggre). The SWI processing using the improved processing removes most of the unwanted rapid aliasing artifacts while enhancing the sub-pixel air bubbles. Image (d) shows that much of the spurious signal loss at the edge of the phantom seen in (c) can be removed by using a combination of HP filtered GDAC phase and HP filtered original phase information.

filtered GDAC phase images are used to generate pSWI images (see edges of the phantom in Figure 24.11c). Conversely, there is no such erroneous local dipolar phase in the original SWI phase images or in the HP filtered original phase images. Combining the information in the HP filtered original phase and the HP filtered GDAC phase, by choosing minimum absolute phase between the two, one can generate a better HP filtered phase image and consequently an improved susceptibility weighted magnitude image as shown in Figure 24.11d.

PHASE CORRECTION IN HUMAN DATA Having validated in simulations and phantom results that the field estimation method based on equation (24.17) can be used for correcting geometry-dependent phase artifacts, our goal in this section is to show that the same procedure can be employed in human SWI images to correct the dramatic phase effects near the sinus–tissue interface. Materials and Methods Three healthy volunteers were imaged in a 1.5 T Siemens Sonata magnet with the sequence parameters given in Table 24.2. Informed consent was obtained from all the volunteers in accordance with the Wayne State Institutional Review Board guidelines. Slightly different parameters were used in different volunteers due to magnet time constraints. The key parameter differences that might influence the results are the ones in echo time and bandwidth of the T1-weighted sequence, which are dealt in the ‘‘discussion’’ section. However, despite these possible influences, it is shown that improvements with the new processing are significant. The T1-weighted complex data obtained at two TEs in each volunteer were used to create phase images with an effective TE of 1 ms in volunteers 1 and 2 and a TE of 2 ms for volunteer 3 by complex division. The magnitude image from the T1-weighted data with the shortest echo time was used to obtain the geometries of the head and relevant air cavities in each volunteer.

438

RAPID CALCULATION OF MAGNETIC FIELD PERTURBATIONS

TABLE 24.2 List of imaging parameters used for the three volunteers Imaging Parameters Volunteer 1 3D T1-weighted rf spoiled gradient echo sequence TR in ms 20 TE in ms 5 and 6 FA in degrees 20 Resolution in mm (read x phase x slice) 1 1  2 BW (Hz/pixel) 400 slices 128 SWI TR in ms 50 TE in ms 40 FA in degrees 20 Resolution in mm (read  phase  slice) 1 1  2 BW (Hz/pixel) 400 slices 112

Volunteer 2

Volunteer 3

15 5 and 6 20 1 1  2 400 128

15 7 and 9 20 1 1  2 255 128

44 40 20 1 1  2 260 80

45 40 20 1 1  2 255 88

The magnitude 3D T1-weighted gradient echo data acquired at the shortest echo time, 5 ms for volunteers 1 and 2 and 7 ms in volunteer 3, were used to extract geometries of maxillary, frontal, sphenoid, ethmoid, maxillary sinuses, mastoid cavity (a signal void due to the presence of bone and air cells) and of the head. Similar to the phantom case, the complex threshold method (CTM) algorithm [18] was used to distinguish noise pixels from signal. Voxels identified as tissue voxels were assigned a value of unity and those identified as sinus or cavity regions to a value of zero. Although the algorithm was successful in identifying the sinuses/cavity regions automatically, some manual intervention was required around the skull and near the sinuses to avoid sharp edges in the boundaries. The geometry of the whole head up to the jaw and neck regions was included for field calculation as it has been shown that inclusion structures beyond the neck region (i.e., shoulder and torso geometry) does not appreciably change the calculated field perturbation values in the brain region [13]. Figure 24.12 shows axial (a–c) and saggital (d) views of the geometry extracted from volunteer 2. To estimate the Dw values between different sinuses and brain tissue, Dwsinus–tissue ¼ wtissue  wair, and between the brain tissue and mastoid cavity, Dwmastoid–tissue ¼ wtissue  wmastoid, the extracted geometries were used to simulate phase at 1 ms, for volunteers 1 and 2, and at 2 ms for volunteer 3, using equation (24.17) with varying w values of the brain tissue from 2 to 16 ppm. A value w ¼ 0 was assigned to the sinuses, mastoid cavity, and the region outside the head. With brain tissue predominantly containing water, its w value with respect to air is generally expected to be in the neighborhood of –9 ppm. However, the primary reason for sampling such a broad range of Dw for either Dwsinus–tissue and Dwmastoid–tissue was that it is well known that the sinuses (which include the frontal, ethmoid, sphenoid, maxillary, and nasal cavity) predominantly contain air but the mastoid region is known to have both bone and air. Consequently, it is reasonable to anticipate that the mastoid cavity might have a different Dw value with respect to brain tissue compared to Dw between sinuses and brain tissue. The simulated phase was complex divided into the corresponding 1 or 2 ms effective TE phase data to generate 15 residual phase map volumes for each volunteer. The phase in the immediate vicinity of an air space is predominantly influenced by the susceptibility difference between that air space and the brain tissue. Hence, the

PHASE CORRECTION IN HUMAN DATA

439

FIGURE 24.12

(a, b, and c) Axial images of the sinus and mastoid cavity geometry extracted from magnitude images of Volunteer 2; (d) Sagittal view of the extracted air-space geometry. Figures (e), (f) and (g) illustrate, how image (c), containing multiple air-spaces can be represented as the sum of the individual air-space structures and the sinuses.

sresidual_phase from two volumes of interest, one chosen in close proximity to the sinuses and the other chosen in close proximity to the mastoid cavity, was evaluated and plotted as a function of the Dw value. On average, the two VOIs chosen contained 6000 voxels in each. The Dw values corresponding to the minimum sresidual_phase were taken as the required Dwsinus–tissue and Dwmastoid–tissue values. Modified SWI Phase Processing For each volunteer, the phase at TE ¼ 40 ms was calculated using equation (24.17) and the estimated susceptibilities. This estimated phase was subtracted from the original SWI phase images through complex division to obtain GDAC phase images. GDAC phase and the original phase images were subsequently used for generating the corresponding processed SWI magnitude images, GDAC-processed SWI (pSWI) and the original pSWI, respectively. Their results were qualitatively compared for the amount of brain signal recovered using the GDAC phase compared to the original phase. Furthermore, it has been shown that unwrapping the original phase images and subsequent high-pass filtering can provide better HP filtered phase images and consequently produce better pSWI magnitude images [21]. Similar to the original phase images, GDAC phase images can also be used as input for any of the existing phase unwrapping algorithms. Since most of the rapid aliasing near air–tissues interface is already removed, using GDAC phase should provide an improved result in such processing as well. To validate this, a simple two-dimensional least squares phase unwrapping algorithm [22] was applied on both the original phase and the GDAC phase images. The results were subsequently HP filtered to generate the respective pSWI images. The resultant pSWI images generated using unwrapped, HP filtered original phase images are denoted as U-original-pSWI and those generated using unwrapped, HP filtered GDAC phase images

440

RAPID CALCULATION OF MAGNETIC FIELD PERTURBATIONS

FIGURE 24.13 Flow chart of the steps involved in the new SWI processing. pSWI refers to processed susceptibility weighted magnitude images. The resultant pSWI images obtained using HP filtered original phase (original-pSWI) and those obtained using HP filtered GDAC phase (GDAC-pSWI) are qualitatively compared. Similarly, pSWI images obtained using unwrapped-HP filtered original phase (U-originalpSWI) and those using unwrapped-HP filtered GDAC phase are also compared.

are denoted as U-GDAC-pSWI. A qualitative comparison of U-original-pSWI and UGDAC-pSWI was done by evaluating the amount of brain signal retained using GDAC phase compared to the original phase. A flowchart delineating the steps involved in the new processing is shown in Figure 24.13. Human Imaging Results Two volumes of interest containing, on average, 6000 voxels each were selected in each volunteer in the vicinity of the mastoid cavity (adjacent to the tissue–air space boundary) and the sinuses. Figure 24.14 shows the plot of sresidual_phase versus Dw values for each of the three volunteers. The Dwsinus–tissue value corresponding to the minimum sresidual_phase is equal to 11 ppm for volunteer 1, 13 ppm for volunteer 2, and 7 ppm for volunteer 3. The Dwmastoid–tissue values are 7 ppm for volunteer 1, 6 ppm for volunteer 2, and 5 ppm in volunteer 3. Figure 24.14d illustrates the regions where the volumes of interest were chosen. The results show that the effective Dwsinus–tissue is considerably different from Dwmastoid–tissue value in all three volunteers. Furthermore, these values also change from volunteer to volunteer. The quantified Dwsinus–tissue and Dwmastoid–tissue were then used to predict the phase at 40 ms echo time. Figure 24.15 shows the simulated phase, the SWI phase image, and the corresponding GDAC phase images in these volunteers. Most of the aliasing due to the air spaces is removed in GDAC phase images (Figure 24.15c, e, and i) after the subtraction of simulated phase from the SWI phase images. Figure 24.16b shows the phase at 40 ms due to air–tissue interfaces in volunteer 2, calculated using the estimated Dw values (same image shown in Figure 24.15d). Almost all the geometry-induced background phase and the resulting aliasing are removed in the GDAC phase image, generated by complex dividing SWI phase images by the calculated

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441

FIGURE 24.14 Plot of sresidual_phase vs. Dw for volunteers 1 (a), 2 (b) and 3 (c). Values for both Dwsinus-tissue and Dwmastoid-tissue are plotted. The value of Dw corresponding to the minimum sresidual_phase is considered for phase estimation. d) Representative examples of regions of interest (ROI) from 3 slices are shown which are part of the VOIs chosen. Left and right images in (d) show two ROIs chosen in the vicinity of the mastoid cavity and the middle image shows an ROI chosen in the vicinity of the sinuses.

phase. Figure 24.16e shows the improvement in the HP filtered GDAC phase image when compared to the HP filtered original phase. This translates to a significant improvement in the corresponding pSWI images (Figure 24.16h) and makes it possible to properly process the frontal and midbrain regions and visualize the veins in these regions better. Figure 24.17 shows the improvement in the visualization of vessels in the frontal region of the brain that were heretofore obscured by the conventional SWI processing. Despite the potential error in estimating Dw, the results after phase subtraction are devoid of most of the rapid aliasing near the air–tissue interface. Further, high-pass filtering removes any remnant low spatial frequency aliasing, giving much smoother phase images and consequently better pSWI images. Figure 24.18 shows results from all three volunteers. The images are taken from three different levels of the head along the craniocaudal axis to show that considerable improvement in the image quality is obtained in all volunteers and in multiple regions of the pSWI images by using GDAC phase. The result of using first phase unwrapping and then HP filtering for generating pSWI images is shown in Figure 24.19. There is improvement in the image quality when the GDAC phase is used (Figure 24.19b) compared to when original phase image is used (Figure 4.19a). The histogram plot, Figure 24.19d, of the region shown in images a and b shows the number of voxels recovered in the U-GDAC-pSWI image compared to the U-original-pSWI.

442

RAPID CALCULATION OF MAGNETIC FIELD PERTURBATIONS

FIGURE 24.15 (a, d and g) Simulated phase images for volunteer 1, 2 and 3 respectively, calculated using their corresponding quantified Dw values; (b, e and h) Corresponding SWI phase images; (c, f and i) Corresponding GDAC phase images obtained after complex subtraction of original (a, d and g) from (b, e and h) respectively.

DISCUSSION The ability to remove the unwanted background fields, especially the deleterious effects of geometry-dependent fields from air–tissue interfaces, has relied on the use of a high-pass filter approach that assumes that all background phase errors are low spatial frequency in nature. Although the results to date have been reasonable in some parts of the brain, there have been problems in the midbrain and near the sinuses. Removing rapid phase aliasing

DISCUSSION

443

FIGURE 24.16 a) Original SWI phase image; b) predicted phase at 40ms from the head geometry using the quantified Dw values; c) result of complex subtraction of (b) from (a); d) result of HP filtering (a); e) result of HP filtering (c); f) corresponding unprocessed magnitude SWI image; g) pSWI image generated using phase mask from (d); h) pSWI image generated using the phase mask from (e); i) result of subtracting (g) from (h). The arrow heads point to the region of the midbrain where considerable signal is retained in the pSWI image using the GDAC phase. Corresponding magnitude and phase images have been adjusted to the same contrast levels. Unless mentioned otherwise, the size of the high pass filter is 64x64. These images are from volunteer 2.

444

RAPID CALCULATION OF MAGNETIC FIELD PERTURBATIONS

FIGURE 24.17 (a and c) Original-pSWI images (b and d) GDAC-pSWI images. The venous vessels, otherwise obscured by the conventional SWI processing, are now clearly visible using the modified SWI processing. The arrow heads point to the regions where considerable improvement is seen in the GDACpSWI images. Images (a) and (b) are mIPped over 4 slices (8mm), whereas images (c) and (d) have a thickness of 2mm and all of them are from volunteer 1.

near sinuses using the geometry information can facilitate use of a milder filter leading to better contrast and more accurate local phase information. By removing this geometrydependent phase or reducing its effects, this method opens the possibility for SWI to become a viable technique in other areas in the body as well, such as in imaging of spine, breast, knee, and perhaps even in the heart. In the data presented here, care has been taken to have the slice orientation in the acquired images strictly perpendicular to B0, such that the slice direction becomes the direction of B0. However, in practical clinical imaging scenario, slice orientation is often aligned along an imaginary line joining the anterior commissure (AC) and posterior commissure (PC) in the brain (AC-PC line). Under such circumstances, when the normal direction to the slice is not along B0, the angle between slice normal direction and B0 will have to be taken into account in the field calculation formula [12, 15]. For example, a clockwise rotation about the ^y axis (i.e., an axial slice turned slightly toward coronal direction) transforms equation (24.9) to " wðrÞ ¼ gBdz ðrÞTE ¼ gB0 TE  =

1

1 ðkz cos ukx sin uÞ2  =ðwðrÞÞ  3 kx2 þ ky2 þ kz2

!# ð24:19Þ

Previous works using the Fourier-based field estimation method [15] have estimated the static field deviation due to air–tissue interface in brain by obtaining the geometry of the

DISCUSSION

445

FIGURE 24.18 (a,d and g) Original-pSWI; (b,e and f) GDAC-pSWI; (c, f and i) difference images of (b - a), (e - d) and (h - g) respectively. Images (a) through (c) are from volunteer 2; (d) through (f) are from volunteer 3 and (g) through (i) are from volunteer 1. A venous vessel(arrow), otherwise obscured by the conventional SWI processing in (g), is now clearly visible in (h). The arrow heads point to the regions where considerable brain signal is recovered in the GDAC-pSWI compared to original-pSWI images.

head from computed tomography (CT) images and assuming a susceptibility of 9.2 ppm between brain tissue and air and a susceptibility of 11.4 ppm between bone and air [13]. However, it is not always possible to obtain CT images of the subject being imaged, nor is the subject MR image registration with a fixed CT template always feasible. Moreover, the nasal cavity and the sinus fluid levels do change on a daily basis due to the normal ‘‘nasal cycle’’ [23]. Any considerable change in nasal cavity dimensions or fluid in the sinuses can affect their effective susceptibility value. Thus, it is necessary to incorporate the actual

446

RAPID CALCULATION OF MAGNETIC FIELD PERTURBATIONS

FIGURE 24.19 U-original-pSWI; b) U-GDAC-pSWI; c) difference image (b - c); d) histogram plot of pixels taken from the ROIs shown in a & b. The histogram curve of U-original-pSWI shows a bi-modal distribution signifying the erroneous signal loss region and the normal region. The curve from the UGDAC-pSWI image shows an unimodal distribution clearly recovering the erroneously lost signal intensity.

structural information in the geometry modeling. Hence, in this work, we used T1-weighted MR magnitude images to obtain the head and sinus–tissue interface geometry. A fast proton density weighted sequence might also be used as an alternative to this. However, one must be aware that the shape and the size of the structures extracted will be a function of echo time and bandwidth of the MR sequence used. For example, the frontal sinus is about 1.5 cm in diameter but can easily appear to be 1.7 cm in diameter on a gradient echo image due to T2* signal loss. This overestimate of the sinus size can change its estimated Dw with respect to brain tissue from, say, 9.05 to 6.23 ppm. That is, we need to use a Dw of 6.23 ppm for the 1.7 cm diameter structure so that the phase outside is the same as from a structure of 1.5 cm diameter and Dw of 9.05 ppm. Furthermore, the internal structure of the extracted geometries although not included (either due to T2* loss or due to complete lack of signal as in the case of bone) do physically influence their effective Dw value. Because of these factors, Dw values were evaluated for each volunteer. Data sets collected at two echo times separated by a DTE were used here for approximate estimation of Dw. This, in principle, can be cut down to one data set that is collected at sufficiently short echo time and its phase properly unwrapped [24, 25]. In segmentation of the images for geometry extraction, there can be

DISCUSSION

447

small ‘‘nibbles’’ or localized signal losses at the tissue–sinus interface that cause pockets of irregular regions. In practice, we smooth over these regions to represent a continuous smooth interface. As pointed out previously [12, 13, 15], the accuracy of the FT-based field estimation method is quite dependent on the object size/FOV ratio. In the simulations, although the outer diameter of the shell geometry considered is almost 85% of the field of view, the result obtained is within 5% of the actual value. The primary reason for this is that because we choose a VOI closer to the inner sphere (since the actual geometry relevant here is the inner sphere that has a certain Dw with respect to the outer sphere). Since the size of the inner sphere is on the order of only 20% of the total field of view considered, error in its calculated phase is very small in the VOI chosen. Nevertheless, the minimum in Figure 24.9 is found to be at 9.8 ppm instead of 9.5 ppm. This error of about 3% could be due to discretization error in the representation of the inner sphere. The results from the three human volunteers show that Dwsinus–tissue differs considerably from Dwmastoid–tissue. Although corroborated by the simulation results, to exclude the possibility that the difference in these values is arising due to an error in the field estimation method itself, Dw values were estimated in volunteer 3 by simulating the field in an FOV 1.25 times the actual field of view. This reduced the ratio of the head size to the FOV from approximately 0.80 to 0.65. However, the estimated values of Dwsinus–tissue and Dwmastoid–tissue remained the same (7 and 5 ppm). The values of Dw estimated are specific to the voxel aspect ratio of the geometry, which is in this case 1:1:2, and are not to be taken as absolute Dw values. The variability in Dwmastoid–tissue and Dwsinus–tissue between volunteers is not surprising as these are dependent on the actual internal structure of the nasal cavity and the mastoid cavity (septal cartilage distribution and distribution of air cells and bone, which is not included in the geometry defined using MR magnitude images) that varies from volunteer to volunteer. In fact, these can vary within a person from time to time due to the natural ‘‘nasal cycle.’’ Variation in magnetic field shimming prior to imaging these volunteers might also be one of the factors influencing the intersubject variability of the Dw values. The Fourier-based field estimation method does not take into account the additional field variation due to shimming and eddy currents. The significant intrasubject difference between Dwmastoid–tissue and Dwsinus–tissue would however be unaffected by this. The different acquisition parameters used for different volunteers could also, in principle, influence the intersubject variability of Dw values, but any such effects are expected to be very small. An important advantage of this method is that it can be used as a precursor to existing methods of phase unwrapping or filtering to further improve these methods (see Figure 24.19). The time limiting steps in generating GDAC phase images are obtaining the geometry of the sinuses and estimation of Dw values, which are done manually. Currently, these steps take about 2–3 h. Once these steps are done, generation of GDAC phase images for a data set of size 256  256  128 takes about 3 min of computation in Matlab on a system with a 64-bit AMD Turion processor with 2 GB RAM memory. As these steps become automated, the total processing time should drop dramatically. In conclusion, we have demonstrated that the Fourier transform-based field estimation method can be successfully employed for removing the unwanted phase from air–tissue interfaces caused by the structure of the brain and air spaces within for susceptibility weighted imaging. This makes it possible to better evaluate of veins and to quantitate iron in the midbrain and the frontal brain and can be of particular value in trauma cases

448

RAPID CALCULATION OF MAGNETIC FIELD PERTURBATIONS

where microhemorrhages and venous damage can occur in these areas. Overall, it is one more step to removing artifacts in susceptibility weighted imaging to make it more robust for clinical applications.

QUANTIFYING MAGNETIC SUSCEPTIBILITY OF AN ARBITRARILY SHAPED OBJECT FROM A LEAST SQUARES FIT Introduction MR susceptometry, to find the susceptibility of a sample of interest, for example, blood or contrast agent [26, 27], a straightforward approach has been to place the sample in a container of a standard geometry, for example, sphere or cylinder, and to fit subsequently the measured B(r) field profile outside the sample to the analytically known 1/r3 or 1/r2 field variation. Minimization of the error in such cases was done in one dimension (1D), that is, fitting an array of measured B(r) values to the analytically known expression. A similar approach can be employed using the field estimation method, to estimate the susceptibility value of a substance with an arbitrary shape, by carrying out a least squares fit in three dimensions. The advantage now is that of being able to deal with arbitrarily shaped objects. The error minimization process can be summarized in an equation form as follows: f ¼

 n  X Bi wB0 gi 2

ð24:20Þ

dBi

i¼1

where n is the total number of voxels used in the fit, Bi is the measured magnetic field perturbation from MR images at each voxel i, gi is the induced field per unit susceptibility and per unit main field calculated using equation (24.13) and dBi is the uncertainty of the measured field. Since we use phase of the MR signal for measuring the field perturbation (through the relation wi ¼ g  Bi  TE), equation (24.20) written in terms of phase becomes f ¼

 n  X Bi w  B0  gi 2 i¼1

dBi

¼

 n  X w g  TE  w  B0  gi 2 i

i¼1

¼

n X

dwi SNR2i ðwi g  TE  w  B0  gi Þ2

ð24:21Þ

i¼1

where g is the gyromagnetic ratio, TE is the echo time, and SNRi is the signal to noise ratio at each voxel from the magnitude image corresponding to the phase (since SNRmagnitude ¼ 1/sphase). Note that gi depends on the geometry of the object, field of view, and the Green’s function used in its calculation (i.e., discrete versus continuous). By minimizing function f in equation (24.21) with respect to w, that is, qf/qw ¼ 0, we obtain the following equation: Pn ðw =gTEÞ  gi  SNR2i wB0 ¼ i¼1Pin 2 ð24:22Þ 2 i¼1 gi  SNRi

449

QUANTIFICATION OF w THROUGH A LEAST SQUARES METHOD

The uncertainty of w can be found through the error propagation method [28] as dw ¼

1 qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi ffi Pn 2  SNR2 g g  TE  B0 i I¼1 i

ð24:23Þ

Equations (24.22) and (24.23) show that the uncertainty of susceptibility measurements can be reduced when SNR is increased. It is important to note that equations (24.22) and (24.23) will fail if phase aliasing is not properly unwrapped. The phase aliasing may be removed by complex dividing two phase images acquired at two different echo times with a short difference, DTE, between them. However, due to rapid field change within a voxel, usually phase aliasing would exist at voxels with low SNRs. For this reason, we exclude those voxels from our analyses. Furthermore, voxels outside imaged objects containing no sufficient SNR in the magnitude images are also removed. However, it can be seen from equations (24.22) and (24.23) that voxels with low SNR used in the fitting analysis will not significantly affect the susceptibility quantification or its uncertainty, provided that enough voxels with sufficient SNR have been used in the analysis. When acquiring images, a uniform phase w0 can exist due to central frequency adjustment by the scanner or rf excitation in the pulse sequence. Therefore, even for imaging one single object, practically, equation (24.21) should be modified to read f ¼

n X

SNR2i ðwi w0 g  TE  w  B0  gi Þ

ð24:24Þ

i

Similar to the above derivation of equations (24.22) and (24.23), values of both f0 and w and their associated standard deviations (i.e., uncertainties) can be derived by minimizing the function f and error propagation, respectively [28].

QUANTIFICATION OF w THROUGH A LEAST SQUARES METHOD Simulations To validate the least squares fit approach for susceptibility quantification, we again turn to simulating standard geometries where we know the analytic field distribution. First, we consider the case of no white noise as it provides us with an understanding of the quantification accuracy under ideal circumstance of very high signal to noise ratio. Simulation of the least squares fitting procedure under these ideal circumstances allows us to better study and understand the kinds of error and/or bias due to different factors involved, such as object size/FOV ratio or the kind of Green’s function used, and so on. Unless mentioned otherwise, in all simulations, the input main field is 1 T and the input susceptibility is 1 ppm in SI units and the objects are assumed to be surrounded by the vacuum. Starting from a radius of 16 voxels, analytic fields due to a sphere and a cylinder were evaluated for 14 different radii in increments of 8 voxels. The field of view was always fixed at 256 voxels along each dimension. Then, equation (24.13) is used to simulate magnetic fields based on both discrete and continuous Green’s functions for each object size. Equation (24.22) can now be used to quantify the susceptibility of the objects at each radius by fitting the estimated field outside the objects to the corresponding analytic field. With no white noise included in the simulations, we can assume a constant SNR in all voxels

450

RAPID CALCULATION OF MAGNETIC FIELD PERTURBATIONS

FIGURE 24.20 Images of the simulated spherical shell with a magnitude SNR of 5:1. (a) Transverse magnitude image. (b) Its associated phase image at echo time of 4ms. Voxels inside the dashed box shown in (a) were used for susceptibility quantification.

and equation (24.22) is much more simplified. Note here that one can choose to use all the voxels outside the object for calculation in equation (24.22) or a subset of those voxels. In this case, we calculated two susceptibility values, one considering field values in all the voxels outside the object, and the other considering field values from a spherical shell or an annular ring, whose locations of voxels satisfy R þ 1 < r R þ 5, where R is the radius of the object. The difference between the calculated and the input susceptibility basically indicates the difference in accuracy of the field estimation method when discrete versus continuous Green’s function is used. In a simulation more close to practical imaging situations, we simulate magnitude and phase images for a spherical shell defined by two concentric spheres with white noise added. Noise was added such that the magnitude SNR was 5:1 (equivalent to a standard deviation of 0.2 rad in phase images). The inner sphere has a radius of 16 voxels and the outer sphere a radius of 96 voxels. Figure 24.20 shows magnitude and phase images of the simulated spherical shell. The field of view again is 256 voxels in each dimension. The input susceptibility used in this case is 10 ppm within the shell and zero elsewhere. The main field strength is 1 T. Analytic field for the spherical shell was evaluated using equation (24.18) from which phase at TE 4 ms was calculated such that there is slight phase aliasing near the boundary of the inner sphere. To simulate effects of scanner central frequency adjustment or rf pulse phase, a constant background phase value w0 ¼ 1 radian is added to the calculated phase images. Since field calculated using discrete Green’s function has much less error, field due to the spherical shell is estimated using equation (24.13) by employing discrete Green’s function only. Through minimizing f in equation (24.24), the least squares fit approach allows us to determine both the susceptibility and the constant background phase, w0 . The actual phase value due to the object at the ith voxel is wi w0 , where, in this case, wi is the simulated phase value. In order to exclude aliased phase voxels from the fitting procedure, the following criterion is used: wi w0 g  TE  w  B0  gi p  si;phase

ð24:25Þ

QUANTIFICATION OF w THROUGH A LEAST SQUARES METHOD

451

where p is the thresholding limit and si,phase is the standard deviation of measured phase within the voxel. We choose p as an integer usually equal to 1 or 2 such that 68% or 95% of the nonaliased phase values are included in the susceptibility quantification. This thresholding also ensures that only voxels with high phase SNR are included in the fitting analysis. Due to this thresholding criterion, an iterative procedure is used for the quantification of w and w0 . A flowchart of the iterative procedure is shown in Figure 24.21. The convergence criterion is defined as a change of less than 0.1% in the quantified susceptibility value between two consecutive iterations. Results From Simulations For both a sphere and a cylinder, Figure 24.22 shows the % error in quantified susceptibility value with respect to the input value of 1 ppm for different object radii (presented as object diameter/FOV ratio). Figure 24.23 shows the corresponding % error in w when only voxels from within the spherical shell or annular ring are considered. Both show that the method using the discrete Green’s function is better than the method using the continuous Green’s function. When all the pixels outside the object and the discrete Green’s function are used for susceptibility quantification, no significant error is produced by the method itself if the diameter of the sphere or the cylinder studied is less than 40% of the field of view (see Figure 24.22). If only certain pixels in spherical shells or annular rings are used, as shown in Figure 24.23, the method using the discrete Green’s functions produces no significant error for objects with diameters up to almost 60% of the field of view. The results shown in Table 24.1 and Figures 24.22 and 24.23 imply that voxels close to the object are more important for an accurate quantification with the Fourier-based method than voxels away from the object. Several important results are observed in the simulation of the spherical shell with noise. First, if we include all voxels within the shell for susceptibility quantification, then we end up with an error of roughly 7% in the susceptibility value. However, if we use only the central 1283 voxels of the shell for the susceptibility quantification, the error reduces to less than 1%. This essentially agrees with the result shown in Figures 24.22 and 24.23, indicating that as more voxels far away from susceptibility boundary and close to the edge of the FOV are included in the fitting analysis, the error in quantified w value increases. Thus, for a more accurate quantification, for all future simulations, we used only the central 1283 voxels of the shell. Second, when the initial choice of the susceptibility is between 7 and 10 ppm, the final answers from the iterative procedure do not seem to be affected. Third, whether one, two, or three standard deviations (i.e., p ¼ 1, 2, or 3) are used in equation (24.25), it does not seem to affect the final quantified value. These results are summarized in Table 24.3a. As the chi-square per number of points in each least squares calculation is close to one, it indicates that each result is from a good fit. Although, in general, the results in Table 24.3(a) are in very good agreement with the input values, the differences between the calculated values and the input values for p ¼ 1 and 2 are due to the Fourier-based method itself (or the Green’s function). As the number of voxels in the quantification is large, the statistical uncertainty is small in the shell calculation. Furthermore, often the exact location of the center of an object or geometry of an object may not be perfectly defined in MRI magnitude images due to the partial volume effect, distortion, or signal loss. Thus, the uncertainty due to the object geometry can be of concern in such quantification procedures. To simulate the effect of such an error, we purposely introduced an error in the field simulation geometry. Radius of the inner sphere

452

RAPID CALCULATION OF MAGNETIC FIELD PERTURBATIONS

FIGURE 24.21 A flow chart showing the iterative procedure for solving for the susceptibility through the least-squares fitting method.

QUANTIFICATION OF w THROUGH A LEAST SQUARES METHOD

453

FIGURE 24.22 Percent error in quantified susceptibility versus the ratio of object diameter to the field of view plotted for (a) spheres and (b) cylinders. The notations Gc and Gd represent the continuous and discrete Green’s functions, respectively. All pixels outside the objects are used in the quantifications.

(Ri) within the shell was changed from 16 to 17 voxels and field perturbation and consequent phase was estimated using the discrete Green’s function. This phase was subsequently fit to the calculated analytic phase (shell’s original phase with Ri ¼ 16 and Ro ¼ 96). The calculated susceptibility through the least squares fit deviated from the input value by roughly 18%. This agrees with the volume increase of the inner sphere as the magnetic field distribution is proportional to the magnetic moment of the object, which is in turn proportional to the product of the volume and the susceptibility. It is interesting to note that although the quantified susceptibility itself has an error, the net

454

RAPID CALCULATION OF MAGNETIC FIELD PERTURBATIONS

FIGURE 24.23 Percent error in Susceptibility plotted as a function of the ratio of the object diameter to the field of view for (a) spheres and (b) cylinders. This figure is similar to figure 24.22 but only certain pixels outside each object are used in the quantifications, as described in the text.

magnetic moment, which is proportional to product of object volume and its susceptibility, remains invariant. Least Squares Analysis for w in Phantoms An object of somewhat complicated geometry was considered for the phantom study. The goal of the experiment was to show that susceptibility of a single arbitrarily shaped object

QUANTIFICATION OF w THROUGH A LEAST SQUARES METHOD

455

FIGURE 24.24 Images of the water phantom. (a) Transverse magnitude image at TE ¼ 6.58 ms. (b) Its associated phase image. (c) The phase image with an effective TE of 3ms obtained after applying the complex division method. Voxels inside the dashed box shown in (a) were used for susceptibility quantification.

can be extracted from its phase data. The phantom consisted of a water-filled cylindrical polypropylene container (wall thickness 1.3 mm, height 180 mm, and diameter 120 mm) fitted with a small hollow cylindrical post at one of its flat ends. The post had varying crosssectional diameter along its length, with a diameter of 12 mm at its base to 9 mm at its apex. The phantom was imaged twice with TE values 6.58 and 9.58 ms at 1.5 T (Siemens Sonata) using the SWI sequence, a fully flow compensated, 3D rf spoiled gradient echo sequence, with a TR 15 ms, FA 6 , voxel size 0.78  0.78  0.78 mm3, matrix size 256  256  192, and BW 610 Hz/pixel. A large bandwidth was used to ensure minimal geometric distortion. Prior to the scans, a standard spherical phantom (with a diameter of 170 mm) containing the NiSO4 solution for the system quality control was used for shimming. The full width at half-maximum frequency was reduced to 6 Hz at the end of the shimming process. All the first- and second-order shim current values were noted and were subsequently used while imaging the phantom. This ensured the uniformity of B0 field

456

RAPID CALCULATION OF MAGNETIC FIELD PERTURBATIONS

before the phantom was placed in the magnet and, hence, ensured that the field map obtained from phantom phase images was the true field deviation caused by its presence in an otherwise uniform magnetic field. Data collected at TE 6.58 ms were complex divided into that acquired at TE 9.58 ms to obtain phase with an effective echo time of 3 ms that was then used for susceptibility quantification. The SNR of the complex divided images was roughly 5:1, indicating that the standard deviation of phase within the effective TE 3 ms phase maps was roughly 0.2 rad. Complex data collected at TE 6.58 ms was used to obtain the geometry of the phantom using a complex thresholding (CTM) algorithm [18]. The extracted geometry was ascribed unit susceptibility and placed at the center of a 256  256  256 matrix. Susceptibility outside the geometry was set to zero. The iterative procedure shown in Figure 24.21 was used for the susceptibility quantification. Using the experience gained from simulations presented in the earlier section, phase information from only the central half of the field of view was used in w quantification. The initial values of w0 and w used in the iterative program were 0 rad and 6 ppm, respectively. Results in Phantoms and Discussion Figure 24.24 shows the magnitude and corresponding phase images of the imaged phantom. Most of the results of the phantom study are similar to the results of the shell simulation. To remove any significant error due to the method itself, we again restrict ourselves to the analysis of the central 1283 voxels of the magnitude and complex divided images (see the dashed box shown in Figure 24.24a). The results are summarized in Table 24.3(b). The calculated susceptibilities are within 3% of the theoretical susceptibility of water relative to air, which is 9.4 ppm in SI units [29]. The results indicate that the statistical uncertainties are smaller than the actual uncertainties that are probably due to the nonprefect definition of the object geometry. Figure 24.25 shows the voxels selected for the least squares fit at the convergence of the iterative procedure for different values of p (1, 2, or 3). As expected, the aliased voxels are automatically removed from the fitting analysis by the algorithm and progressively more and more voxels are included, as we increase p from 1 to 3. In this work, to minimize voxels with aliased phase values, a complex divided data set with appropriate DTE was used. This can be replaced with unwrapped phase maps [24, 25], TABLE 24.3 The Results from the (a) Simulated Shell and the (b) Phantom Study p

Iterations

1 2 3

20 8 5

1 2 3

24 9 6

w (ppm) (a) 10.021 0.0070 10.025 0.0058 10.000 0.0057 (b) 9.199 0.0044 9.186 0.0035 9.131 0.0034

w0

w2/N

0.997 0.00017 0.999 0.00014 1.000 0.00014

0.29 0.78 1.01

0.748 0.00024 0.750 0.00020 0.749 0.00019

0.30 0.84 1.15

The first column lists the number of standard deviations used in the algorithm. The second column lists the number of iterations it took for convergence. The third column lists the calculated susceptibilities and their associated statistical uncertainties from the fit. The fourth column lists the calculated background phase values and their associated uncertainties. The last column lists the chi-square per number of points used in the program. The input susceptibility and background phase were 10 ppm and 1 rad, respectively, for the simulated shell shown in (a). The theoretically expected susceptibility for the phantom study in (b) is 9.4 ppm.

QUANTIFICATION OF w THROUGH A LEAST SQUARES METHOD

457

FIGURE 24.25 A transverse slice through the phantom (the same slice number corresponding to that shown in Figure 24.24) indicating the voxels chosen for susceptibility quantification at the end of the iterative procedure for different values of p. (a) p ¼ 1, (b) p ¼ 2 and (c) p ¼ 3.

which then allow us to include more points closer to the object boundary in the least squares analysis. Alternatively, our iterative procedure can automatically exclude the phase aliasing voxels. This is better than selecting nonaliasing voxels manually as we want to keep voxels close to the object having high phase to noise ratios. Induced eddy currents or shimming performed on the scanner can change the phase values in images. The latter problem is minimized by shimming a spherical phantom for quality control prior to scans. The background phase value, w0, may be estimated from the phase value at the k ¼ 0 point and be used as an initial value in the iterative program. In theory, this is true if an object has a uniform zero phase value or certain symmetry in its complex images. We have confirmed this conjecture from our simulated shell. In addition, the phase is roughly 0.54 rad at the k ¼ 0 point from the phantom images, while our program found a w0 of roughly 0.75 rad (Table 24.2). Nonetheless, whether one starts w0 with a zero estimate or the central k-space estimate seems to make little difference in our least squares fit algorithm. To further obtain a better set of initial values, the value p can be assigned to 3 first and then reduced to either 1 or 2 in the program. The program seems to converge faster with a higher value of p. However, the higher the value of p, the more the noisy data are included and including voxels containing low phase SNR can lead to high uncertainty in the quantification of object susceptibility. Despite the fact that the statistical uncertainty of each susceptibility value shown in Table 24.3a and b is very small, the statistical uncertainty is not large enough to explain the difference between the quantified susceptibility and the true susceptibility. This means that the uncertainty of the method itself (see, for example, Figures 24.22 and 24.23) rather than the statistical uncertainty from white noise is a major source of the uncertainty. Fundamentally, the Fourier-based method will completely fail when the object size is equal to the image resolution [30, 31]. Practically, the geometry of small objects and their induced field distributions cannot be accurately prescribed without sufficient resolution. The problem is that the magnetic field will decrease quickly so that there will not be enough voxels to accurately estimate the susceptibility. In addition, due to the partial volume effect or the signal loss, the definition of the object geometry can also significantly affect the answer. As a result, the uncertainty of susceptibility quantification will increase. These factors warrant further careful studies of this method. In summary, we have presented in this chapter a Fourier kernel-based method for estimating field perturbations induced by biological tissue in a uniform magnetic field. It is shown that the field estimation theory presented can be used both for quantifying magnetic susceptibility of arbitrarily shaped objects and for correcting bulk susceptibility-based

458

RAPID CALCULATION OF MAGNETIC FIELD PERTURBATIONS

artifacts in SWI images. The susceptibility quantification method presented here is based on 3D least squares field fitting procedure. Other methods of susceptibility quantification based on direct inversion of the Fourier kernel have also been recently proposed that possibly allow calculation of direct susceptibility maps from phase data. This is the subject of the next chapter.

REFERENCES 1. Case TA, Durney CH, Ailion DC, Cutillo AG, Morris AH. A mathematical model of diamagnetic line broadening in lung tissue and similar heterogeneous systems: calculations and measurements. J. Magn. Reson. 1987;73(2):304–314. 2. Durney CH, Bertolina J, Ailion DC, Christman R, Cutillo AG, Morris AH, Hashemi S. Calculation and interpretation of inhomogeneous line broadening in models of lungs and other heterogeneous structures. J. Magn. Reson. 1989;85:554–570. 3. Ford JC, Wehrli FW, Chung HW. Magnetic field distribution in models of trabecular bone. Magn. Reson. Med. 1993;30(3):373–379. 4. Deville G, Bernier M, Delrieux J. NMR multiple echoes observed in solid 3He. Phys. Rev. B. 1979;19:5666. 5. Bhagwandien R, Moerland MA, Bakker CJ, Beersma R, Lagendijk JJ. Numerical analysis of the magnetic field for arbitrary magnetic susceptibility distributions in 3D. Magn. Reson. Imaging 1994;12(1):101–107. 6. de Munck JC, Bhagwandien R, Muller SH, Verster FC, van Herk MB. The computation of MR image distortions caused by tissue susceptibility using the boundary element method. IEEE Trans. Med. Imaging 1996;15(5):620–627. 7. Li S, Dardzinski BJ, Collins CM, Yang QX, Smith MB. Three-dimensional mapping of the static magnetic field inside the human head. Magn. Reson. Med. 1996;36(5):705–714. 8. Collins CM, Yang B, Yang QX, Smith MB. Numerical calculations of the static magnetic field in three-dimensional multi-tissue models of the human head. Magn. Reson. Imaging 2002;20 (5):413–424. 9. Salomir R, de Senneville BD, Moonen CTW. A fast calculation method for magnetic field inhomogeneity due to an arbitrary distribution of bulk susceptibility. Concepts Magn. Reson. B 2003;19B(1):26–34. 10. Yoder DA, Zhao Y, Paschal CB, Fitzpatrick JM. MRI simulator with object-specific field map calculations. Magn. Reson. Imaging 2004;22(3):315–328. 11. Jenkinson M, Wilson JL, Jezzard P. Perturbation method for magnetic field calculations of nonconductive objects. Magn. Reson. Med. 2004;52(3):471–477. 12. Marques JP, Bowtell R. Application of a Fourier-based method for rapid calculation of field inhomogeneity due to spatial variation of magnetic susceptibility. Concepts Magn. Reson. B 2005;25B(1):65–78. 13. Koch KM, Papademetris X, Rothman DL, de Graaf RA. Rapid calculations of susceptibilityinduced magnetostatic field perturbations for in vivo magnetic resonance. Phys. Med. Biol. 2006;51(24):6381–6402. 14. Pathak AP, Ward BD, Schmainda KM. A novel technique for modeling susceptibility-based contrast mechanisms for arbitrary microvascular geometries: the finite perturber method. Neuroimage 2008;40(3):1130–1143. 15. Cheng YC, Neelavalli J, Haacke EM. Limitations of calculating field distributions and magnetic susceptibilities in MRI using a Fourier based method. Phys. Med. Biol. 2009;54(5):1169–1189.

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16. Schenck JF. The role of magnetic susceptibility in magnetic resonance imaging: MRI magnetic compatibility of the first and second kinds. Med. Phys. 1996;23(6):815–850. 17. Haacke EM, Brown RW, Thompson MR, and Venkatesan R, Magnetic Resonance Imaging: Physical Principles and Sequence Design. Wiley, New York, 1999. 18. Pandian DS, Ciulla C, Haacke EM, Jiang J, Ayaz M. Complex threshold method for identifying pixels that contain predominantly noise in magnetic resonance images. J. Magn. Reson. Imaging 2008;28(3):727–735. 19. Haacke EM, Xu Y, Cheng YCN, Reichenbach JR. Susceptibility weighted imaging (SWI). Magn. Reson. Med. 2004;52(3):612–618. 20. Wang Y, Yu Y, Li D, Bae KT, Brown JJ, Lin W, Haacke EM. Artery and vein separation using susceptibility-dependent phase in contrast-enhanced MRA. J. Magn. Reson. Imaging 2000;12 (5):661–670. 21. Rauscher A, Barth M, Herrmann KH, Witoszynskyj S, Deistung A, Reichenbach JR. Improved elimination of phase effects from background field inhomogeneities for susceptibility weighted imaging at high magnetic field strengths. Magn. Reson. Imaging 2008;26(8):1145–1151. 22. Ghiglia DC, Romero LA. Robust 2-dimensional weighted and unweighted phase unwrapping that uses fast transforms and iterative methods. J. Opt. Soc. Am. A 1994;11(1):107–117. 23. Kennedy DW, Zinreich SJ, Kumar AJ, Rosenbaum AE, Johns ME. Physiologic mucosal changes within the nose and ethmoid sinus: imaging of the nasal cycle by MRI. Laryngoscope 1988;98 (9):928–933. 24. Rauscher A, Barth M, Reichenbach JR, Stollberger R, Moser E. Automated unwrapping of MR phase images applied to BOLD MR-venography at 3 Tesla. J. Magn. Reson. Imaging 2003;18 (2):175–180. 25. Jenkinson M. Fast, automated, N-dimensional phase-unwrapping algorithm. Magn. Reson. Med. 2003;49(1):193–197. 26. Chu SC, Xu Y, Balschi JA, Springer CS Jr. Bulk magnetic susceptibility shifts in NMR studies of compartmentalized samples: use of paramagnetic reagents. Magn. Reson. Med. 1990;13 (2):239–262. 27. Weisskoff RM, Kiihne S. MRI susceptometry: image-based measurement of absolute susceptibility of MR contrast agents and human blood. Magn. Reson. Med. 1992;24(2):375–383. 28. Bevington PR, Robinson DK. Data Reduction and Error Analysis for the Physical Sciences, 2nd edn 1992; McGraw-Hill, New York, xvii, p. 328. 29. David R Lide. editor. CRC Handbook of Chemistry and Physics, 89th edn (Internet Version 2009), CRC Press/Taylor and Francis, Boca Raton, FL, 2009. 30. Sepulveda NG, Thomas IM, Wikswo JP. Magnetic susceptibility tomography for 3-dimensional imaging of diamagnetic and paramagnetic objects. IEEE Trans. Magn. 1994;30(6):5062–5069. 31. Tan SF, Ma YP, Thomas IM, Wikswo JP Jr. Reconstruction of two-dimensional magnetization and susceptibility distributions from the magnetic field of soft magnetic materials. IEEE Trans. Magn. 1996;32(1):230–234.

25 SWIM: Susceptibility Mapping as a Means to Visualize Veins and Quantify Oxygen Saturation Jin Tang, Jaladhar Neelavalli, Saifeng Liu, Yu-Chung Norman Cheng, and E. Mark Haacke

INTRODUCTION Susceptibility weighted imaging has been used for some time as a means to enhance venous signal using high-pass filtered phase images [1, 2]. The special image created by SWI processing relies on an asymmetric voxel aspect ratio. Therefore, when SWI is collected with high-resolution isotropic data, the conventional processing will fail. To overcome this problem, we propose using a form of susceptibility mapping to produce an image of veins from SWI phase data [1]. Such a map would make it easier to image venous vessels independent of their size and orientation, which we refer to here as susceptibility mapping of veins. We refer to this overall approach of Susceptibility Weighted Imaging and susceptibility Mapping as SWIM. The ability to quantify local magnetic susceptibility is tantamount to being able to measure the amount of calcium or iron in the body whether it is calcium in breast [3] or iron in the form of nonheme iron (such as ferritin or hemosiderin) or heme iron (deoxyhemoglobin). In the past few years, there have been a number of papers discussing different methods for doing this using a fast Fourier transform approach [4–10]. All of these methods are based on the simple expression in k-space for analyzing distant dipolar

Susceptibility Weighted Imaging in MRI, By E. Mark Haacke and J€urgen R. Reichenbach Copyright
2011 by Wiley-Blackwell

461

462

SWIM: SUSCEPTIBILITY MAPPING AS A MEANS TO VISUALIZE VEINS

fields from a given source of susceptibility distributions first given by Deville et al. [11] in 1979. One of the methods utilizes the inverse of the Green’s function [8]. This is, however, fraught with difficulties as it is an ill-posed problem due to singularities in the inverse of the Green’s function. To this end, different groups have tried regularization or multiple scans acquired with the object being rotated between scans [8, 9]. In this chapter, we show that good quality magnetic source images or susceptibility maps (SMs) of the veins in the brain can be obtained when the inverse is regularized and other sources of phase noise are removed.

THE PROCESS OF CREATING A SUSCEPTIBILITY MAP Inverse Filter Regularization To reconstruct the susceptibility distribution, a regularized inverse filter, g
1(k), was applied to the Fourier transform of the high-pass filtered phase image. The forward filter, as introduced previously in Chapter 24 is defined by 1 k2 gðkÞ ¼
z2 3 jkj

ð25:1Þ

where kx, ky, kz denote the coordinates in k-space and |k|2 ¼ kx2 þ ky2 þ kz2 . The filter g(k) goes to zero when 2kz2 ¼ kx2 þ ky2 , making g
1(k) undefined (we refer to these kz values that satisfy this equation as kzo). Hence, to reconstruct the susceptibility distribution, a regularized version of the inverse filter g
1(k) is applied to the Fourier transform of the unwrapped/high-pass filtered phase image, w(k). It should be noted here that ‘‘k-space’’ in this chapter refers to the Fourier or frequency domain of unwrapped/high-pass filtered phase images (i.e., obtained by directly taking their discrete Fourier transform), rather than the usual acquired k-space data in MRI. In our approach to this problem, we regularize g
1(k) as follows. First, we restrict g(k) to have a minimum value a so that its inverse remains well defined. That is, for any k where |g(k)| < a, g(k) is set to
a or a depending on the sign of g(k) (i.e., g
1(k) is set to a minimum of
1/a or a maximum of 1/a). This first step prevents g
1(k) from becoming too large and enhancing noise points near singularities. Second, the inverse, g
1(k), is brought smoothly to zero as k approaches kzo such that the discontinuity at kz ¼ kzo is removed. This smoothing is accomplished by multiplying g
1(k) by a2(kz) where a(kz) is defined as  ðkz
kz0 Þ=ðb  Dkz Þ aðkz Þ ¼ 1

for when

jkz
kzo j < b  Dkz jkz
kzo j  b  Dkz

ð25:2Þ

where kz is the z component of that particular point in k-space, kzo is the point at which the function g
1(k) becomes undefined and Dkz is the k-space sampling interval along the z direction. This filter starts to reduce the maximum of g
1(k) starting b pixels away from the singularity and rapidly brings it to zero at the singularity. The choice of b is discussed below. Denoting the regularized inverse filter by g
1 reg ðkÞ, the susceptibility map for the 3D data set is calculated via xðrÞ ¼ FT
1 ðg
1 reg ðkÞwzf-proc ðkÞÞ=ðgB0 TEÞ

ð25:3Þ

THE PROCESS OF CREATING A SUSCEPTIBILITY MAP

463

where wzf-proc(k) is the Fourier transform of the high-pass filtered phase wzf-proc(r). The subscript ‘‘zf-proc’’ refers to the high-pass filtered, zero filled phase images as described in Refs 1 and 2. Note, that we impose the condition g
1 reg (kx ¼ 0, ky ¼ 0, kz ¼ 0) ¼ 0 in the regularized filter. This in turn implies that the quantification is only valid for relative susceptibility differences, that is, only Dx, and not for absolute x values. Selection of a and b The choice of threshold value is particularly important in determining the quality of the susceptibility map. The choice of threshold a for g(k) determines to a large degree the amount of streaking that will occur. The reason for this is based more so on the discretization errors and ill-posedness of this inverse approach. To find an appropriate threshold value, phase due to a cylinder of diameter 8 voxels perpendicular to the main magnetic field was simulated (for simulation details see the next section). A Dc of 0.45 ppm, B0 of 3 T, and TE of 5 ms was assumed. Susceptibility maps were generated using g
1 reg ðkÞ in equation (25.3) for varying a values. In the resultant SM, mean and standard deviation (SD) of susceptibility values inside the vessel were measured. The squared mean and standard deviation of the values outside the vessel were also used to measure artifact levels in the background. We varied the value of a from 0.05 to 0.30 in steps of 0.05. Although setting the threshold value, a, prevents g
1(k) from becoming ill defined, it creates an abrupt step-like discontinuity in the behavior of g
1(k) in the neighborhood of kz ¼ kzo. To avoid these abrupt transitions, we use a(kz), defined with a parameter b, to bring the inverse filter smoothly to zero. When |g(k)| < a, the filter smoothly reduces the value of g
1(k) starting b pixels away from the singularity and rapidly brings it to zero at the singularity. The value of b in turn depends on the value of a since b ¼ jkza
kzo j=ðDkz Þ

ð25:4Þ

where kza is the kz coordinate value where |g(k)| ¼ a, for a given kx and ky coordinates. One can now rewrite equation (25.2) as aðkz Þ ¼ ðkz
kzo Þ=jkza
kzo j

ð25:5Þ

Simulation To study the effects of partial voluming, noise, phase aliasing and high-pass filtering of phase on the susceptibility mapping process, we simulated the phase of cylinders of varying size, oriented perpendicular to the main magnetic field. The susceptibility maps of these cylinders were generated using the regularized filter g
1 reg ðkÞ with an a value of 0.1. In these simulations, instead of calculating the phase of each of the cylinders on discrete grid points directly using the analytical formula for an infinitely long cylinder, we performed a process analogous to the MRI image acquisition. We start by simulating the cylinder magnitude and its phase on a large grid consisting of a 4096  4096 matrix. We then obtain the lower resolution version of the phase by taking the central part of its Fourier transform and applying an inverse Fourier transform to this central k-space matrix, say 512  512 for isotropic voxel size. So, for example, for a cylinder that is 64 voxels wide in a 512 matrix size, this started out as a 512 voxels wide cylinder in the 4096 matrix. In that sense, if the 512  512 matrix represents 0.5  0.5 mm resolution, then we are using a resolution of 62.5 mm to first sample the object discretely and by taking the central k-space, we mimic a

464

SWIM: SUSCEPTIBILITY MAPPING AS A MEANS TO VISUALIZE VEINS

more analytical Fourier transform representation of the final resolution’s k-space signal. Data generated in this manner exhibit the usual experimental artifacts such as Gibbs ringing and partial volume effects not seen with an analytical solution. We refer to these input phase images in this paper as the ‘‘simulated phase’’ images. All simulations assumed a B0 value of 3 T and Dx of 0.45 ppm and a cylindrical geometry perpendicular to the main magnetic field is considered. A magnitude image for the cylinder with a signal of 10 arbitrary units inside the cylinder and 1 arbitrary unit outside was used for generating the high resolution data in all simulations unless specified otherwise. To estimate the effect of partial voluming, cylinders with different radii (r ¼ 0.25, 0.5, 1, 2, 4, 8, 16, and 32 voxels) perpendicular to the main magnetic field were simulated, each with voxel aspect ratios of 1:1, 1:2, and 1:4. For example, a phase image with a voxel aspect ratio of 1:2 is generated by inverse Fourier transforming only the central 512  256 points of the original 4096  4096 point k-space (and for 1:4 aspect ratio, it is the central 512  128 points). Subsequently, their corresponding susceptibility maps were generated and the mean and standard deviation of the resultant susceptibilities were measured. Two echo times, TE ¼ 5 ms and TE ¼ 20 ms, were considered for this simulation to study the effect of phase aliasing on the estimated susceptibility values. While TE ¼ 5 ms does not lead to any phase aliasing, the phase image at TE ¼ 20 ms has considerable phase aliasing. Different voxel aspect ratios here are meant to represent the ratio of in-plane to through-plane voxel dimensions for typical transversely orientated SWI data. The effect of high-pass filtering the phase data on the susceptibility maps was also simulated and studied. Again, simulated phase images of cylindrical geometry with radii of 1 through 40 voxels, in steps of 1 voxel were considered. Homodyne high-pass filters [1, 2] of size 8, 16, 32 and 64 were applied on these phase images before being used for susceptibility mapping process. The mean and standard deviation of the susceptibility value for each simulated case were measured. To study the effect of noise in phase images on the noise in the resultant susceptibility map, we simulated a complex data set for a cylinder of diameter 8 voxels with Gaussian noise added. Noise was added to both real and imaginary channel images such that the resultant signal to noise ratio (SNR) in the magnitude image was 40:1, leading to a standard deviation in the phase image of 0.025 rad. After performing the process outlined in equation (25.3) to get the susceptibility map, this phase noise will be altered in some manner by the susceptibility mapping process. We measure the noise mean and standard deviation outside the object in the SM map. In vivo MR Data Collection and Processing To reconstruct a susceptibility map of venous vessels with minimal artifacts, the following steps were carried out: (i) collect an isotropic high-resolution SWI data set, (ii) high-pass filter the phase images, (iii) interpolate k-space, (iv) remove spurious phase noise sources from the phase images, and (v) regularize the data. These steps are described in more detail below. (i) Susceptibility weighted imaging sequence, which is a high-resolution 3D gradient echo sequence with velocity compensation in all three directions, was used for data collection. The sequence parameters used were TR ¼ 26 ms, flip angle 11 , and bandwidth 80 Hz/pixel in the read direction. We collected images with 0.5 mm isotropic resolution at 4 T field strength at three echo times of 11.6, 15, and 19.2 ms

THE PROCESS OF CREATING A SUSCEPTIBILITY MAP

(ii)

(iii)

(iv)

(v)

465

and with a matrix size of 352  512 (phase  read directions) respectively. A total of 88 slices were collected. The k-space data were then truncated in the slice select direction to mimic 1 and 2 mm thick slices and zero filled to interpolate the images to 0.5 mm slice thickness in order to create maximum intensity projections (MIPs) that would match when comparing MIPs over the different resolution reconstructions. The images were acquired in absolute transverse orientation without any angulation to coronal or sagittal direction. Phase data were high-pass filtered using an n  n central low-pass filtered image [1, 2] divided into the original complex image. This gives a homodyne or effective highpass filtered phase image, j(x), which removes most of the low spatial frequency phase. In order to keep the field of view in x, y, and z directions in ratios of 1:1:4, k-space was interpolated by zero filling the phase images, jzf-proc(r), in all three directions to a 512  512  128 matrix size. Note that zero filling in z direction could have been done to 512 slices, so that the fields of view in all three directions would be same. However, the large memory required for carrying out the 3D Fourier transform of a 512  512  512 matrix prohibited this. This 3D image set, jzf-proc(r), was then Fourier transformed to create a k-space data set jzf-proc(k). Zero filling the initial input phase images to a larger matrix also helps in reducing the pseudo ghosting that gets introduced in the SM due to artifacts associated with the Fourier transform and application of the inverse filter. Note that ghosting referred to here is a form of structural aliasing and in this sense refers to the replication of information in the image domain when the data are undersampled. Elsewhere in this chapter, we use the term aliasing to refer to phase information that has aliased back into the interval [
p, p). Noise in the nontissue region in the phase images was removed, by using a complex thresholding [12] approach on the magnitude image, followed by a skull stripping algorithm. The regularized inverse filter discussed earlier was applied to the Fourier transform of the high-pass filtered phase image.

To assess the sensitivity of SM maps to changes in venous oxygenation levels, we compare the susceptibility map data before and after ingestion of 200 mg caffeine (NoDoz, BristolMyers Squibb, New York, NY) for a normal healthy male volunteer. The data were acquired at 3 T on a Siemens VERIO system with a voxel size of 0.5  0.5  2 mm, flip angle of 15 , and a bandwidth of 100 Hz/pixel at an echo time of 20 ms. SWI images were acquired before the ingestion of caffeine and about 50 min after the ingestion of caffeine. Furthermore, microbleeds are a common occurrence in traumatic brain injury (TBI), cerebral amyloid angiopathy (CAA), mild cognitive impairment subjects, and Alzheimer’s and other neurological/neurovascular conditions. To demonstrate that the susceptibility mapping process can also help in better visualization of microbleeds, susceptibility mapping was applied on data collected from a TBI patient who had multiple microhemorrhages in the brain. Informed consent was acquired from both the volunteer (for the caffeine study) and the TBI patient prior to data collection. The following parameters were used for data collection in this subject for the SWI sequence: TR ¼ 29 ms, flip angle ¼ 15 , TE ¼ 20 ms, matrix size ¼ 384  512 (phase  read) with a voxel size of 0.5  0.5  2 mm. A total of 64 slices were collected. Phase images were subjected to the same preprocessing of high-pass

466

SWIM: SUSCEPTIBILITY MAPPING AS A MEANS TO VISUALIZE VEINS

filtering, noise removal, and zero filling as explained earlier. In addition, phase noise in the center of the microbleed (due to T2* signal loss in the magnitude image) is replaced by a zero phase. These phase images were then used for the susceptibility mapping process.

RESULTS Simulations There are six major sources of error in creating venous susceptibility maps:(i) errors in the inversion process, that is, those due to g
1 reg ðkÞ itself; (ii) voxel aspect ratio effects (i.e., partial voluming); (iii) aliasing in input phase images caused by longer echo times; (iv) errors caused by high-pass filtered phase data; (v) errors due to discrete sampling in MRI; and (vi) thermal noise in the phase data. We consider each of these in the following paragraphs. (i) Even with regularization, and with no thermal noise considered, the inversion process is not perfect. In this case, it depends on the choice of a. In Table 25.1, we show the root mean squared error (RMSE) both inside and outside the cylinder along with percent error of the quantified susceptibility with respect to the input value of 0.45 ppm. Please note that RMSE outside the cylinder is taken only from an annular region centered around the cylinder with a thickness of 20 voxels (i.e., an annular region defined by inner radius ¼ 4 and outer radius ¼ 24 voxels). This is done so because as we move away from the object, the errors become more and more negligible (discussed later in this section). The errors inside the object seem to be minimized at a ¼ 0.15. However, empirically, a choice of a anywhere between 0.05 and 0.2 provides a reasonable estimate for the susceptibility without causing much noise/‘‘ghosting’’ artifacts outside the object. Nonetheless, for the sake of consistency, we have used an a value of 0.1 for all the results presented in this manuscript. To appreciate the distribution of errors, we show the phase of a cylinder perpendicular to the field and its corresponding susceptibility map in Figure 25.1a and b, respectively. As we can see, within the susceptibility maps, the errors can be divided into three regions: (a) within the object itself, (b) errors along the streak TABLE 25.1 Root Mean Squared Errors in Susceptibility Values, Measured Within and Outside a Cylinder of 8 Voxels Diameter, for Different Threshold Values a

a 0.05 0.1 0.15 0.2 0.25 0.3

Root Mean Square Error (RMSE) outside cylinder (units ¼ 1000  Dx in ppm)

RMSE inside cylinder (units ¼ 1000  Dx in ppm)

% Error in mean Dx value within the cylinder

60.8 55.7 54.4 53.6 52.8 51.1

93.0 73.2 68.5 82.1 108.3 141.6


3.4 3.5 9.6 15.9 22.8 30.8

Errors outside the cylinder were measured within a concentric annular ring with an inner radius ¼ 4 and outer radius ¼ 24 voxels. Also shown is the corresponding percent error in quantified mean Dx with respect to an expected 0.450 ppm. Errors outside the cylinder increase with increasing a value whereas for the error within the cylinder, an a value of 0.15 seems to be optimal. However, in general a threshold value of 0.05–0.2 could be used depending on the contrast needed in the SM map.

RESULTS

467

FIGURE 25.1 The original phase at TE ¼ 5 ms (a), high-pass filtered phase (c), and their corresponding susceptibility maps (b) and (d) for a cylinder with a diameter ¼ 8 pixels. Streak artifacts are clear in both parts (b) and (d). The arrow in part (a) indicates the direction of B0.

artifacts corresponding to the cone of singularity in g
1 reg ðkÞ in k-space, that is, points in the neighborhood of kz ¼ kzo where |g
1(k)| > 1/a, and (c) errors outside these regions. Notice that while the cone of singularity in g
1(k) is defined in k-space at kz ¼ kzo (i.e., where 2kz2 ¼ kx2 þ ky2 ), the streak artifacts in the image domain occur along z2 ¼ 2x2 þ 2y2. (ii) Errors outside the object, along the streak artifacts: Along the streak artifacts (see Figure 25.2a), the error in the susceptibility map measured in a region of interest the size of the vessel (near the boundary of the object) is within
5% of the input susceptibility value in voxels close to the boundary of the cylinder and drops off quickly within the next few voxels to less than
2% (see insert in 25.2a) and then slowly after that to less that
0.25% at the edge of the field of view. Since the errors outside the object scale with the input susceptibility value of the vessel, the errors here are quoted as its percentage. However, if we observe plots 25.2c and 25.2e, it is clear

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FIGURE 25.2 Susceptibility profile plots illustrating the quantitative nature of artifacts under different vessel-background signal conditions. Susceptibility profile plots along the streak artifact (a, c) and along the x-axis (b, d) plotted for the central 64  64 pixels of the 512  512 image. The insert in (a) shows the profile across the full length of the streak artifact. Source phase data for all the plots here was generated from a high resolution 4096  4096 complex data set containing a magnitude and 2D phase representation of the cylinder. For plots in (a) and (b) a magnitude image for the cylinder was simulated in which the signal from cylinder and the surrounding background was taken to be same, i.e. 1 arbitrary unit (a.u.). For plots in (c) and (d), a signal of 4 a.u. was assumed inside the cylinder and a signal of 1 a.u. for the background outside. Conversely, for plots in (e) and (f) a signal of 1 a.u. inside the cylinder and 4 a.u. outside the cylinder was assumed in the magnitude. The difference in the susceptibility map profiles from (a,b) through (e,f) can be clearly seen. This difference in profiles is a direct result of Gibbs ringing that arises in the simulated data due to magnitude signal differences between the vessel and the background. In general, the errors near the boundary of the object are large but decay quickly to zero, away from the object. The gray lines show errors in the susceptibility maps from the high-pass filtered phase images (filter size 32  32). The diameter of the cylinder considered here is 8 pixels.

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that the error profile along the streak also depends on Gibbs ringing. The plots in 25.2a and b were generated assuming no magnitude signal difference between the vessel and the surrounding background region. This provides us with minimal Gibbs ringing artifact (arising only due to phase differences between inside and outside the vein). However, practically magnitude signal from the veins is usually different from the surrounding tissue, either lower or higher, depending on the data acquisition parameters. For example, signal from veins can be higher than the parenchyma at shorter echo times and usually at isotropic resolution where partial voluming affects are minimal; and venous signal is usually lower than the surrounding tissue at longer echo times when there is increased T2* loss (this can also happen at shorter echo times in the presence of a exogenous T2* based contrast agent) or when there is intra-voxel signal dephasing (due to partial voluming). Both these circumstances lead to additional Gibbs ringing contribution from magnitude signal differences and lead to slightly different behavior in the susceptibility maps as illustrated in Figures 25.2c and 25.2e. Errors outside the object and outside the streak artifacts: Outside of these two regions, the errors in the susceptibility maps (basically the systematic ‘‘noise’’ generated outside the object due to the susceptibility mapping process) are close to
25% in the immediate boundary of the object and drop off rapidly to less than
0.25% for most of the field of view (see Figure 25.2b). Again, this error in the immediate neighborhood of the object is further modified by Gibbs ringing due to magnitude signal differences. When the ratio of magnitude signal between the vein and surrounding tissue is 4:1, this error can increase to a maximum of
46% in voxels adjacent to the object boundary. However, one important point to note is that this near vessel error is negative so that when maximum intensity projections of the susceptibility maps are taken to display the veins as contiguous objects, this error is not visually apparent. Errors within the cylinder: Figure 25.3a plots the mean and standard deviation of the measured susceptibility values across different radii and different voxel aspect ratios, for an input phase at TE ¼ 5 ms. With an isotropic resolution and a vessel diameter greater than 8 pixels, the susceptibility is underestimated by roughly 11% (with respect to the input Dx value of 0.45 ppm). For objects smaller than 4 pixels, again the estimated susceptibility drops but this time more drastically as the error here depends on partial volume effects. For a diameter of 2 pixels, the susceptibility is already down to two-thirds of its expected value and after that it heads rapidly toward zero with the amount of signal in the susceptibility map depending on the volume of the vessel occupying the pixel. Furthermore, since through-plane resolution is often less than in-plane resolution, it is interesting to look at the results for different voxel aspect ratios. It is not surprising to find that as the slice thickness to vessel diameter ratio increases, the estimates for susceptibility get worse due to increasing partial voluming. With a voxel aspect ratio of in-plane to slice thickness of 1:1 or 1:2, the susceptibility is estimated reasonably well (Figure 25.3a), but for an aspect ratio of 1:4, even for an object that is 4 pixels in diameter, the estimated susceptibility is beginning to significantly deviate from the actual susceptibility value. (iii) Longer echo times can lead to signal loss and aliasing in the phase data. This leads to an effective increase in the size of the vessel and hence a reduction in the

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(a) 600

Δχ (ppm × 1000)

500 400 300

Δχ (512 × 512)

200

Δχ (512 × 256) Δχ (512 × 128)

100 0 64

32

16

8

4

2

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(b) 450 400

Δχ (ppm × 1000)

350 300 250 200

Δχ (512 × 512)

150

Δχ (512 × 256)

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Δχ (512 × 128)

50 0 64

32

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8 4 2 Diameters (pixel)

1

0.5

FIGURE 25.3 Plots of the measured susceptibility as a function of both diameter of a vessel and the aspect ratio for TE ¼ 5 ms (a) and TE ¼ 20 ms (b). The 512  512 simulation (created from the original 4096  4096 data) represents a voxel aspect ratio for an in-plane resolution to slice thickness of 1:1. The 512  256 simulation represents an aspect ratio of 1:2 and the 512  128 simulation represents an aspect ratio of 1:4. Note that the susceptibility values are multiplied by 1000 for display purposes. Error bars are shown for the isotropic case to demonstrate the systematic error. The errors in the 1:1 and 1:2 aspect ratios are similar and the errors in the 1:4 case are somewhat larger. Mean and standard deviation of susceptibility values were measured by zooming objects twice for cylinders with diameter 2, three times for a diameter of 1 and four times for diameter of 0.5 voxels to 8 pixels, zooming three or four times for cylinders with diameters 0.5 and 1 pixel. While no phase aliasing is present for part (a), aliasing at TE 20 ms leads to an additional effect on the susceptibility quantification in part (b). The input susceptibility value for all simulations was 0.45 ppm (i.e., 450 in the plot).

predicted susceptibility. Comparing the TE ¼ 5 ms susceptibility data in Figure 25.3a with the TE ¼ 20 ms data in Figure 25.3b, we can see that all the susceptibility values are lower in the latter case and this reduction becomes more dramatic as the vessel size decreases. This is caused by the phase aliasing that

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FIGURE 25.4 Plots show the effect of high-pass filtering on the quantified susceptibility values. Results for four filter sizes Nf (8  8, 16  16, 32  32, and 64  64) along with ‘No filter’ case are shown here for different object sizes. Error bars are only shown for the ‘No filter’ case for visual clarity in the plot. Standard deviation measures (i.e. error bars) for the other curves are also on the same order of magnitude and follow the same trend shown here. It is seen that quantitative error in susceptibility values increases with increasing filter size. However, for very small objects, typically smaller than 10 voxels across, the error is less than
15% for filter size 32  32 or smaller. Applying a high-pass filter of a given size leads to a major loss of phase information in objects that are larger than (N/Nf) voxels, where N is the matrix size and Nf is the filter size along a given direction.

occurs at the longer echo time of 20 ms, which in turn affects the expected diameter of the vessel and the susceptibility. Furthermore, with aliasing, the effect of vessel partial voluming due to nonisotropic voxel dimensions follows a more drastic trend than that seen at TE 5 ms. (iv) High-pass filtering: Figure 25.4 shows the effect of phase high-pass filtering on the measured susceptibility values within cylinders of different size. Effects of filter sizes, 8  8, 16  16, 32  32, and 64  64 are plotted. As expected, different errors are seen for different filter sizes. Generally, the larger the filter size, the greater the quantitative error in the susceptibility value. However, in values from very small objects, about 10 voxels across or smaller, there is little variation with filter size with error being within
15% for filter sizes up to 32  32. Only at the filter size of 64  64, the error increases to
28% for an object 10 pixels wide. In fact, at a filter size of 16  16, mean susceptibility values for objects up to 20 voxels wide can be quantified with an error less than
12%. As a rule of thumb, applying a high-pass filter of a given size, Nf, along a particular direction leads to loss of phase information varying over a spatial extent defined by the ratio N/Nf or greater, where N is the matrix size in that direction. Thus, filtering out phase from smaller structures needs larger filter sizes. It has to be noted here that the values presented here will be slightly influenced by the Gibbs ringing introduced due to magnitude signal differences between the vessel and the background. This Gibbs ringing affect will have lesser influence in larger objects compared to smaller objects. The gray lines plotted in

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SWIM: SUSCEPTIBILITY MAPPING AS A MEANS TO VISUALIZE VEINS

Figure 25.2 show the effect of high-pass filtering on the ‘‘noise’’-errors outside the object and along the streak artifacts. Apart from influencing the susceptibility value inside the cylinder, high-pass filtering also causes a proportional change in the error around the boundary of the object. In general, it is seen that the susceptibility profiles from high-pass filtered phase are always lower than the susceptibility profile from unfiltered phase data, clearly illustrating the effect of loss of phase information. As noted earlier, the error at the edge of the vessel is negative so that when MIPs are taken of the veins to display them as contiguous objects, this error does not contribute to the final MIPped image of the veins. (v) The discretization errors can lead to improper representation of the object in the phase images because of partial volume effects. This explains in part the errors seen in Figure 25.3 as object size decreases. In principle, if the measured diameter of the object (dm) is compared to the actual input value (da) and used to predict the area change, then we can predict the magnetic moment rather than the susceptibility. Since the magnetic moment is related to the cross-sectional area of the vessel times the susceptibility, the corrected value, Dxactual, can be calculated from Dx measured (dm/da)2. (vi) The systematic errors described above are distinct from the effects of thermal noise. There we see that an SNR of 2.5% in the magnitude image leads to a thermal noise or error in the phase image of 0.025 rad. If the inverse filter did not affect the phase noise at all, the noise error in the susceptibility map would be expected to be around 0.0063 ppm. However, the inverse filter amplifies the noise near the streak artifacts and this leads to noise outside the magnetic source (the cylinder) of 0.035 ppm in the susceptibility map, in regions outside the streak artifacts (Figure 25.5). Note that this systematic error from thermal noise is independent of the object susceptibility value and hence errors are quoted in ppm rather than as percentage of the object susceptibility.

Susceptibility Maps of In Vivo Data Set In the following, we review the results of the implementation of the susceptibility mapping process as applied to an in vivo data set. First, we show how a vessel changes its phase behavior as it courses through the brain making different angles to the main magnetic field (Figure 25.6a). Using the conventional SWI processing here would enhance the veins parallel to the field but would incorrectly enhance the outside of the veins perpendicular to the field. After the susceptibility mapping process (Figure 25.6b), the vein appears as one contiguous object. A second example of this is given in the simpler in-plane case where larger veins show a clear dipole effect (Figure 25.7a). Again the susceptibility map shows a bright vessel along the entire path (Figure 25.7b), and the negative Gibbs ringing effect can also be seen. Figure 25.6c and 25.6d show another pair of a phase image and its corresponding susceptibility map. In this case (Figure 25.6c), we can clearly see the dipolar effect of a vessel oriented perpendicular to the slice orientation and to the main magnetic field. This dipolar phase is completely deconvolved by the susceptibility mapping process (Figure 25.6d). Since we are interested in displaying the susceptibility map of the veins, we present next an example set of susceptibility maps to compare with the original phase data. In Figure 25.8a, we show an MIP of the phase (from a right-handed system) with 0.5 mm isotropic resolution with an echo time of 19.2 ms. The vessels are clearly shown with

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FIGURE 25.5 Thermal noise added to the simulated phase of a cylinder with diameter ¼ 8 voxels, oriented perpendicular to the main magnetic field (a). Following parameters were assumed: susceptibility ¼ 0.45 ppm, B0 ¼ 3 T, and TE ¼ 5 ms. Gaussian noise was added to the real and imaginary channels such that magnitude SNR was 40:1 resulting in thermal noise in the phase image of 0.025 rad. Corresponding susceptibility map (b). The SNR in this image is measured outside the streak artifacts. The noise in these areas increases to 0.035 ppm (instead of the expected 0.0063 ppm corresponding to a phase standard deviation of 0.025 rad) independent of the susceptibility of the cylinder. The susceptibility value inside the cylinder is 0.42  0.067 ppm. High-pass filtered phase image (64  64 central filter) (c) and the corresponding susceptibility map (d). The susceptibility value inside the cylinder is now increased to 0.46  0.075 ppm. This is caused by the high-pass filter effect on the phase. Note there is a negative error in susceptibility around the cylinder as seen in Figures 25.1 and 25.2.

reduced intensity. In Figure 25.8b, c, and d, we show the corresponding susceptibility maps for TEs of 11.6, 15, and 19.2 ms, respectively. From the venous vessel perspective, these images from different echo times are almost identical to each other. There are a few key observations to be made here. First, the image with the shortest echo time is the most noisy as it has much less phase information, that is, less phase SNR. Please note that phase SNR here refers to ðg  DB  TEÞ=sphase , where g is the gyromagnetic ratio, DB is the field perturbation and sphase is the phase standard deviation for a given imaging

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SWIM: SUSCEPTIBILITY MAPPING AS A MEANS TO VISUALIZE VEINS

FIGURE 25.6 A sagittal cut demonstrating the change in phase at TE ¼ 19.2 ms, as a vein courses through the brain (a). For proper visualization of the whole vessel section, information from two sagittal slices (i.e., total thickness 1 mm) was combined. In the phase image, the dipole effect is clearly seen with the vessel appearing dark in the phase image when perpendicular to the field and bright when parallel to the field. The distance from the top of the vessel (upper arrow) to the bottom of the vessel (lower arrow) is 3.5 mm. The fact that the phase is clearly seen in one slice with the correct sign suggests that the vein is on the order of 1 or 2 pixels in diameter (i.e., 0.5–1 mm). The same vein is shown in the corresponding susceptibility map (b). Clearly, most of the dipolar phase around the vessel is removed and susceptibility of the vessel is highlighted throughout, independent of its orientation with the main magnetic field. Another pair of a phase (c) and corresponding SM (d). The arrow head in part (c) points to the dipolar phase of a vessel coursing perpendicular to the main magnetic field and to the sagittal plane. Corresponding vessel is seen as a bright cross section in the susceptibility map (d, arrow head) with the dipolar phase completely deconvolved. Also seen is another vessel (arrow in parts (c) and (d)) with varying angle with respect to B0 clearly enhanced in the susceptibility map.

FIGURE 25.7 High-pass filtered phase image showing the dipole effects for the TE ¼ 19.2 ms case (a). Corresponding susceptibility map (b). Note there is a small negative band at the edge of the major vessels as also seen in the simulations, but overall the vessels are clearly highlighted without a varying dipole effect obscuring vascular information.

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FIGURE 25.8 mIP (minimum intensity projection) over 16 mm (32 slices) of the phase images collected at TE ¼ 15 ms (a) along with the corresponding susceptibility maps from TE ¼ 11 ms (b), TE ¼ 15 ms, (c) and TE ¼ 19.2 ms (d) phase data. Phase data were filtered with a 64  64 central filter. The image in part (a) represents mIP over 16 mm for a right-handed system and all the corresponding susceptibility maps are MIPped over the same 16 mm.

experiment in a voxel that relates to magnitude SNR as sphase ¼ 1/SNRmagnitude. Second, the contrast between gray matter and white matter improves at longer echo times. Third, the smaller vessels become more visible and better defined at longer echo times because there is more phase information available outside the vessel. Quantitatively speaking, all of the above points are related to the initial SNR in the phase image (unlike magnitude SNR, phase SNR actually increases initially with increasing TE, so long as T2* loss is not significant and there is no phase aliasing). The higher this phase SNR, the better the corresponding susceptibility map image. Fourth, the heavy air/tissue interface artifacts present in normal SWI data are also present in the susceptibility map data. This can be seen from the very bright area in the right frontal part of the brain that could have been manually removed, but it is left in the figure to demonstrate this potential problem. Fifth, the original phase MIP

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SWIM: SUSCEPTIBILITY MAPPING AS A MEANS TO VISUALIZE VEINS

TABLE 25.2 Mean and Standard Deviation for the Susceptibility Values of Three Veins (in ppm  1000) Chosen from the 0.5  0.5  0.5 Isotropic Voxel Data Shown in Figure 25.8 TE\Vein

V1

V2

V3

11.6 ms 15 ms 19.2 ms

278/78 331/98 323/90

289/62 303/85 280/64

435/70 461/163 434/119

V1 and V2 are for the left and right thalamostriate veins respectively, and V3 for the vein of Galen. There is not much variation of susceptibility value with echo time, as would be theoretically expected.

shown in Figure 25.8a sometimes shows small vessels better than the susceptibility map data and sometimes the susceptibility map data show better images of the vessels. To validate that the results for the vessels were almost independent of TE, we measured the susceptibility in three large veins (Table 25.2). The largest vein had a susceptibility close to the normal expected value for the venous blood’s susceptibility of 0.45 ppm (see below for further explanation). The mean values for the different echo times lay within 10% of the means despite the large variance. The large variance for each individual measurement was caused, in part, by a broad distribution of values since the region of interest was drawn to cover the entire vessel. When only the central part of the vessel was used however, the standard deviations were much smaller. Practically, these isotropic scans take a long time to collect and have limited coverage. If parallel imaging is used, it would be possible to reduce the scan times by a factor of 2–4. Therefore, the next step is to see if reasonable susceptibility maps can be derived from slices that are 1 mm thick (Figure 25.9a) or 2 mm thick (Figure 25.9b) as are acquired today in most SWI applications. Figure 25.9 shows that the thicker slices have better SNR but poorer contrast for displaying the veins. Although a few vessels have begun to become less defined

FIGURE 25.9

Thicker initial slices of 1 mm (a) or 2 mm (b), projected (MIP) over the same thickness as in Figure 25.8, show the pros and cons of susceptibility mapping for lower resolution images. The thicker slice images were created from the original 0.5 mm isotropic data so there is no misregistration between the images in Figure 25.8 and here. Note that the thicker the slice the better the SNR (especially for the gray matter and white matter), but the less clearly small vessels are seen. This is because the phase information in the voxel is now corrupted by integration of the complex signal across the slice.

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FIGURE 25.10 Minimum intensity projections of SWI images before (a) and after (b) caffeine administration (8 mm thick sections). Corresponding susceptibility maps before (c) and after (d) caffeine administration. A thalamostriate vein and a small vein are shown within the circles. It is in these regions where the oxygen saturation measurements were made. Note that images (c) and (d) are set to the same intensity window levels to have a fair comparison. We can clearly see the overall enhancement of the venous structures in the post-caffeine image (d). Similarly, window levels for images (a) and (b) are also set at the same values for appropriate visual comparison.

with 1 mm thick slices, there is a much greater loss of small vessel information in the 2 mm slices. However, the thicker the slice, the better the gray matter/white matter contrast. For the vein of Galen, the susceptibility values remain essentially unchanged close to the expected value of 0.45 ppm (see the following discussion).

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SWIM: SUSCEPTIBILITY MAPPING AS A MEANS TO VISUALIZE VEINS

The expected value of the susceptibility difference between a venous vessel and surrounding tissue, assuming a normal hematocrit of 0.45, an oxygen saturation of 0.55, and a susceptibility difference between fully oxygenated and deoxygenated blood, cdo, of 2.26 ppm, is 0.45 ppm in SI units [13]. For display purposes, the susceptibilities are scaled by 1000, so the numbers quoted in the figures and tables should be on the order of 450. As shown in Figure 25.3, as the slice thickness increases (i.e., the aspect ratio changes from 1:1 to 1:2 to 1:4) relative to the cylindrical objects, a reduction in the effective susceptibility is expected. For the thicker slices, the peak susceptibility drops to 0.41 ppm for 1 mm thick slices, and to 0.30 ppm for the 2 mm thick slices showing that the partial volume effect is degrading the contrast in the images. As another example, we compare the susceptibility maps before and after ingestion of 200 mg caffeine (NoDoz, Bristol-Myers Squibb, New York, NY) to examine the changes in oxygenation levels in the veins and to see if any obvious changes are visible in other parts of the brain such as the basal ganglia. It has been suggested that iron content in the basal ganglia as revealed by SWI data or susceptibility map data may have some contribution from the BOLD (blood oxygenation level-dependent) effect and if that is the case there should be some change in oxygen saturation after ingestion of caffeine. Figure 25.10 shows the projection of the data over 4 slices or 8 mm both before and after ingestion of 200 mg of caffeine. There is a clear increase in the susceptibility indicating an increase in deoxyhemoglobin levels post-caffeine administration. The susceptibility values in the thalamostriate vein increased from 0.121  0.007 to 0.166  0.008 ppm while that in the smaller veins increased from 0.095  0.006 to 0.122  0.007 ppm (Figure 25.11). No change in basal ganglia iron content was measured. Some small shifts in GM iron content could be found. (For further discussion on this effect, see Chapter 21.) Microbleeds can also be clearly depicted in the susceptibility map with the surrounding 1/r3 phase behavior deconvolved. SWI magnitude and phase images of a TBI patient are shown in Figure 25.12a and b. Microbleeds are seen as focal hypointense regions in the magnitude image and with associated 1/r3 phase decay seen in the phase images. Corresponding susceptibility maps of the microbleeds shown in Figure 25.12c are devoid of this dipolar phase behavior, with the center of the bleed seen as a bright focal spot. For accurate quantitative susceptibility measurement of the microbleeds, however, further 25 Pre-caffeine

No. of voxels

20

Post-caffeine 15

10

5

0

0

50

100

150

200

250

300

Susceptibility value from SWIM map

FIGURE 25.11 Histogram of the susceptibility in the thalamostriate vein showing a clear shift to the right post-caffeine administration. The susceptibility values are 1000 times the actual value (so a value of 200 represents 0.2 ppm in SI units).

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FIGURE 25.12 Processed SWI magnitude image (4 mm) (a). Corresponding phase image acquired at TE ¼ 20 ms (b) where microbleeds can be seen with negative phase inside and a bright ring corresponding to the 1/r3 phase decay around it. Corresponding susceptibility map (c) showing the microbleeds as bright focal spots, with most of the dipolar phase behavior deconvolved. Note that there is still a negative dip causing a dark halo in the immediate neighborhood of the microbleed (arrows). However, this negative dip does not appear in the maximum intensity projection (over 8 mm) image shown in part (d). Information from two slices (2 mm thick) was combined to show the full extent of the microbleeds and the shear injury seen in white matter (arrow head in part (a)).

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careful study of the effect of partial voluming, echo time, and systematic noise is warranted. Nonetheless, the fact that the susceptibility mapping process is able to deconvolve dipolar phase of the microbleed and show its paramagnetic nature with respect to the surrounding tissue is quite encouraging and could be a useful visualization tool in unambiguous distinction between diamagnetic calcium and paramagnetic iron depositions.

DISCUSSION Effects of Inverse Filter Regularization The basic concept of using a simple Fourier transformation method to predict the magnetic field distribution from a given susceptibility distribution was described first by Deville et al. [11]. Since then a number of papers have used this simple k-space filter to predict the magnetic field perturbation in MR [4–7]. However, the inverse problem, that is, obtaining the source susceptibility distribution from magnetic field measurements, is more complicated. Provided that the shape/geometry of the susceptibility source is known, this problem can also be tackled as a forward problem with a nonlinear regularization approach by fitting the predicted field to the measured field [6, 7]. Another way to solve this problem is by taking the direct inverse of the k-space kernel function. However, this inverse filter has a singularity at all points that satisfy the equation 1/3 ¼ kz2 =k2 , and only regularization methods [8] or multiple acquisition methods [9] have heretofore been used to remove most of these artifacts. In our approach, we have regularized the signal based on the proximity of the sampled point in k-space to the cone of singularity. The closer a k-space point is to the point of singularity, the more rapidly it is set to zero. This creates a smooth approach to zero from either side of the singularity where the function jumps rapidly from very small numbers to very large numbers. This appears to work fairly well in simulations giving systematic errors that depend on the object size. The signal to noise ratio in the final susceptibility maps appears to be reasonably well behaved with an error of 7.8% for 0.45 ppm (i.e., 0.035 ppm) at 3 T and TE ¼ 5 ms (assuming an initial 40:1 SNR in the magnitude images). As susceptibility increases, the effective SNR for the SM data will also increase. The SNR as a function of echo time is a bit more complicated. If there were no T2* effects, then the SNR would be expected to vary linearly with phase, that is, it increases with phase. However, since the signal decays according to exp(
TE/T2* ), it is well known that this gives an optimal echo time of TE ¼ T2* . Practically, images acquired at longer echo times (such as TE 25 ms at 3 T, which is roughly the T2* value for normal venous blood) suffer from serious problems associated with signal loss and aliasing at the edge of the vein and also at air/tissue interfaces. High-pass filtering the phase data also has a strong influence on the quantitative accuracy of the susceptibility values (see Figure 25.4). Fortunately, for vessels that are on the order of 5mm wide or less (i.e. 10 voxels or less), the error is only 15% for a filter size of 32  32. Most of the veins in the brain lie close to or less than this diameter. For a filter size of 64  64 the error increases to 28%. This prediction is close to what we see from the real data where we used a 64  64 filter size. The typical value measured in veins in vivo is around 0.3ppm (see Table 25.2) which is about 30% of the physiologically expected normal value of 0.45ppm. It is however, important to bare in mind that Gibbs ringing due to magnitude signal differences between the vein and the surrounding tissue, can influence the average value measured within the vessels (especially for small vessels). Another important aspect to

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FIGURE 25.13 Susceptibility maps from the 0.5 mm  0.5 mm  0.5 mm isotropic voxel human brain data with threshold values (a) 0.02, (b) 0.05, (c) 0.1, (d) 0.2, and (e) 0.3. The ‘‘ghosting’’ artifact is seen to reduce with increasing a.

consider here is the direction of high-pass filtering with respect to the vessel geometry. The homodyne implementation of the high-pass filter is typically implemented in 2D mode i.e. applied slice-by-slice [2]. The results presented in simulations here are for a cylinder perpendicular to the field and the imaging slice contains the cylinder (or vessel) cross section. A 2D high-pass filter will have more severe effects if the vessel lies in the plane of the image (i.e. the vessel is visible along its length in the slice) [14]. Susceptibility maps from a human brain data set with different threshold values are shown in Figure 25.13. The ‘‘noise’’ outside the brain in SMs is significantly decreased with the increase of the threshold value, a. Table 25.3 presents mean and standard deviation of susceptibility values for three different sized veins with different threshold values. Quantitatively, the smaller the threshold value, the more accurate the susceptibility values. However, smaller threshold values also have more serious ‘‘noise’’/artifacts (see Table 25.1). Therefore, when we choose a threshold value, we must compromise between the susceptibility values and artifacts/noise to get an acceptable susceptibility map. The threshold TABLE 25.3 Mean and Standard Deviation of Susceptibility Values (in ppm  1000) Measured from the Same Three Veins as in Table 25.2, Obtained for Different Threshold Values a ¼ 0.02, 0.05, 0.1, 0.2, and 0.3 Vein

a ¼ 0.02

a ¼ 0.05

a ¼ 0.1

a ¼ 0.2

a ¼ 0.3

1 2 3

237/207 324/94 463/73

260/166 315/87 410/93

245/130 289/75 367/66

191/76 225/61 294/33

152/44 168/41 209/25

Phase data from TE ¼ 11.6 ms was used for susceptibility mapping. Increasing a values lead to more and more underestimation of the susceptibilities, in agreement with results in Table 25.1.

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values between 0.05 and 0.2 seem to provide good choices depending on the application. If a more accurate estimate of oxygen saturation is needed, the lower value of 0.1 or 0.15 might be best, while, based on our experience, if it is overall CNR and the ability to evaluate the gray matter and white matter contrast in the susceptibility map, then 0.2 might be best, as suggested by Figure 25.13. Effects of Echo Time on Susceptibility Maps A major feature of the susceptibility map is its theoretical independence of susceptibility to the choice of echo time. This is indicated in Figure 25.8 and Table 25.2. If the magnitude SNR and the phase information in the short echo time images were good enough, one would not need to use the long echo times that we do today for SWI for example. If a susceptibility map could be obtained from an echo time of 11 ms and a repeat time of 15 ms, it would be a much more efficient sequence and one that could also be used as an MRA sequence as well. Nevertheless, as also shown in Figure 25.8, there is indeed a susceptibility map-SNR (SM-SNR) dependence with echo time. We expect the SM-SNR to increase for TE approaching T2* . However, the effect of echo time is complicated since longer echo times will lead to aliasing around the vein. This aliasing coupled with partial volume effects creates a nonphysical phase at the edge of the object. (By nonphysical, we mean that there is no geometry or susceptibility distribution that can act as a physical source for this type of phase and therefore the inverse process will produce artifacts.) The expected dipolar phase without aliasing occurs outside this area and because of this the susceptibility map will have two parts to it. The first part is the correct reconstruction of a widened object based on the fact that the vessels exhibit the expected dipole behavior. The second part will be the systematic artifacts associated with aliasing and nonphysical phase effects. These will lead to systematic noise and ghosting (or structural aliasing) associated with nonphysical phases in the susceptibility maps. However, if the area in question has complete signal dephasing, setting the phase in this region to zero will give a magnetic moment close to the correct value in the widened object without much concern as to this nonperfect choice of central phase. In fact, that is why these images tend to reconstruct quite well despite all the potential problems. However, in closing this discussion, it should be realized that this is also the reason why we do not at this point try and use the quantified results of susceptibility maps to extract oxygen saturation. Finally, ghosting (or structural aliasing) remains even with no noise, creating a negative ring around the vessel. Larger objects suffer more from this error, and it is for this reason that objects larger than 16 pixels tend to have a nearly 10% systematic drop than the expected susceptibility. Methods to Improve Quality of Susceptibility Maps Regularization is not the only means necessary to reconstruct good quality susceptibility maps. There are also key signal processing and image reconstruction concepts that need to be applied to the data to remove other types of artifacts. The first is a more finely sampled k-space. This avoids serious ghosting in the reconstructed susceptibility map. The second is spatial resolution high enough to allow for as many pixels as possible to give useful phase information outside the source. The third is echo time long enough for phase development so as to achieve sufficient phase SNR. The use of all these methods has led to the high-quality images presented in this chapter. High resolution also plays an

DISCUSSION

483

important role in reducing the effects of Gibbs ringing by increasing the number of voxels occupied by a vessel. This should help in improving quantitative accuracy of the susceptibility values (see Figure 25.2). In principle, one could actually collect higher resolution data in the read direction at the possible expense of signal to noise without an increase in acquisition time, while it would increase data acquisition time in either the phase or partition encoding direction. Moreover, reducing the presence of noise in the phase images is crucial in obtaining a high-quality susceptibility map. Not only should the noisy pixels from the magnitude image be thresholded but also areas of wildly varying phase coming from, for example, the skull where out-of-phase fat can cause a serious problem. Setting the phase inside spherical or cylindrical regions to be a constant also helps avoid phase noise effects. Areas of constant phase jumps will also generate a new type of structural ghosting artifact that we refer to as the inverse dipole rippling effect. That is, if the phase appears as a constant without the expected concomitant external phase behavior, then this rippling effect emanating from the source will permeate the image in a nonlocal fashion. A similar effect can be caused by remnant phases that survive the high-pass filter. This leaves a nonphysical phase at the edge of the brain. This could be tackled either by simply eliminating that tissue (and hence not obtaining useful susceptibility images in that part of the brain) or by using the forward model from the magnitude geometry constraints in an attempt to remove air/tissue interface phase effects [15]. The better that this job is done, the less errors will permeate other parts of the brain from the rippling/ghosting effects described above. Partial volume effects can cause a complete loss of phase information when the vein is much smaller than the slice thickness [13]. For example, an aspect ratio of 1:4 appears to give the best cancellation effects and turns the phase inside small vessels from positive to negative for a right-handed system. This leads to the issue of the reduced measured susceptibilities. There are a few causes for the reduced values: partial volume effects, phase aliasing, and loss of signal due to spin dephasing around the magnetic source. In each of these cases, it is necessary to use the estimated size of the source larger than its actual value. For veins (cylinders), this means a reduction in the susceptibility by the ratio of the original area to the enlarged area, and for spheres a reduction in the susceptibility by the ratio of the original volume to the enlarged volume. Again, forcing the phase inside the object to be zero has little impact on the actual estimate for the magnetic moment (which is directly related to the product of the area times susceptibility for the veins or the volume times the susceptibility for a spherical microbleed, for example). On the other hand, the partial volume effect can lead to smoothing effects. Although we do see the negative ring around the vessels in the in vivo data, the expected large dip in the center of the vessels is to a large degree absent. The choice of how many slices to process to create a venous susceptibility map depends not so much on regional and global structural variations (as it does if one is estimating the effects of air/tissue interfaces [15]), but rather on how many slices the vessel phase appears in. This means that one can reconstruct the susceptibility map image with an arbitrary number of the acquired slices if one is interested only in local vessels and if this process removes more noise, it can lead to further improvement in the susceptibility maps. Susceptibility mapping offers a means to study BOLD effects in an entirely different light. Although phase has been used in BOLD fMRI experiments (see Chapter 30), susceptibility values can be used to quantify changes in oxygenation levels and then infer changes in flow as well [16]. In Figure 25.10, there is a clear increase in signal after ingestion of caffeine indicating an increase in deoxyhemoglobin levels in agreement with other

484

SWIM: SUSCEPTIBILITY MAPPING AS A MEANS TO VISUALIZE VEINS

studies [17]. Measurements in other smaller veins together show an overall 30–40% increase in the susceptibility value after caffeine administration. This increase corresponds to a reduction in blood flow of close to 30%, which is larger than what is usually observed for caffeine. This particular person was a non-coffee drinker and so the large amount of caffeine may have had an abnormally large effect. In this particular subject, no change in basal ganglia iron content was measured pre- and post-caffeine. Some small shifts in GM iron content could be found. These measurements may eventually help separate out the fractional contributions to phase from ferritin and deoxyhemoglobin. In pre- and post-caffeine experiment, no change in basal ganglia iron content was measured. In conclusion, we have shown that despite the problems in obtaining consistent susceptibility values for all vessels, it is possible to remove phase variations caused by major vessels in SWI high-pass filtered phase images. This should be useful in creating SWI processed data without the associated nonlocal, long-distance dipole effects. In the future, it may be possible to use this approach to evaluate quantitatively microbleeds and calcifications [18] and to map oxygen saturation from veins throughout the brain (rather than with the single-vessel approach proposed initially in Ref. 16 and used more extensively in recent years [19, 20]). Finally, the images shown here present a new form of MR venography and can serve as a quantitative means to distinguish potential oxygen saturation abnormalities in SWI data. Future applications of susceptibility mapping may include iron measurements in tissue. REFERENCES 1. Reichenbach JR, Venkatesan R, Schillinger DJ, Kido DK, Haacke EM. Small vessels in the human brain: MR venography with deoxyhemoglobin as an intrinsic contrast agent. Radiology 1997;204:272–277. 2. Haacke EM, Xu Y, Cheng Y-CN, Reichenbach JR. Susceptibility weighted imaging (SWI). Magn. Reson. Med. 2004;52:612–618. 3. Ali Fatemi A, Boylan C, Noseworthy MD. Identification of breast calcification using magnetic resonance imaging. Med. Phys. 2009;36(12):5429–5436. 4. Salomir R, Senneville BD, Moonen CT. A fast calculation method for magnetic field inhomogeneity due to an arbitrary distribution of bulk susceptibility. Concepts Magn. Reson. Part B Magn. Reson. Eng. 2003;198:26–34. 5. Marques JP, Bowtell R. Application of Fourier-based method for rapid calculation of field inhomogeneity due to spatial variation of magnetic susceptibility. Concepts Magn. Reson. Part B Magn. Reson. Eng. 2005;25:65–78. 6. Koch KM, Papademetris X, Rothman DL, de Graaf RA. Rapid calculations of susceptibilityinduced magnetostatic field perturbations for in vivo magnetic resonance. Phys. Med. Biol. 2006;51(24):6381–6402. 7. Cheng YCN, Neelavalli J, Haacke EM. Limitations of calculating field distributions and magnetic susceptibilities in MRI using a Fourier based method. Phys. Med. Biol. 2009;54:1169–1189. 8. Kressler B, de Rochefort L, Liu T, Spincemaille P, Jiang Q, Wang Y. Nonlinear regularization for per voxel estimation of magnetic susceptibility distributions from MRI field maps. IEEE Trans. Med. Imaging 2009. 9. Liu T, Spincemaille P, de Rochefort L, Kressler B, Wang Y. Calculation of susceptibility through multiple orientation sampling (COSMOS): a method for conditioning the inverse problem from measured magnetic field map to susceptibility source image in MRI. Magn. Reson. Med. 2009; 61(1):196–204.

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10. Yao B, Li T-Q, Gelderen P, Shmueli K, de Zwart JA, Duyn JH. Susceptibility contrast in high field MRI of human brain as a function of tissue iron content. NeuroImage 2009;44(4):1259–1266. 11. Deville G, Bernier M, Delrieux J. NMR multiple echoes observed in solid 3He. Phys. Rev. B 1979;19:5666–5688. 12. Pandian DS, Ciulla C, Haacke EM, Jiang J, Ayaz M. Complex threshold method for identifying pixels that contain predominantly noise in magnetic resonance images. J. Magn. Reson. Imaging 2008;28:727–735. 13. Xu Y, Haacke EM. The role of voxel aspect ratio in determining apparent phase behavior in susceptibility weighted imaging. Magn. Reson. Imaging 2006;24:155–160. 14. Schafer A, Wharton S, Gowland P, Bowtell R. Using magnetic field simulation to study susceptibility-related phase contrast in gradient echo MRI. Neuroimage 2009; 48: 126-137. 15. Neelavalli J, Cheng YCN, Jiang J, Haacke EM. Removing background phase variations in susceptibility weighted imaging using a fast, forward-field calculation. J. Magn. Reson. Imaging 2009;29:937–948. 16. Haacke EM, Lai S, Reichenbach JR, Kuppusamy K, Hoogenraad FGC, Takeichi H, Lin W. In vivo measurement of blood oxygen saturation using magnetic resonance imaging: a direct validation of the blood oxygen level-dependent concept in functional brain imaging. Hum. Brain Mapp. 1997;5:341–346. 17. Sedlacik J, Helm K, Rauscher A, Stadler J, Memtzel HJ, Reichenbach JR. Investigations on the effect of caffeine on cerebral venous vessel contrast by using susceptibility-weighted imaging (SWI) at 1.5, 3 and 7T. Neuroimage 2008;40:11–18. 18. Wu Z, Mittal S, Kish K, Yu Y, Hu J, Haacke EM. Identification of calcification with MRI using susceptibility-weighted imaging: a case study. J. Magn. Reson. Imaging 2008;29(1):177–182. 19. Barnes S, Haacke EM. Susceptibility weighted imaging: clinical angiographic applications. Magn. Reson. Imaging Clin. N. Am. 2009;17:47–61. 20. Langham MC, Magland JF, Epstein CL, Floyd TF, Wehrli FW. Accuracy and precision of MR blood oximetry based on the long paramagnetic cylinder approximation of large vessels. Magn. Reson. Med. 2009;62:333–340.

26 Effects of Contrast Agents in Susceptibility Weighted Imaging Andreas Deistung and J€ urgen R. Reichenbach

INTRODUCTION MR contrast agents are pharmaceutical preparations administered in various ways to enhance image contrast and obtain dynamic (pharmacokinetic) information. Contrast agents may be distinguished due to their specific physicochemical properties and pharmacokinetic profiles. In general, they alter the intrinsic contrast properties of biological tissues in either of two ways: directly by changing the proton density (e.g., diuretics, hormones) or indirectly by changing the local magnetic field or the resonance properties of tissue and hence its relaxation values (T1, T2, or T2* ). This chapter provides a short overview on different types of contrast agents in magnetic resonance, including in particular their application to susceptibility weighted imaging (SWI). There exists a vast literature on many different contrast agents for magnetic resonance imaging, including agents based on small chelates, macromolecular systems, iron oxides, and other nanosystems, as well as responsive, chemical exchange saturation transfer (CEST), or hyperpolarization agents, that are beyond the scope of this chapter. Rather, this brief survey is restricted to summarize some basic properties of some of the agents that have been applied so far with respect to SWI.

Susceptibility Weighted Imaging in MRI, By E. Mark Haacke and J€urgen R. Reichenbach Copyright
2011 by Wiley-Blackwell

487

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EFFECTS OF CONTRAST AGENTS IN SUSCEPTIBILITY WEIGHTED IMAGING

CONVENTIONAL PARAMAGNETIC MR CONTRAST AGENTS Paramagnetic substances have at least one unpaired electron and thus possess a permanent magnetic moment. The magnetic dipole moment associated with an electron is about 658 times larger than the magnetic moment of a proton [1]. On a microscopic level, the magnetic moments of paramagnetic substances produce small dipolar magnetic fields that lead to rapidly fluctuating local magnetic fields due to the random translational and rotational motion of the paramagnetic atoms or molecules. The interaction of the unpaired electron(s) with the resonating nucleus (dipole–dipole interaction) results in modified (enhanced) nuclear relaxation rates [2]. This shortening of the relaxation times depends not only on the number of unpaired electrons in the paramagnetic substances, but also on the electron spin relaxation time of the paramagnetic ion that has to match the Larmor frequency of protons. Fe3þ , Mn2þ , and Gd3þ ions fulfill both criteria making them effective contrast agents. The simplest contrast agent is a single paramagnetic ion bound to an organic ligand in a chelate, where the paramagnetic ion is usually Gd3þ , and the most common ligands are linear or macrocyclic polyaminocarboxylate/phosphonate derivatives. Due to the toxicity of metal in ionic form, like Gd3þ , in combination with an unfavorable biodistribution owing to accumulation in bones, liver, or spleen, thermodynamically and kinetically stable metal ion complexes (chelates) have been developed [3]. Typical commercially available, low molecular weight agents that are applied in the clinics include gadopentate dimeglumine (Gd-DTPA, Magnevist , Bayer-Schering Pharma AG), gadodiamide (Gd-DTPA-BMA, Omniscan , GE Healthcare), or gadoteridol (Gd-(HP-DO3A)(H2O), Prohance , Bracco Spa), among many others. All these extracellular fluid (ECF) agents have slightly different molecular structures but similar pharmacokinetic profiles. A detailed description of the effects induced by Gd3 þ complexes with reviews on relaxation theory can be found in several excellent reviews [4, 5]. The image-enhancing capability of a paramagnetic contrast agent is directly proportional to its interaction with neighboring water molecules by the paramagnetic ion and leads to an increase in the relaxation rate, either longitudinal (R1 ¼ 1/T1) or transverse (R2 ¼ 1/T2). In particular, it depends on the relaxivities r1 and r2 that constitute the main physicochemical parameters and is defined as the increase in the nuclear relaxation rate of water protons produced by 1 mmol/L of contrast agent. Ri ðcCA Þ ¼

1 1 ¼ þ ri  cCA Ti ðcCA Þ Ti;intrinsic

ð26:1Þ

Ti,intrinsic denotes the intrinsic relaxation time of tissue (in the absence of the contrast agent) and ri is the contrast agent’s specific relaxivity with a unit of L/(s mmol). The subscript i stands for either longitudinal (i ¼ 1) or transverse (i ¼ 2) relaxation. Ri is the relaxation rate and cCA the concentration of the paramagnetic center, given in mmol/L. Although being an important parameter for characterization of a contrast agent, it should be noted that relaxivity is not the only parameter that affects the efficiency of a contrast agent. The distribution of the contrast agent in a voxel, the chemical and physiological environment, diffusion, or proton density all play a role and contribute to the overall efficiency of signal enhancement [6, 7].

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The signal enhancing effects include both inner-sphere (from water molecules directly coordinated to the Gd3 þ ion) and outer-sphere contributions (from nearby H-bonded water molecules) [8]. The latter is usually relatively small and therefore neglected. For Gd3 þ complexes, the inner-sphere relaxivity primarily arises from a dipolar contribution (through-space interactions due to the random fluctuations of the electron field) and can be described by the famous Solomon–Bloembergen–Morgan theory [9, 10]. The corresponding equations that describes the relaxation times of the water protons located in the first coordination sphere of the paramagnetic metal are given by [11] " # " # 1 B 7  tc2 3  tc1 2  A2  S  ðS þ 1Þ t0c2 ¼  þ  þ T1 r6 1 þ ðvS  tc2 Þ2 1 þ ðvI  tc1 Þ2 3h2 1 þ ðvS  t0c2 Þ2 "

#

"

ð26:2Þ #

1 B 6:5  tc2 1:5  tc1 A2  S  ðS þ 1Þ t0c2 ¼ 6 þ þ2  t  þ t0c1 þ c1 T2 r 1 þ ðvS  tc2 Þ2 1 þ ðvI  tc1 Þ2 3h2 1 þ ðvS  t0c2 Þ2

ð26:3Þ where B ¼ 2  g2I  g2S   h2  S  ðS þ 1Þ=15, A= h is a constant that characterizes the scalar interaction, and 1 1 1 1 ¼ þ þ tci tr tm tsi

ð26:4Þ

1 1 1 ¼ þ t0ci tm tsi

ð26:5Þ

tm is the water residence time, tr the rotational correlation time, and tsi the electronic relaxation time. The scalar terms in equations (26.2) and (26.3) (the second terms in both equations) have to be neglected when common lanthanide and rare earths complexes are used for contrast agents. According to this theory, to increase the relaxivity, r1 of a Gd3 þ contrast agent, one has to design a ligand that will enable the complex to have a greater number of inner-sphere water molecules, q; an optimally short water residence time, tm; and a slow tumbling rate, 1/tr while maintaining sufficient thermodynamic stability. The water residence time, tm, is probably the least understood and most important parameter that affects relaxivity. Indeed, it has been demonstrated that the relaxivity of a Gd3 þ complex will increase upon slowing down its molecular tumbling (increasing its molecular weight) insofar as its water residence time is close to optimal [12–14]. The predominant effect of low molecular weight paramagnetic contrast agents at low dose is that of a shortening of T1. A contrast agent that predominantly affects T1 relaxation is referred to as a positive contrast agent, because the enhanced T1 relaxation results in increased signal intensity on T1-weighted images (organs that take up contrast agent will appear bright). On the other hand, a contrast agent that predominantly affects T2 relaxation is referred to as a negative contrast agent, because reduced T2 values result in decreased signal intensity in T2-weighted images. Table 26.1 summarizes some properties of MRI contrast agents that are currently in clinical practice for magnetic field strengths of 1.5 and 3 T.

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TABLE 26.1 Relaxivities of Different Contrast Agents Measured in Blood Plasma at 37 C for Magnetic Field Strengths of 1.5 and 3 T Contrast Agent (Trade Name) Magnevist Omniscan Prohance Multihance Ablavar MION-46L Endorem Sinerem

1.5 T

3T

Vendor

r1

r2

r1

r2

wm,CA

Bayer-Schering GE Healthcare Bracco Spa Bracco Spa Lantheus Medical Imaging

4.1 4.3 4.1 6.3 19

4.6 5.2 5.0 8.7 34

3.7 4.0 3.7 5.5 9.9

5.2 5.6 5.7 11.0 60

339.3 339.3 339.3 339.3 339.3

7 4.5 15.51

18 33 100.4

2.7 6.58

45 127.8

1382.30 5026.55 4272.57

Guerbet Guerbet

Relaxivities are given in L/(mmol s) and were taken from Ref. 6. Relaxivities of MION-46L are estimated from Figures 3 and 4 in Ref. 89. Relaxivities for Sinerem were measured by Simon et al. [90] in Ficoll solution. The molar susceptibility (last column) is given in (106 L/mol) and is based on values from Refs 25 and 91.

Effects of Paramagnetic Contrast Agents on SWI As outlined in previous chapters, the venous vessel contrast in SWI arises from local magnetic field inhomogeneity DB induced by the paramagnetic deoxygenated blood residing in the veins compared to the surrounding tissue. To understand the basic effects of a paramagnetic contrast agent on SWI, we can again resort to the two-compartment model introduced in Chapter 4 and is illustrated in Figure 26.1. The field inhomogeneity induced by the vessel is written as 8     B0 > 2 1 >  > wdo  ð1YÞ  Hct þ cCA  wm;CA  cosðuÞ  < 3 2 DBðrÞ ¼ > 2  > > : wdo  ð1YÞ  Hct þ cCA  wm;CA  sinðuÞ2  a  cosð2fÞ  B0 r2 2

8r < a 8r > a ð26:6Þ

FIGURE 26.1 Scheme of the two-compartment model. Part (a) illustrates a single voxel with parenchymal tissue (with a tissue signal fraction 1  l) that is traversed by a venous vessel with a blood signal fraction l. Without phase effect (w(TE ¼ 0) ¼ 0  ), the tissue and venous signal vectors add constructively to a value assumed for simplicity to be unity (b). If w(TE) ¼ p, the venous signal is inverted (l) causing an additional signal loss (c). Intravenous injection of a paramagnetic T1-shortening contrast agent increases the venous signal fraction from l to l0 , thus making the cancellation effect even more effective. Note that T*2 decay has been neglected for all signal vectors.

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In equation (26.6), we have extended the expression for Dw (within square brackets) by the additional term cCAwm,CA to take into account the additional susceptibility shift due to the presence of the contrast agent. The concentration of the contrast agent in the blood is given by cCA and its molar susceptibility by wm,CA, measured in m3/mol. The other quantities have their original meaning with wdo being the magnetic susceptibility difference between fully deoxygenated and fully oxygenated blood, and Hct and Y denoting the hematocrit and blood’s oxygen saturation, respectively. a is the radius of the cylinder, and u the angle between cylinder axis and B0. The observation point is expressed in polar coordinates r and f, where r describes the distance from the cylinder axis and f the polar angle between r (the perpendicular distance of the observation point from the vessel axis) and the plane defined by B0 and the cylinder axis. For simplicity, we will assume in the following that the contrast agent remains inside the vasculature and does not leak into the tissue. This scenario would mimic the situation of a vessel in brain tissue with an intact blood–brain barrier. As seen from equation (26.6), the presence of the paramagnetic contrast agent will increase DB, and hence induce an additional phase difference between the spins located inside and outside the vein. Additionally, the contrast agent will further catalyze the relaxation processes of the intravascular protons. Since a positive contrast agent at low dose predominantly influences the T1 relaxation time (and less T2 or T2* ), the vascular signal contribution in the two-compartment model becomes larger accordingly and cancels more effectively with the tissue signal contribution (see Figure 26.1). This effect has been previously described as T1 T *2 coupling [16]. The signal intensity of the two-compartment model can be written as SðTEÞ ¼ rv  l  fv ðT1 ; TRÞ  ei  wðTE;Y;cCA  wm;CA Þ  eTE=T 2V þ rt  ð1lÞ  f t ðT 1 ; TRÞ  eTE=T 2t *

*

ð26:7Þ where rv and rt are the proton densities of venous blood and tissue, respectively, and fv and ft contain the imaging parameter dependence of the blood and parenchyma, respectively. w(TE, Y, cCAwm,CA) denotes the phase shift conjointly induced by deoxyhemoglobin molecules and the contrast agent. If the vessel is not parallel to the static magnetic field, additional extravascular field inhomogeneities are present, leading to extra signal cancellation. For an rf-spoiled gradient echo sequence, fv and ft depend on the flip angle a, repetition time TR, and T1: fv ða; TR; T1 Þ ¼ sinðaÞ 

1eTR=T1v  B0 1eTR=T1v  cosðaÞ ð26:8Þ

ft ða; TR; T1 Þ ¼ sinðaÞ 

TR=T1t

1e  B0 1eTR=T1t  cosðaÞ

The factor B0 incorporates the higher sensitivity with increasing field strengths [17]. Administration of contrast agent will shorten the T1 and T2* of venous blood in equations (26.7) and (26.8) according to equations (26.1), whereas the relaxation times of tissue in general will not be affected due to the intact blood–brain barrier. Consequently, the contrast agent increases intravascular signal that, in turn, improves signal cancellation.

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EFFECTS OF CONTRAST AGENTS IN SUSCEPTIBILITY WEIGHTED IMAGING

More insight into the contrast behavior between vessel and tissue in the presence of a contrast agent may be obtained with numerical simulations. Figure 26.2 contains several plots illustrating the effect of different doses of Gd-DTPA (Magnevist) as a function of echo time on magnitude and phase of a voxel containing a small, single cylindrical venous vessel, oriented perpendicular to the B0 field (Figure 26.2a and b). The signal decays were simulated by using a 2D matrix grid with 210  210 points that contained the field distribution inside and outside the vessel and mimicked the voxel. The complex voxel signal was calculated by integrating the venous and the tissue signal over the whole array of the matrix [18, 19]: ð * SðTEÞ ¼ WðrÞ  f ðrÞ  rðrÞ  ei  g  DBðrÞ  TE  eTE=T 2 ðrÞ d 3 r

ð26:9Þ

V

FIGURE 26.2 Numerical simulations of magnitude (a), phase (b), and contrast of a voxel, containing white matter and a vein with different contrast agent doses (blood volume fraction 10%, u ¼ 90  , hematocrit 0.45, oxygen saturation 0.55, B0 ¼ 3 T, ratio between slice thickness and in-plane resolution 4:1). For each echo time (TE), repetition time (TR) was adjusted (TR  TE ¼ 10 ms), as was the flip angle FA (Ernst angle for white matter). Intravenous injection of Gd-DTPA was assumed (75 kg person, r1 ¼ 3.7 L/(mmol s), r2 ¼ 5.2 L/(mmol ), wm,Magnevist ¼ 339.29 ppm L/mol). A time delay of 10 min between sampling of k-space center and injection was assumed, resulting in a reduced concentration in blood plasma of about 20% of the initial dose. The magnitude signal decay of a voxel containing white matter only is shown by the ‘‘’’ symbols in (a). The nonexponential behavior of white matter tissue in (a) results from the adjustment of TR and FA for each simulated TE. The contrast between the venous and a white matter voxel is plotted for the magnitude in (c) and for SWI (i.e., fourfold multiplication of the negative phase mask with the magnitude) in (d).

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Depending on whether the matrix elements belong to the vessel or the tissue, fv or ft was selected from equation (26.8) to calculate the integral in equation (26.9). Proton densities r(r) and relaxation times T2* (r) were also properly chosen. The weighting function W(r) corresponds to the sampling point spread function and takes the voxel shape (e.g., cubic or cuboid-shaped voxel) into account because of the finite and discrete sampling nature of MRI [18]. For the simulations, a male person with body weight w ¼ 75 kg was assumed that corresponds to a blood volume Vbl ¼ 4.6 L, according to the relationship Vbl (L) ¼ 0.041w (kg) þ 1.53 [20]. The standard administration of 0.1 mmol/kg Gd3 þ chelate per body weight was considered as single dose. Furthermore, it was assumed that the k-space center is acquired approximately 10 min after contrast agent injection, which roughly corresponds to the mean distribution time. The pharmacokinetics of intravenously administered Gd-DTPA in normal subjects conforms to a two-compartment open model with mean distribution and elimination half-lives of about 0.2  0.13 and 1.6  0.13 h, respectively [21]. After rapid intravascular distribution, the agent diffuses into the extracellular space. The plasma concentration rapidly drops in a biexponential decay curve with the above-quoted plasma half-life of about 90 min. Ten minutes after administration, the total plasma volume contains about 20% of the given dose [22]. With a plasma volume of 55% and the molar susceptibility of Gd-DTPA of 0.0256 cm3/mol (corresponding to 321.7 106 L/mol in SI) [23], one can estimate the induced paramagnetic shift in susceptibility due to the contrast agent for single dose injection from the values given above to be approximately 0.19 ppm (SI). (Note that the ðCGSÞ volume susceptibility w may be calculated from the molar susceptibility wcm via 3 w ¼ cwm, where c is the concentration in mol.cm and there is an additional factor of 4p to convert w(CGS) to w(SI)). This value has to be compared with the precontrast susceptibility shift between venous blood and surrounding brain tissue that ranges between 0.46 ppm (SI) and 0.69 ppm (SI) and depends on the magnetic susceptibility difference between fully deoxygenated and fully oxygenated red blood cells wdo (assuming Y ¼ 0.55, Hct ¼ 0.45) [24, 25]. As seen in Figure 26.2a, signal decrease and distinct signal oscillations with increasing beating frequencies are observed with increasing dose (and thus increasing intravascular susceptibility). Similar observations are made for the phase (Figure 26.2b). For comparison, the magnitude signal of a single voxel containing only white matter is also plotted in Figure 26.2a as ‘’ symbols. The nonexponential signal time course of white matter tissue is due to the fact that for all curves plotted in Figure 26.2 and for each simulated echo time point, the value of TR was adjusted (TR ¼ TE þ 10 ms), as was the flip angle for each TR (Ernst angle of white matter). The magnitude contrast between two voxels—one containing a venous vessel and the other white matter only—clearly reveals the rise in the beating pattern with dose application (Figure 26.2c). The SWI contrast obtained by fourfold multiplication of the negative phase mask with the magnitude in Figure 26.2d also shows increasing contrast but without beating oscillations for higher doses with the maximum contrast shifting toward shorter echo times. Thus, data acquisition with a paramagnetic contrast agent allows reducing scan time with slightly higher venous contrast and/or improved spatial resolution. To illustrate this aspect in vivo, Figure 26.3 presents venograms acquired before and after injection of Gd-based contrast agents. With equal acquisition parameters, Figure 26.3a and b reveal increased vessel depiction after contrast agent injection, in particular for small penetrating vessels. In another examination, the susceptibility shift induced by the contrast agent was taken into account by reducing echo time and repetition time from 25 to 17 ms and 35 to 27 ms,

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FIGURE 26.3 Minimum intensity projections over 12 mm of susceptibility weighted images. Using

identical parameters (TE/TR/FA/B0 ¼ 25 ms/40 ms/15 /3 T, voxel size ¼ 0.56  0.56  2 mm3), the venograms of a tumor patient were acquired before (a) and 5 min after injection of 0.1 mmol/kg Gadoteridol (Prohance , Bracco Spa) (b). Contrast agent injection slightly increased venous contrast in particular for the small penetrating veins in subcortical regions. The venograms of another patient are shown before (c) and after medication (d) with 0.2 mmol/kg Gd-DTPA (Magnevist  , Bayer-Schering Pharma AG). Data in (c) were acquired using the following parameters: TE/TR/FA/B0 ¼ 25 ms/35 ms/15  /3 T, voxel size ¼ 0.45  0.45  1.8 mm3 resulting in an acquisition time of 7:34 min:s. In comparison, TE and TR were reduced to 17 and 27 ms, respectively, leading to an acquisition time of 5:50 min:s with similar venous contrast (d). Images (a) and (b) are courtesy of Kohsuke Kudo (Advanced Medical Research Center, Iwate Medical University, Morioka, Iwate, Japan).

respectively. Hence, acquisition time was reduced by 23% while producing similar venous contrast (Figure 26.3c and d). Lin et al. were among the first who examined the feasibility of incorporating a clinically available T1 reducing contrast agent with SWI to reduce susceptibility artifacts and imaging time while maintaining the visibility of cerebral veins [26]. They used Omniscan (Gd-DTPA-BMA) as contrast agent with a dose of 0.1 mmol/kg or 0.2 mmol/ kg (double dose) over all eight volunteers, and the experiments were carried out at 1.5 T. In all cases, improvement in the conspicuity of venous vessels was observed compared with the precontrast images. Furthermore, this effect was dose dependent, and with double dose application, superior venous visualization was obtained compared to single dose application. Using a double dose injection, the authors were able to reduce TE from 40 to 25 ms, which led to a concomitant decrease in TR from 57 to 42 ms, allowing a 26% reduction in data acquisition time while maintaining the visibility of cerebral venous vessels and reducing susceptibility artifacts. One further advantage of using shorter echo times in the presence of a contrast agent is that background field inhomogeneity effects are reduced. This work was later extended by Barth et al. who compared the results of contrastenhanced SWI at 3 T with those at 1.5 T in the same patients diagnosed with a known primary brain tumor or metastases by using a protocol with the same volume coverage and measurement time at both field strengths [27]. Using a single dose (0.1 mmol/kg Omniscan), a 33% higher spatial resolution within the same measurement time was possible at 3 T that revealed more details within and around the tumors compared to 1.5 T. In another study, pre- and postcontrast SWI acquisitions were performed with different doses (0.05, 0.1, and 0.2 mmol/L) of gadobenate dimeglumine (Gd-BOPTA, MultiHance) at both 1.5 and 3 T in six healthy volunteers [28]. With contrast-enhanced SWI, significant

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differences were found in the visibility of deep veins, depending on the contrast agent dose. At 3 T, the visibility of deep venous vessels, image quality, and scanning efficiency was reported to be significantly better with a standard contrast agent dose of 0.1 mmol/L compared to the 0.05 mmol/L dose. Visibility of deep venous vessels was considered equal to 0.1 mmol/L of the contrast agent compared to the precontrast images, but with a significantly reduced scan time. The authors concluded that a standard dose (0.1 mmol/kg) of Gd-BOPTA is sufficient to achieve optimum susceptibility effect and image quality at 3 T, together with a reduced scan time. These results can be attributed to the higher relaxivity of gadobenate dimeglumine (r1 ¼ 5.5 s1 mM1, r2 ¼ 11.0 s1 mM1 in plasma at 3 T and 37 C compared to r1 ¼ 3.7 s1 mM1, r2 ¼ 5.2 s1 mM1 for Gd-DTPA) [6]. In a follow-up clinical study on patients with malignant brain tumors at 3 T, it was demonstrated that the conspicuity of susceptibility effects and image quality were improved in postcontrast images compared to precontrast images and that the scan time could be reduced from 9 min (precontrast) to 7 min (postcontrast) [29]. At even higher concentrations (i.e., a triple dose), a hyperintense artifact following the course of the vein was observed that was attributed to the large susceptibility difference between vessel and surrounding tissue causing large frequency changes and misregistration [15]. Blood Pool Agents One limitation of conventional extracellular paramagnetic contrast agents refers to their nonspecific distribution in the blood plasma and extracellular space of the body after administration. Due to their hydrophilic properties, most of these agents have a rapid renal excretion with an elimination half-life of about 15–90 min. Extravasation of the contrast agent or breakdown of the blood–brain barrier leads to increased tissue signal that can confound vascular interpretability. Different strategies exist to increase the intravascular plasma half-life time of contrast agents, including reversible binding of gadolinium chelates to plasma proteins [30], design of large gadolinium-bearing molecules with no or little renal extravasation [31], or of ultrasmall superparamagnetic iron oxides (USPIOs) with long circulation times [32]. These contrast agents are commonly denoted as intravascular contrast agents or blood pool agents (BPA). Gd-Based Blood Pool Agents Currently, the only Gd-based blood pool agent approved for use with magnetic resonance angiography (MRA) is gadofosveset trisodium (Gadofosveset trisodium (originally known as MS-325 when developed by EPIX) was commercially marketed as Ablavar in the US by Lantheus Medical Imaging (Billerica, MA, USA) and was formerly marketed as Vasovist in Europe and other countries by Bayer-Schering AG (Berlin, Germany). In July, 2010, Lantheus Medical Imaging picked up the worlwide rights for gadofosveset trisodium. Currently, it is open when this contrast agent will return to the European market). The complex gadofosveset trisodium allows a reversible, noncovalent binding of the molecule to proteins, specifically with human serum albumin (HSA) [6]. With a binding ratio during the equilibrium state of about 85% bound and 15% unbound molecules in the human blood, the pharmacokinetic properties and the relaxivity of the agent are different from the conventional Gd chelate containing

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contrast agents. The compound not only has a significantly longer retention time for the active substance in blood circulation, which makes it an ideal agent for vascular imaging, but also has significantly increased relaxivities r1 and r2 due to the change of the molecular tumbling rate with the binding to albumin. Compared to conventional Gd chelate containing contrast agents, for example, Gd-DTPA (Magnevist , BayerSchering Pharma AG, Berlin, Germany), the T1 relaxivity is approximately four to five times higher at 1.5 T (Table 26.1). Hence, the Gd dosage can be reduced accordingly and is approved at a dose of 0.03 mmol/kg body weight. The compound can be used as a firstpass contrast agent, as well as for scanning in the equilibrium phase with prolonged T1 shortening in the blood pool over several minutes. Although high spatial resolution imaging in the steady state with submillimeter isotropic voxel resolution allows evaluation of venous beds in most body parts without any constraints to timing requirements and with superb clinical results, there is no direct gain compared to conventional Gd-based contrast agents when considering the specific susceptibility-based contrast mechanism of SWI, as expressed in equation (26.9). Although a single dose of

FIGURE 26.4 Simulations of magnitude (a), phase (b), magnitude contrast (c), and SWI contrast (d) of a vein embedded in a white matter voxel for single dose injections of different contrast agents. The simulation setting was the same as in Figure 26.2. The relaxivities and molar susceptibilities were taken from Table 26.1. Since the curves of the extracellular contrast media (Magnevist, Omniscan, and Multihance) fall together, the slight differences in r1 and r2 of the extracellular contrast media do not influence signal and contrast significantly. The longer half-life time of MS-325 (T1/2  28 min [94]) compensates its lower dose (0.03 mmol/kg), producing venous contrast comparable to the extracellular agents. Due to its high susceptibility and transverse relaxivity, Endorem (dosage: 15 mmol Fe/kg) produced the highest contrast in SWI.

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gadofosveset trisodium (0.03 mmol/kg) is approximately one third the dose of conventional contrast agents, its prolonged plasma half-life time compensates the lower concentration leading to similar additional susceptibility shifts (as described above) already at approximately 10 min after injection. This is also reflected in Figure 26.4, which summarizes simulations with respect to contrast behavior of a vein embedded in white matter tissue for a single dose injection of different contrast agents. So far, no studies on SWI have been published on administration of gadofosveset trisodium. Iron Particulate Contrast Agents Superparamagnetic iron oxide (SPIO) colloids consist of nonstoichiometric microcrystalline magnetite cores coated with dextranes or siloxanes. SPIO particles exhibit extremely high magnetic moments and are much more effective in affecting MR relaxation than their paramagnetic counterparts (Gd3 þ chelates). Further advantages of SPIO compounds include their fine-tuning potential for specific applications (e.g., receptor specificity), nontoxicity, and rapid clearance from the organism [3]. Commonly, superparamagnetic iron oxide particles are classified into oral (large) SPIO agents, standard SPIO (SSPIO), ultrasmall SPIO (USPIO), and monocrystalline iron oxide (MION) agents [33]. The former three kinds of agents have already been approved for clinical application or are being clinically tested, whereas the MION agents are still at the experimental study stage. Iron particulate contrast agents cause significant reduction of T2* in blood and higher susceptibility difference Dw between blood and surrounding tissue than Gd-based contrast agents. Thus, iron-based contrast agents seem to be particularly suited for vascular imaging with SWI. To address this aspect further, Figure 26.4 displays numerical signal and contrast simulations for different types of contrast agents. The molar susceptibilities were assumed to be equal for all Gd-based contrast agents (assuming a single dose application). Despite different relaxivities of the extracellular Gd-based contrast agents (Magnevist, Omniscan, and Multihance), the simulations revealed nearly identical signal and contrast curves. With the lower dose but prolonged half-life time in blood plasma, the susceptibility shift of godofosvent trisodium was similar compared to that of the extracellular Gd agents and yielded slightly decreased magnitude contrast but similar SWI contrast. A single dose of the SPIO Endorem, however, induces significantly higher susceptibility shifts that lead to increased signal oscillations in magnitude signal and magnitude contrast. Fourfold multiplication of the phase mask with magnitude signal removed these oscillations almost completely, as illustrated in Figure 26.4d. The largest SWI contrast was found for a broad range of TE values between 20 and 35 ms. Due to the extravascular field contributions of veins oriented perpendicular to B0, the susceptibility shift induced by the contrast agent (depending on the molar susceptibility) appears to be the major contributing factor in venous vessel representation with SWI. Recently, Bolan et al. [34] combined time of flight MR angiography and T2* -weighted, high resolution 3D imaging to assess the cortical microstructure in the visual cortex using both endogenous BOLD effects and an exogenous contrast agent in cats at 9.4 T (Figure 26.5). The time of flight images were used to distinguish arteries from veins: arteries appeared bright due to inflowing blood, and veins appeared dark due to the BOLD effect. T2* -weighted images acquired with monocrystalline iron oxide contrast agent (MION, 7–10 mg Fe/kg) gave high sensitivity in detecting both arteries and veins, but showed an exaggerated vessel diameter due to extravascular dephasing effects. The post-

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FIGURE 26.5 Series of three gradient echo images (a–c) of a cat brain in axial orientation (TR/TE/ B0 ¼ 32 ms/5.5 ms/9.4 T, voxel size ¼ 78  78  156 mm3). The native flow weighted image (FA ¼ 30  ) is shown in (a). T*2-weighted images (FA ¼ 10  ) before and after MION injection are presented in (b) and (c), respectively. In (d) the subtraction of the post-MION image from the pre-MION image is displayed. The arrows indicate arteries that are bright in (a), undetectable in (b), and dark in the postcontrast image (c). The veins indicated by the arrowheads are hypointense in T*2-weighted images. The diameter of these veins significantly increased after USPIO injection (c) due to the increased susceptibility shift between vessel and its surrounding tissue. Both arterial (arrows) and venous vessels (arrowheads) appear bright in the subtraction image. The ring-like appearance of veins in the subtraction image (d) results from already dark veins in the pre-MION acquisition (b). In addition, background tissue signal intensity is decreased in the contrast-enhanced image (c) compared to the native T*2-weighted image (b). Reprinted from Ref. 34, with permission from Academic Press Inc./Elsevier Science.

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MION image had the greatest sensitivity for detecting small vessels of both types, whereas the flow weighted image (MRA) and pre-MION T2* weighted image could be compared to identify whether a vessel was an artery or a vein. Since MION particles are much smaller than erythrocytes, they easily traverse capillary beds and cause lower signal intensities in parenchymal tissue after injection (Figure 26.5). Thus, this method allows visualization of the cortical neurovasculature with microscopic-scale resolution. Intravascular USPIO (Sinerem , Guerbet, France, 12.5 mg/kg) was applied in another animal study to assess the potential of contrast-enhanced SWI at a field strength of 7 T for depicting the brain vasculature in healthy mice and mice carrying intracerebral glioma xenografts [35]. With USPIO-enhanced SWI, the authors obtained highly improved visualization of the mouse brain vasculature and information on both the feeding and draining vessels in tumor supply, independent of blood flow, which was in agreement with histological findings. Using a paramagnetic intravascular contrast agent (USPIO) on anesthetized rats, Lee et al. were able to strongly increase the intravascular susceptibility shift by an estimate of eightfold relative to that of deoxyhemoglobin with the aim to estimate the contribution of deoxyhemoglobin to phase contrast between gray and white matter [36]. To compare quantitatively the frequency difference between gray and white matter, regions of interest for cortex and corpus callosum were carefully drawn excluding the cortical surface areas to avoid surface veins. Based on 2D multi-echo gradient echo phase imaging on a 7 T animal system, the authors found that the contrast between the gray (cortex) and the white matter (corpus callosum) was only minimally affected by the strong increase in the intravascular susceptibility induced by the contrast agent. This indicated that the much smaller susceptibility shifts caused by deoxyhemoglobin in the cerebral vasculature do not significantly contribute to the gray–white matter phase contrast, seen regularly on susceptibility weighted phase images. Still several other potential factors remain contributing, including higher concentrations of paramagnetic iron compounds in gray matter, higher concentrations of diamagnetic myelin in white matter, or higher macromolecular concentrations in gray matter, which require further research for full understanding (see Chapter 8). Contrast Agents That Influence the Blood Oxygenation As introduced previously, gadolinium- or iron-based contrast agents are administered into the blood circulatory system to influence the relaxation properties of blood and to enhance venous contrast in SWI. However, there also exist substances that affect cerebral blood oxygenation and influence venous contrast in SWI. Changes in blood oxygenation, Y, change both the magnetic susceptibility and the relaxation times of blood. The relationship between R*2 ¼ 1/T2* and Y is commonly approximated with a polynomial function [37–39] R*2 ðYÞ ¼ A* þ B*  ð1YÞ þ C*  ð1YÞ2

ð26:10Þ

where the coefficients A , B , and C depend on the field strength and the hematocrit of blood (Table 26.2). The high sensitivity of SWI to changes in cerebral blood oxygenation can be exploited to monitor physiological processes associated with these changes, including cerebrovascular

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TABLE 26.2 Polynomial Coefficients (in s1) for Describing Blood’s Relaxation Rate R*2 as a Function of Blood Oxygenation According to Equation (26.10) Field Strength (T)

1.5

3

4.7

Hematocrit

A

B

C

Reference

0.28

4.8

5.1

20

[37]

0.44

6.9

3.7

30

[37]

0.64

8.6

1.6

35

[37]

0.21

14.5

33.2

55.4

[38]

0.44

17.5

39.1

119

[38]

0.57

18.3

56.0

128

[38]

0.21

38

18

171

[37]

0.40

42

17

350

[37]

0.75

44

11

317

[37]

reactivity, tumor classification, traumatic brain injury assessment, or even potentially tissue oxygenation. This section briefly describes physiological effects arising from several medical gases (e.g., oxygen, carbogen) and stimulant drugs (e.g., caffeine) and reviews their role with respect to SWI. Medical Gases A straightforward technique to induce changes in cerebral blood oxygenation is the application of respiratory challenges, such as breath holding (apnea) or hyperventilation. Voluntary hyperventilation lowers arterial CO2 tension and reduces cerebral blood flow (CBF) down to 50% of the control value [40–42], which in turn reduces oxygen delivery but does not decrease cerebral oxygen consumption (CMRO2) in healthy persons [43]. This leads to a transiently increased concentration of deoxyhemoglobin in veins. During breath holding (except for extreme cases), CBF significantly increases by a range of 59–71% in both feeding arteries and the venous sinus [44]. This transports more blood to compensate for the decreased oxygen saturation without reducing oxygen consumption. Ge et al. were able to demonstrate these opposing cerebral blood oxygenation changes induced by breath holding (apnea) and hyperventilation using SWI measurements in volunteers at 3 T [45]. They observed slight signal increases in venous structures during breath holding and marked signal decreases during hyperventilation (compare Figure 26.10), as a result of different responses of vascular tone to CO2. One limitation with voluntary hyperventilation or breath holding, however, is the difficulty to induce reproducible changes of blood oxygenation. This limitation can be overcome by administering gaseous agents with defined oxygen content, such as pure oxygen or carbogen (95% O2, 5% CO2). Inhalation of normobaric pure oxygen causes arterial vasoconstriction in the brain with an associated small (10–15%) reduction in CBF [41] that alters both cerebral blood volume (CBV) and tissue’s relaxation times. Recent CBF measurements using continuous and pulsed arterial spin labeling (ASL) are consistent with these original nitrous oxide tracer kinetic methods by observing a similar trend toward a global CBF decrease of 5–7% when breathing 100% oxygen [46, 47]. Breathing a gas mixture enriched with CO2 enhances the arterial partial pressure of carbon dioxide (pCO2), which in turn relaxes the tone of the smooth muscles of the arteriolar

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resistance vessels, and thus effectively counteracts the tendency of pure oxygen to decreased perfusion. Acting as a vasodilator, CBF increases by about 50% [41], resulting in increased oxygenation of the capillary bed and venous vessels. Sedlacik et al. were able to demonstrate directly the change in venous blood oxygenation in small cerebral veins induced by carbogen breathing in a volunteer by using a 3D multiecho gradient echo sequence [18]. The blood oxygen level of cerebral veins increased from about 0.5 to 0.7 when breathing carbogen compared to breathing air. Another study on volunteers investigated signal changes associated with the response to carbogen and oxygen breathing in different brain regions by using SWI [48]. In the magnitude images, inhalation of carbogen led to a significant increase in signal intensity ranging from 4.5  1.8% to 9.5  1.4% in gray matter but no significant changes in thalamus, putamen, or white matter. Venous contrast almost vanished during carbogen breathing compared to room air breathing (Figure 26.6), whereas contrast in the basal ganglia (indicating nonheme iron) appeared to be independent on the breathing condition. Analyzing the phase data from these data sets, the authors were able to demonstrate the BOLD effect directly on phase images around a single venous vessel oriented perpendicular to B0 (Figure 26.7). The vein exhibits the typical field pattern of a cylinder having a different susceptibility compared to its surroundings, as demonstrated in Figure 26.7d by the strong extravascular field inhomogeneities during air breathing. Modulating the blood oxygenation changes this susceptibility difference, causing only slightly decreased inhomogeneities during 100% oxygen breathing (Figure 26.7e) but strongly reduced inhomogeneities during carbogen breathing (Figure 26.7f). Adding CO2 in the gas mixture can induce significant discomfort to volunteers and patients due to respiratory acidosis, leading to faster and stronger breathing and undesired movements during the MRI scans that cause image artifacts. Hypothesizing that lower CO2 concentrations are better tolerated while still being able to induce sufficient signal changes in the vessels, Sedlacik et al. investigated contrast changes in SW magnitude and

FIGURE 26.6 Minimum intensity projections over 15 mm of SWI data acquired during breathing air (a), pure oxygen (b), and carbogen (c). The increased blood oxygenation during inhaling oxygen and carbogen results in lower field inhomogeneities around veins and smaller phase shifts between spins inside the vessel and outside the vessel. Consequently, the signal of veins increased and the contrast between venous vessels and parenchyma is slightly reduced during oxygen inhalation and dramatically reduced during carbogen inhalation.

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FIGURE 26.7

In vivo visualization of the BOLD mechanism. Phase images acquired during breathing ambient air, pure oxygen, and carbogen are presented in (a, d), (b, e), and (c, f), respectively. The field inhomogeneity around a single venous vessel is shown in the lower row. Lines in (a) demonstrate the view direction along the vessel axis and indicate the location of the four adjacent phase images that are presented via average projection in (d–f). The location of the vessel is indicated by the dashed circle in (d–f). The magnetic field inhomogeneity decreases with increased blood oxygenation. Image quality and contrast may not be optimal due to conversion from color to grayscale display. Please see the color plates section for the original version of this figure.

phase images during inhalation of various CO2 concentrations (0%, 1.67%, 3.33%, and 5% CO2) in volunteers [49]. Highly significant signal changes in deeply located and cortical veins were still observed with a CO2 concentration of 3.3% (Table 26.3). It therefore seems reasonable to use a lower CO2 concentration, thereby reducing motion artifacts and discomfort. From a clinical point of view, this may have interesting ramifications, in particular with respect to tumor imaging and assessment of tumor oxygenation. Considerable research has been carried out in the past on techniques that aimed to increase radiosensitivity of cancer cells to improve the efficacy of radiation treatment. Increasing the oxygen available to these cells can be accomplished by inhaling 100% oxygen [50], hyperbaric oxygen [51] and other high-oxygen gas mixtures, such as carbogen [52–57]. Another important part of the characterization of tumors lies in understanding the angiographic behavior of lesions with respect to angiogenesis and microhemorrhages. Aggressive tumors tend to have rapidly growing vasculature and many microhemorrhages. Hence, the ability to detect these changes in the tumor could lead to a better determination of the tumor status. Combining the enhanced sensitivity of SWI to venous blood and the susceptibility

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TABLE 26.3 Mean Signal Change in Percent of Magnitude and Phase in Cerebral Veins and Gray and White Matter with Respect to 0% CO2, Averaged over 15 Subjects [49] Vessel or Tissue type Signal changes of magnitude

Deep brain veins Cortical veins Ventricle White matter Gray matter

Signal changes of phase

White matter Gray matter WM-GM

1.67% CO2 

8.3  6.5 3.5  3.8 0.2  2.3 0.08  0.89 0.24  0.66

3.3% CO2 

16.0  7.2 10.3  4.5 0.8  2.6 0.31 1.13 0.77  0.86

0.87  4.89 0.83  2.72 1.49  5.65 1.99  3.99 0.62  1.91 1.16  2.25

5% CO2 35.6  9.4 22.7  8.8 1.0  4.5 0.99  1.18 2.41 1.43 1.7  3.87 3.31  5.43 1.61  3.24

Statistical significance is indicated by.

differences between blood products and normal tissue with carbogen stimulation may then lead to better contrast in detecting tumor boundaries and tumor hemorrhages and improved understanding of tumor tissue oxygenation. First steps in this direction have been undertaken by performing high-resolution SWI in conjunction with carbogen inhalation to noninvasively probe the response of tumors (Figure 26.8) [58]. Certainly, more research is necessary to assess the response of individual tumors to physiological challenges along these lines and to help identify those patients who are likely to benefit from such approaches with respect to improved radiosensitivity of the malignant cells. Application of Anesthetics Anesthesia is a medical treatment that puts a patient in a condition of controlled unconsciousness. Commonly, gases (e.g., nitrous oxide (N2O), xenon) or vaporized fluids (volatile, for example, sevoflurane) are applied via inhalation, or drugs, such as ketamine or propofol, are injected intravenously. Since anesthetics affect respiration and the cardiovascular system, it is quite likely that a correlation exists between general anesthesia and venous contrast in SWI. First indications on attenuation of signal intensity on SWI and poor demonstration of the venous anatomy were reported on pediatric patients undergoing anesthesia (2–3% sevoflurane in oxygen) [59]. The reason for the loss of contrast is that sevoflurane slightly decreases the regional oxygen extraction fraction (rOEF) compared to awake patients. Since the attenuation of venous vessels varied among anesthetic patients, it was suggested that the depth of anesthesia might be responsible for this variation. To prove this hypothesis, Sedlacik et al. monitored blood pressure and end tidal CO2 to assess the depth of anesthesia (anesthetic: propofol, 150–300 mg/kg/min) in 108 SWI pediatric examinations [60]. Based on the significantly lower venous contrast in case of reduced blood pressure and increased end tidal CO2 and vice versa, the authors concluded that the attenuation of veins in SWI indeed depends on the depth of anesthesia (Figure 26.9). Due to the correlation between depth of anesthesia and CBF, the source for the venous contrast variations is most likely due to CBF changes induced by anesthesia. However, due to the different characteristics of anesthetic agents (see Table 26.4), further studies are required to improve the understanding of the relationship of anesthetic agent, concentration, and CBF on venous contrast in SWI. Anesthetics are also used to sedate animals for imaging. In mouse and rat experiments, intraperitoneal injection of a mixture of ketamine, xylazine, and atropine has

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FIGURE 26.8 T1-weighted spin echo scan (TR/TE/FA ¼ 575 ms/14 ms/70  ) before (a) and after application of Magnevist  (b) of a patient with glioblastoma multiforme. Corresponding venograms acquired during breathing ambient air are shown in (c) and (d). The heterogeneous overlay in (d) maps signal increases of the tumor signal induced by carbogen inhalation. The active perimeter can be clearly distinguished from the inactive center of the tumor. Reprinted from Ref. 58, with permission from Georg Thieme Verlag KG. Image quality and contrast may not be optimal due to conversion from color to grayscale display. Please see the color plates section for the original version of this figure.

allowed to delineate cerebral veins in SW images with high quality. Another agent for sedating animals is isoflurane, applied along with air or with a mixture of 20% oxygen and 80% nitrogen. In this case, however, the venous response on SWI strongly depends on the partial pressure of oxygen (pO2) in the supplied gas, which can lead to a dramatic loss of venous contrast if isoflurane is used along with pure oxygen (see Chapter 35).

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FIGURE 26.9 Minimum intensity projection over a 16 mm thick slab of SWI data of a 7-year-old patient at two different MRI examinations with identical acquisition parameters. The patient was anesthetized by injecting propofol (adjusted between 150 and 300 mg/kg/min). The table summarizes the physiological parameters during data acquisition of (a) and (b). Courtesy of Jan Sedlacik (Department of Radiological Sciences, St. Jude Children’s Research Hospital, Memphis, TN, USA).

TABLE 26.4 Impact of Anesthetic Agents on Regional Oxygen Extraction Fraction and Regional Cerebral Blood Flow (rCBF) Compared to Awake Subjects Measured with 15O-Labeled Positron Emission Tomography (Based on Refs 92 and 93) Anesthetic

rOEF

rCBF

Sevoflurane (8%)/oxygen (92%) Sevoflurane (8%)/70% N2O/22% oxygen Ketamine Propofol Propofol and N2O

Decreased More decreased Decreased Constant Constant

Decreased Decreased Increased Decreased Decreased

Other Intravenous and Oral Drugs There exist a variety of substances that influence cerebral blood flow and act as potent cerebral vasodilators. Acetazolamide (C4H6N4O3S2), for instance, which is used in the treatment of epileptic seizures, benign intracranial hypertension, glaucoma, or altitude sickness and is injected intravenously (>10 mg/kg), has been shown to increase cerebral blood flow from 30% [61] to about 50% [62, 63], and venous oxygen saturation by approximately 20% compared to the native condition [62]. Therefore, it is frequently used

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FIGURE 26.10 Venograms (upper row, projection length ¼ 12 mm, TE/TR/FA/B0 ¼ 40 ms/49 ms/20  / 1.5 T, voxel size ¼ 0.57  0.57  3 mm3) and CBF maps (lower row) of a single volunteer to monitor the response to several respiratory modulations. Compared to the resting state, hyperventilation decreased CBF and improved venous contrast. For oxygen, carbogen, and acetazolamide, CBF increases whereas venous conspicuity decreases compared to the resting state. The CBF maps were obtained with ASL by using a flow-sensitive alternating inversion recovery (FAIR) sequence (TE/TR/FA/NEX ¼ 8.7 ms/ 2000 ms/20  /50, voxel size ¼ 4  4  8 mm3, slice selective inversion slab ¼ 10 cm, duration of tagging bolus (TI1) ¼ 700 ms, postlabeling delay time ¼ 1000 ms, image acquisition carried out at TI2 ¼ 1700 ms). CBF values are given in mL/100 g/min. Courtesy of Kohsuke Kudo (Advanced Medical Research Center, Iwate Medical University, Morioka, Iwate, Japan).

to assess the hemodynamic reserve and vasomotor reactivity in clinical studies [64]. Acetazolamide penetrates the blood–brain barrier slowly and inhibits carbonic anhydrase that reversibly catalyses the conversion of CO2 and H2O to H2CO3, which in turn produces H þ and HCO3. HCO3 induces a local extracellular acidosis by increasing the concentrations of CO2 and H þ in the extracellular fluid in the brain, which is assumed to act as a stimulus for the increase in blood flow [65]. Due to the rapid and significant increase in CBF, which is not paralleled by the oxidative metabolism, SWI should thus be quite sensitive to induced signal intensity changes. Figure 26.10 summarizes the effects of different physiological challenges on the contrast seen on minimum intensity projections of SWI data in a volunteer. The challenges applied include hyperventilation, breathing oxygen, and carbogen, as well as intravenous administration of acetazolamide. Furthermore, ASL data were collected concomitantly with the SWI data. Since ASL allows measurement of perfusion by using magnetically labeled arterial blood as an endogeneous tracer, the information of the perfusion maps reflecting increases or decreases of cerebral blood flow is complementary to the reduced or increased venous vessel contrast nicely seen on the SWI projections. This reflects the correspondingly increased or decreased venous oxygenation saturations. Another widely used substance affecting both blood flow and neural activity is caffeine, which is naturally available and mainly consumed in the form of coffee and tea. Caffeine is a member of the methylxanthine family of drugs that are adenosine antagonists [66]. Vasoconstriction due to caffeine is thought to primarily reflect the antagonism of adenosine A2 receptors [66]. As binding of adenosine to A2 receptors is associated with vasodilation, caffeine-related antagonism may reduce the ability of adenosine to contribute to functional increases in cerebral blood flow [67–69]. Of interest are the physiological effects that arise at low concentrations, such as of a single cup of coffee containing typically 100 mg to 150 mg caffeine [70]. Since brain activity remains constant or even increases, the decrease of CBF in

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the presence of caffeine should thus increase the oxygen extraction fraction (OEF) in order to maintain CMRO2. Haacke et al. were among the first who applied caffeine to collect high-resolution SW images to observe the difference in signal loss pre- and post-caffeine intake [71]. They observed signal changes in SWI experiments that were focused more on the vascular areas, rather than on the parenchyma. To illustrate the effect of caffeine, Figure 26.11 shows venograms acquired before and 50 min after caffeine intake. The decreased blood oxygenation due to caffeine ingestion increased the field inhomogeneities around veins and induced phase shifts between spins inside and outside the vessels. Such changes can be monitored by relative signal changes in magnitude (Figure 26.11c) and phase (Figure 26.11d). In a follow-up study, Sedlacik et al. quantified caffeine-induced signal changes in venous vessels using SWI during the first 60 min after intake [72]. Healthy volunteers underwent a native SWI scan followed by 200 mg caffeine ingestion and several single-echo SWI scans to sample the signal influenced by caffeine. The volunteers were furthermore divided in two groups consisting of coffee drinkers (n ¼ 12) and coffee abstainers (n ¼ 15). Applying a region of interest based analysis, the authors reported approximately exponential signal decay in venous vessels with time (Figure 26.12) that was in agreement with a linear pharmacokinetic model of oral absorption of caffeine [73]. Both venous time courses reached a minimum in the time interval of between 40 and 50 min, while allowing a significant differentiation between coffee drinkers (venous signal change: 16.5  6.5%) and abstainers (venous signal change: 22.7  8.3%). Only small signal changes of about 2  1% were found in both gray and white matter and 1  2% in the ventricles, in accordance to earlier findings. The effects of caffeine have also been investigated with respect to functional BOLD imaging. Since factors that alter baseline CBF can modulate temporal dynamics of the BOLD response through alterations in the strength of neurovascular coupling, caffeine has been used to demonstrate increases in the speed of the visual BOLD response, suggesting that neurovascular coupling is strengthened when CBF decreases [74–79]. Quantitative Assessment of Contrast Agent-Induced Effects In this final section, we will briefly touch on the possibility to assess quantitatively linear susceptibility effects induced by the presence of a contrast agent in a vessel. To this end, we will consider gradient echo phase information, wðrÞ ¼ g  DBðrÞ  TE, collected with and without a contrast agent. Assuming no motion, no distortions, and equal shimming parameters for all scans, subtraction of phase images before, wref ðrÞ, and after administration of a contrast agent, wCA ðrÞ, eliminates static magnetic susceptibility-induced field shifts, thus revealing the field contribution, DBCA ðrÞ, that varies between both acquisitions: DBCA ðrÞ ¼

wðrÞwCA ðrÞ g  TE

ð26:11Þ

As long as no phase aliasing occurs, there is a unique one-to-one map of phase differences to the magnetic field. The underlying magnetic susceptibility change Dwðrin Þ inside the vessel can then, in principle, be extracted by assuming the infinite cylinder model (see equation (26.6)): wref ðrin ÞwCA ðrin Þ Dwðrin Þ ¼ 2  ð26:12Þ g  TE  B0  ðcos2 u1=3Þ

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FIGURE 26.11 Minimum intensity projections over 17 mm of SWI data (TE/TR/FA/B0 ¼ 20ms/57 ms/ 20  /3 T) acquired before (a) and 50 min after caffeine ingestion (b). Relative signal changes between preand post-caffeine uptake are shown for signal magnitude (c) and phase (d). The decreased blood oxygenation after caffeine intake increases field inhomogeneities around veins and the phase shifts between spins inside and outside the vessel. Consequently, the venous signal decreases and, hence, improves the contrast between veins and parenchyma. Image quality and contrast may not be optimal due to conversion from color to grayscale display. Please see the color plates section for the original version of this figure.

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FIGURE 26.12 Time course of T*2 signal change in venous regions of interest for two groups of subjects (caffeine abstainers, caffeine users) at 1.5 T. The y-error bars indicate the mean standard error over the number of subjects of each group. The x-error bars denote the standard deviation of the time points that were averaged to a single point. According to a linear pharmacological model of caffeine, the dotted lines indicate fitted exponential curves for venous signal change. Reprinted from Ref. 72, with permission from Academic Press Inc./Elsevier Science.

In case of a lanthanide-based contrast agent, for instance, DwðrÞ refers to the product wm;CA  cCA ðrÞ as introduced in equation (26.6). In a recent animal study, this approach was actually used to quantify contrast agent concentrations in vessels of living mice [80]. Phasedifference imaging with a gradient echo sequence at short echo times was used to map variations in Larmor frequency induced by a dysprosium chelate (Dy-DOTA). According to the geometry conditions, the frequency shift could be directly linked to the real concentration of the agent in arterial and venous vessels that were oriented parallel to B0 [80]. In a similar way, phase information derived from high-resolution 3D gradient echo scans has been used to estimate oxygenation levels in single venous vessels with defined orientation to the static field in volunteers [81, 82]. Mean oxygenation values of Ymean ¼ 0.544  0.029 [82] and Ymean ¼ 0.53  0.03 [18] were reported in good agreement with values known from physiology textbooks or with values obtained with different imaging methods, such as positron emission tomography (PET). Ito et al. reported a cerebral oxygenation extraction fraction of OEF ¼ 0.44  0.06 in 70 healthy volunteers, which corresponds to a blood oxygenation of Y  0.56 [83]. The model of an infinite cylinder has, of course, limited applicability. In case of a general magnetic susceptibility distribution wðrÞ, which is not restricted to a special geometry, such as cylinders or spheres, the resulting magnetic field DBðrÞ may be quite complicated.

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Consequently, calculation of the magnetic susceptibility based on the measured phase information that represents the magnetic field will not be straightforward, but will become an ill-posed inverse problem. There exist several approaches, however, that have been proposed to overcome these problems, including Fourier-based methods, which rely on the local relationship between the magnetization of a sample and the field perturbation that it generates and that holds in the Fourier domain [84, 85], or inversion methods that aim to estimate the magnetic properties through least squares fitting of the measured field [86]. However, these methods are beyond the scope of this chapter, and the readers are referred to Chapter 24 and 25 for further details.

CONCLUSION In this chapter, we have briefly reviewed some contrast mechanisms arising from different types of contrast media, including paramagnetic agents, iron particulate agents, and agents that affect cerebral blood oxygenation, with respect to SWI. As illustrated by simulations and animal MRI experiments, iron particulate agents are able to enhance the vascular contrast in SWI substantially. Altering the SWI contrast by administration of paramagnetic agents [27] or by modulating blood oxygenation [48] may prove valuable for tumor characterization and may provide further insights into tumor vascularization. For instance, hemorrhages that can mimic intratumoral or peritumoral venous structures due to their similar paramagnetic behavior may be identified by analyzing susceptibility weighted images before and after contrast agent application since their signal intensity will remain constant, whereas signal intensity of vessels will change [87]. An interesting application may be to combine the administration of a T1-shortening extracellular agent with the intake of caffeine in a single echo SWI scan to improve simultaneous assessment of bright arteries and dark veins in magnitude and susceptibility weighted images, respectively [88]. In conclusion, targeted modification of SWI contrast by applying contrast agents is a versatile tool for modulating the visibility of the macroscopic venous vasculature and for obtaining insights into cerebral anatomy and physiological processes such as tissue oxygenation or cerebrovascular reactivity.

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27 Oxygen Saturation: Quantification E. Mark Haacke, Karthik Prabhakaran, Ilaya Raja Elangovan, Zhen Wu, and Jaladhar Neelavalli

INTRODUCTION Quantifying physiological effects in BOLD (blood oxygenation level-dependent) imaging depends critically on understanding the magnetic properties of blood. The current literature is replete with papers quoting an older value of the in vitro susceptibility of blood coming from the pioneering work of Weisskoff and Kiihne [1]. They used a series of measurements with varying amounts of oxygen in the blood and measured the field changes outside the cylindrical tubes containing the blood. They performed these experiments using an asymmetric-echo, spin-echo sequence to obtain phase measurements from which the magnetic field can be calculated. These were then fitted to a dipole formula for a cylinder perpendicular to the main field. From these measurements, they were able to ascertain the relative difference between fully oxygenated wo and deoxygenated wd blood that they referred to as wdo ¼ wd  wo. They found wdo ¼ 0.18 ppm (cgs units). This value has been used in the determination of in vivo oxygenation levels in the brain and in many other papers trying to understand changes in oxygenation in BOLD imaging. More recently, Spees et al. [2] have suggested that this result is wrong, being two-third of the correct value for wdo as originally determined by Pauling and Coryell in 1936 [3]. They proceeded to perform a series of superconducting quantum interface device (SQUID) experiments to determine wdo and discovered that Pauling and Coryell’s result appeared to be correct. So the open question remains: ‘‘Why are these two results different and what is the correct value to use in an in vivo MR imaging experiment?’’ In this chapter, we present evidence that points to the higher value of wdo ¼ 0.27 ppm as being correct. We discuss the ramifications of using either wdo ¼ 0.18 ppm or wdo ¼ 0.27 ppm Susceptibility Weighted Imaging in MRI, By E. Mark Haacke and J€urgen R. Reichenbach Copyright
2011 by Wiley-Blackwell

517

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to determine local oxygen saturation in vivo using MRI. In practice, T2* has been used as a measure for changes in oxygen saturation [4, 5]. However, the best test would be a straightforward proof by a direct MRI measurement of the local oxygen saturation and from this determine the value of x do. Furthermore, once an accurate measure of oxygen saturation becomes possible, measures such as those from T2* can be better validated or calibrated. Our approach is to measure the local field inside a major vein in vivo running as close to parallel to the main field as possible. This is most easily implemented in the leg where there is little motion, negligible respiratory effects and no problems with swallowing [6]. More recently, this approach has also been tried by Fernandez-Seara et al. [7]. In our approach, we use a 3D flow compensated gradient echo susceptibility weighted imaging (SWI) approach to remove any phase effects from blood flow [8, 9].

MATERIALS AND METHODS The main concept of using phase to estimate oxygen saturation comes about because of the sensitivity of the phase to the local susceptibility of the tissue. Oxygen saturation (Y) can in theory be extracted from the phase of a vessel making any angle to the field if it is large enough relative to the pixel size and the pristine phase information is not distorted. For example, for a right-handed system and a cylinder making an angle u to the main field, the phase (j) inside a vessel is given by w ¼ gx do B0 Hct ð1YÞ TE ð3 cos2 u1Þ=6

ð27:1Þ

If a specific substitution for xdo is made, for example, 0.18 ppm, then a certain value for Y (the oxygen saturation) can be found once the other variables, Hct (hematocrit), B0 (the main field), and TE (the echo time), are known. If on the other hand, Y is known as well, then xdo can be determined. Since xdo is usually assumed to be 0.18 ppm, one can look instead for the deviation of xdo from this value. Here, the phase difference between arterial and venous blood is used to determine oxygen saturation (see Figure 27.1 and further discussion later in this section). Therefore, substituting wdo with Awdo and using k ¼ 2p  42.58  4p  0.18  1.5/6, for B0 ¼ 1.5 T, A (and hence wdo) can be found from A ¼ ½wðVein ÞwðArt Þ=½k Hct ð1YÞ TE ð3 cos2 u1Þ

ð27:2Þ

where j(Vein)  j(Art) is the difference between the venous (Vein) and arterial (Art) phase. Different approaches are described below in an attempt to determine if A ¼ 1 (wdo ¼ 0.18 ppm) or A ¼ 1.5 (wdo ¼ 0.27 ppm).

Imaging Methods All data were acquired using a Siemens 1.5 T Magnetom Sonata MR scanner with a flexible four channel surface array coil in the thigh region of the leg. The goal was to obtain highresolution cross-sectional images of the femoral vein. Six healthy volunteers (aged 23–49) were recruited for the study following an internal review board (IRB) approved process and data were collected only after volunteers had signed an IRB approved consent form. Each

MATERIALS AND METHODS

519

FIGURE 27.1 The top right image represents the magnitude image from a TE ¼ 25 ms scan. The top left image is the associated phase image. The phase values along the profile (black line starting from bottom right moving to top left of the line) in the phase image run through the background tissue, artery, and vein that are measured. The phase values from the background are then fitted to a parabola and subtracted from the phases along the profile (black line) to create a background corrected phase of the artery (larger vessel) and vein (smaller vessel). Reprinted from article Barnes SR et al. Magn Reson Imaging Clin N Am. 2009 Feb;17(1):47–61., with permission from Elsevier Science.

subject was positioned inside the magnet feet first in a supine posture. A localizer scan was run to get a set of scout or reference images. The scout images were used to determine the imaging volume over which a 2D time of flight magnetic resonance venographic (MRV) sequence was run transversely with a saturation band to reduce signal from the inflowing arterial blood so as to obtain just the venous blood signal from the imaging volume. The imaging parameters were TR ¼ 30 ms, TE ¼ 6 ms, FOV ¼ 240 mm  240 mm, Nx ¼ Ny ¼ 256, FA ¼ 20 , BW ¼ 400 Hz/pixel, Nz ¼ 64, and phase encoding direction laterally (left to right). Using these venous images, 3D projection images were generated to determine how best to acquire the next set of 3D gradient echo images so that the vein would be perpendicular to the imaging slab in the center of the imaging volume. Shimming was

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then performed in the imaging volume to optimize the static field homogeneity. Transverse images were acquired typically using a flow compensated, strongly T2* -weighted, high bandwidth, four or five echo gradient echo susceptibility weighted imaging sequence [8]. This sequence was designed with a symmetric echo for each echo. For the multi-echo SWI sequence, TR was 35 ms in subject 1 and 4 and 30 ms for subjects 2 and 3. Echo times ranged from 5 to 25 ms in increments of 5 ms but in case 4, 25 ms was replaced by 30 ms to see if choosing a longer echo time made any difference in determining the slope (from a phase change versus an echo time plot). The flip angles were 20 for subject 1, and then lower for the rest (to reduce any ghosting artifacts) as follows: 13 for subjects 2 and 3 and 15 for subject 4. The slice thickness in all cases was 2 mm (32 slices). The in-plane resolution was 0.9 mm  0.9 mm (bandwidth 380 Hz/pixel) with matrix size 256  256 (FOV 230 mm  230 mm) for subjects 1 and 4 and 0.78 mm  0.78 mm (bandwidth 320 Hz/pixel) with matrix size 256  256 (FOV 200 mm  200 mm) for subjects 2 and 3. Two subjects (5 and 6) were also run with a single-echo sequence several times with echo times ranging from 20 to 35 ms and a bandwidth of 78 Hz/pixel, but the results were inconsistent, perhaps due to patient motion or flow effects through a long readout and long echo time. These results are not shown, but they did serve to give the experience necessary to create a stable environment, collect and process the oxygen saturation measurements for the blood, and understand the sensitivities required related to flow effects and data analysis. Different parts of the veins were measured depending on the image quality and the straightness of the vessel segments. Since the veins were not exactly parallel to the main magnetic field, depending on which segment of the vein is measured, we used the 3D venous data to measure the angle the vein made with the main magnetic field. For a given segment, the center of the vein was measured in the starting slice and again in the ending slice (referred to as the nth slice). The coordinates of the centers were used to find the distance ‘‘d’’ between the center of each cross section of the vein under investigation. The angle of the vessel, with respect to the main magnetic field direction (z), was found from u ¼ tan1 ½dDx=½ðn  1ÞDz

ð27:3Þ

where, Dx is the resolution in the x direction and Dz the resolution in the z direction. Finding Oxygen Saturation and Hematocrit In order to calculate the oxygen saturation, the subject’s hematocrit is required. To validate the MRI-measured oxygen saturation, the oxygen saturation in the blood should be measured by another means. In the latter case, we found that three different methods were necessary in an attempt to determine the correct choice for the susceptibility of blood. In the first approach, blood samples were acquired in the subjects three times within 30 min to ascertain the errors in the measurements of Hct and Y. Blood was drawn from the antecubital vein in the arm on each volunteer by the research nurse on site. (The University Institutional Review Board would not allow drawing blood from the major vein behind the knee as there is a potential for increased bleeding, bruising, and discomfort when blood is taken from a weight-bearing appendage.) These blood samples were immersed in ice to prevent clotting and rushed to the Detroit Medical Center University Laboratories for blood gas analysis. Hematocrit and oxygen saturation, Y, were determined using an IL synthesis blood gas analyzer (Instrumentation Laboratory Company, Lexington, MA). The results for

MATERIALS AND METHODS

521

Y varied from the ridiculously low values of 35% to high values of 90% such that the integrity of the system to measure oxygen saturation was called into play. The company representatives tried to adjust calibration for the system, but they admitted that too many variables made it very difficult for this system to measure venous oxygen saturation accurately. These systems are basically made to handle arterial blood with oxygen saturations in the 90% range. In the second approach to directly measuring the oxygen saturation, we measured the blood T2* and then attempted to infer the oxygen saturation value from the measured T2* of blood. We chose to use the formula for R*2 from Li et al. [5]: * R*2 ¼ 1=T2* ¼ 1=T2o þ AT2 ð1  YÞ ¼ 13:29ð1  YÞ þ 6:59

ð27:4Þ

* where T2o is the T2* of fully oxygenated blood, Y is the fraction of oxygenated hemoglobin in blood, and AT2 is the coefficient of linear dependence of R*2 on (1  Y), respectively. Li et al. [5] investigated a quadratic version of this relationship over a wide range of oxygen saturation levels but for (1  Y) less than 0.4 (i.e., an oxygen saturation of greater than 60%), one could use equation (27.4) to estimate Y from R*2 . For T2* measurements, the magnitude SWI images were checked for image quality and the presence of any motion or flow artifacts, then a region of interest was drawn inside the vein in the transverse images as shown in Figure 27.1 and the mean signal intensities measured and T2* calculated from the ratio of the first and last echoes. In the third approach, we simply plotted A (as described above in the theory subsection) as a function of Y so that a clinical knowledge of Y, or a priori knowledge from more invasive measures of Y, could be used to draw conclusions about the correct value for A. These issues led us to calculating A values for a range of oxygen saturation, Y, varying from 40% to 75%.

Determining the Phase Difference Between Arteries and Veins The next step in estimating the susceptibilities for a given oxygen saturation was to plot the venous and arterial phase as a function of echo time. Since our interest lies in the difference in field caused by changes in oxygen saturation, the difference between the venous (Vein) and arterial (Art) phase, j(Vein)  j(Art), was plotted against TE and fitted to a straight line and the slope was obtained. An A value of unity would imply wdo ¼ 0.18 ppm/unit of Hct in cgs units while an A value of 1.5 would imply that wdo ¼ 0.27 ppm/unit of Hct in cgs units. Therefore, in order to determine A, given that TE is known and j(Vein)  j(Art) is found from the multi-echo data, both Hct and Y must be determined. An error analysis for linear equations was used to determine the errors in each term, including the phase, the angle of the vein with the main field, Hct, and Y to estimate errors in A as a function of Y. Two approaches were taken to estimate the phase variation between arteries and veins and the background tissue. First, the phase values were measured in phase images on which a high-pass phase filter was applied. The high-pass filter removes the overall, spatially slowly varying background phase in the images. However, it must be kept in mind that such filtering can modify to some extent the absolute differences in j(Vein)  j(Art). Second, we start with original phase images and remove any potential baseline shift in phase, arising from background field variations, by first fitting the phase of the surrounding muscle to a two-

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dimensional quadratic function and use this to predict background phase throughout the entire region of interest. The central phase in each artery or vein was then corrected by subtracting out the background static field variations predicted at these points (see Figure 27.1). Phase was measured by drawing a region of interest inside the vein and the artery in the phase images, the mean of the phase and its standard deviation were obtained. This was performed for 8–10 contiguous slices and the mean phase and SD were evaluated for both the venous and the arterial blood. The values of phase differences between venous and arterial blood at different TEs were then used to calculate A. High-Resolution Imaging to Visualize Signal Variations in the Veins In order to understand the magnitude and phase variations seen in the vessels in the leg, a series of experiments was run on four other volunteers. Two had no outstanding problems and the other two were parent and child, one aged 56 and one aged 18. Blood flow measurements were taken from a pulse trigger with Vencs of 10 and 25 cm/s for the parent and 50 and 100 cm/s for the child. The imaging parameters for this sequence were TE ¼ 12 ms, TR ¼ 50 ms, FA ¼ 20 , resolution ¼ 0.8 mm  0.8 mm, 256  256 matrix size, and a slice thickness of 4 mm. This was a 2D gated scan that took approximately 3 min to run depending on the success of the gating window. A high-resolution SWI scan was run several times with read and phase encoding switched to see if this would explain the variations in signal intensity (for the child) and supine and prone (for the adult). The imaging parameters for this sequence were TE ¼ 10.2 ms, TR ¼ 21 ms, FA ¼ 15 , resolution ¼ 0.5 mm  0.5 mm  2 mm, and 512  512 matrix size.

RESULTS Since we were unable to validate the oxygen saturation of the veins by direct measurement, we next reverted to the use of R*2 measurements to estimate Y. T2* was measured over as many slices as possible for the femoral vein. It is often the case that the femoral vein does not appear circular but can appear compressed. Generally, the central region of the 3D slab was well behaved in terms of uniform signal within the vessel. As the vessel became smaller and nearer the edges of the slab, the signal was nonuniform and was not used to calculate T2* . An example of the T2* variation across a series of 12 slices is shown in Figure 27.2. In this example, we obtained fairly uniform T2* but this was not always the case. These measurements yielded the following results for T2* for mean/standard deviation for the four subjects: 77/2, 79/2, 73/1, and 67/3 ms. A T2* of 80 ms, according to equation (27.4), still yields a Y value near 0.55. The lower the T2* , the lower the value of Y. From these T2* measurements, one would assume that A ¼ 1. The resulting measurements for the slope of the phase difference between veins and arteries, the angle of the vein measured, and the hematocrit of the blood in vitro are given in Table 27.1 along with the errors in each measurement. These were substituted into equation (27.4) to predict A as a function of oxygen saturation, Y for the phase filtered approach (Table 27.2, Figure 27.3), and the polynomial fit to the background approach (Table 27.3, Figure 27.4). The polynomial fit approach brought all four results into line with each other. These data show that if A ¼ 1, Y, must be about 55% in the femoral vein, similar to the results found in the brain in Ref. 9, and if A ¼ 1.5, Y must be about 70%.

523

RESULTS

100.00 90.00 80.00

T2* (ms)

70.00 60.00 50.00 40.00 30.00 20.00 10.00 0.00 0

5

10

15

20

25

Slice no.

FIGURE 27.2

T2* as a function of slice number for 12 slices for volunteer 2.

TABLE 27.1 The Parameters Measured from the Data Acquired on the Four Usable Subjects for Calculating A Subject

(w (Vein)  w (A))/TE

Angle (u)

Hct

SUB 1 SUB 2 SUB 3 SUB 4

29  0.49 34  1.54 30  0.23 33  0.56

16  4 16  6 17  6 20  3

0.405  0.020 0.444  0.020 0.407  0.020 0.469  0.020

The phase difference between arteries and veins given in Siemens phase units (spu) divided by TE in ms, spu are converted into radians by multiplying by p/2048. The measured angle of the vessels is given in degrees.

The parent/child relationship was most revealing for the effects of changes in flow and vessel size. Swapping read and phase encoding had no effect on the phase images (as expected if the sequence is fully flow compensated). Phase response was reasonably uniform for the child and initially for the parent as well. However, after 30 min in the magnet, the parent’s venous signal dramatically changed (Figures 27.5 and 27.6). In the first set of experiments, the parent was supine. When the parent was taken out and imaged again in the prone position, the vessels that had the most inhomogeneous response at the later times now became clearly outlined and had a more uniform response (Figures 27.5c and 27.6b). Blood flow measurements revealed a peak velocity of 10 cm/s for the parent and 40 cm/s for the child. The child’s popliteal vein was 5 mm while that of the parent was 10 mm. TABLE 27.2 The Corresponding Values of A as a Function of Y for the Four Subjects Using a High-Pass Filter Approach to Remove the Background Phase Y SUB 1 SUB 2 SUB 3 SUB 4

50

55

60

65

70

75

0.84 1.11 0.74 1.00

0.93 1.23 0.82 1.11

1.05 1.39 0.92 1.25

1.20 1.58 1.05 1.43

1.40 1.85 1.23 1.67

1.68 2.22 1.47 2.01

A versus Y 2.5 SUB 1 SUB 2

2

SUB 3

A value

SUB 4

1.5

1

0.5

0 50

55

60

65

70

75

Oxygen saturation (%)

FIGURE 27.3 Plot of Table 27.2 giving the corresponding values of A as a function of Y for the four subjects using a high-pass filter approach to remove low spatial frequency background. Reprinted from article Barnes SR et al. Magn Reson Imaging Clin N Am. 2009 Feb;17(1):47–61., with permission from Elsevier Science. TABLE 27.3 The Corresponding Values of A as a Function of Y for the Four Subjects with Parabolic Curve Fitting Used to Remove the Background Phase Y SUB 1 SUB 2 SUB 3 SUB 4

50

55

60

65

70

75

0.82 0.87 0.86 0.86

0.91 0.97 0.95 0.96

1.02 1.1 1.07 1.08

1.17 1.25 1.22 1.24

1.37 1.46 1.43 1.44

1.64 1.75 1.71 1.73

A versus Y 1.8 1.7

SUB 1

1.6

SUB 3

A value

1.5

SUB 2 SUB 4

1.4 1.3 1.2 1.1 1 0.9 0.8 50

55

60

65

70

75

Oxygen saturation (%)

FIGURE 27.4

Plot of Table 27.3 giving the corresponding values of A as a function of Y for the four subjects with parabolic curve fitting used to remove the background phase. Reprinted from article Barnes SR et al. Magn Reson Imaging Clin N Am. 2009 Feb;17(1):47–61., with permission from Elsevier Science.

DISCUSSION AND CONCLUSIONS

525

FIGURE 27.5 SWI processed magnitude image (a) and SWI filtered phase image (b). These images were acquired supine 30 min after the volunteer was placed on the table. SWI filtered phase image (c) acquired in the prone position within a few minutes of the subject being placed on the table. Note the vessels appear completely different in the supine versus prone positions. In the former case, it is hard to differentiate the full scope of the circular cross section of some vessels, while in the latter case the boundaries are clearly seen.

DISCUSSION AND CONCLUSIONS The inability to measure Y accurately or to use R*2 to find Y accurately is disappointing but important technically as well. First, measuring venous blood oxygen saturation is a difficult problem, one often done with in vivo invasive procedures [10]. Second, it indicates that when an MR model, such as that presented here, can be used in confidence, then oxygen saturation could be ascertained noninvasively. Third, R*2 measurements are also difficult and if this MR phase approach proves viable, it may help to better fine tune such R*2 maps to oxygen saturation. The advantage that R*2 has theoretically is that there is no geometry dependence on R*2 as there is for phase inside the vein. The nonuniformities in the veins led us to investigate a high-resolution scan repeated several times in the same sitting. Initially, we thought that the source of artifacts might be due to the valves in the veins. But the valves are spaced centimeters apart and could not explain the variations from slice to slice. The results presented in Figures 27.5 and 27.6 demonstrate that the source of artifacts is likely due to settling of the blood. This should serve as a warning for others attempting these measurements in the future. Subjects should be imaged immediately before they become too comfortable and as an insurance policy the flow in the vessels should be measured as well. Here, we found that the vessels in the parent were twice as large as those in the child and as expected the peak velocity was nearly four times less. This slow flow seems to have allowed the blood to settle in the adult but not in the child. These variations in signal intensity may explain the rather low T2* values, and perhaps a lower phase than one might expect. The need to correlate the phase difference between arteries and veins meant that an accurate technique was required to remove background phase. High-pass filtering is usually used with SWI phase images, but this can modify the background phase values (depending on size of the object and size of the filter used). Therefore, we chose to fit the background without any other structures of interest present (which would otherwise have had the same deleterious effect on background phase values [11, 12]. This fitting procedure for removing the background phase brought all four measurements in line from the rather broadly scattered results in Figure 27.3 to those in Figure 27.4 [13]. Although this likely would not have changed the conclusion for the value of A, it does add more confidence in the conclusion that if the resting state oxygen saturation of the femoral vein is 70% then A is most likely 1.5.

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FIGURE 27.6 Figure 27.5b and c is blown up by a factor of 2 to produce parts (a) and (b), respectively, to reveal the critical separation of the blood pool into three components. This is more clearly shown in the further zoomed image (by a factor of 8) in part (c). Something that must be akin to water (plasma) in the top most layer (arrow label A) as it is hard to separate from muscle; a second layer showing some susceptibility effect (arrow label B); and a third layer with a strong phase change (arrow label C). The three downward pointing arrows in part (a) point to three of the veins that are affected in the supine resting condition but are completely visible in the prone position. Note that in part (b), the darkening now appears at the top of the vessels as only minor settling appears to have taken place. The vessels are clearly circumscribed in the prone position but their boundaries are difficult to see in the resting supine position. As a side note, the upward pointing arrow in parts (a) and (c) shows the vessel wall of the artery at the bottom and top of the vessel, respectively, making it possible to more clearly separate the artery from the vein. Using a longer echo time would make this even more visible.

There are a few studies comparing muscle oxygenation and femoral venous oxygen saturation Yfv during exercise. In these studies, the subjects were healthy volunteers and in a sitting or supine position. A venous catheter was inserted to the femoral vein. Blood samples were acquired and evaluated using a blood gas electrolyte analyzer. Esaki et al. [14] investigated five healthy male subjects, with a mean weight ¼ 67.1  5 kg, height ¼ 177.8  4.8 cm, and age ¼ 25  2 years. They reported Yfv for subjects in the sitting position was 56.0% and femoral artery blood flow was 180  20 mL/min [14]. Costes et al. [15] investigated six healthy male subjects with mean weight ¼ 68  6 kg, height ¼ 179  5 cm, and age ¼ 22  3 years. They reported Yfv for subjects in the supine position was 74.3  9.9% and in the sitting position 49.2  13.8% [15]. Results from Ref. 16 showed Y in the femoral vein was 70% even after exercise and that of the measured steady-state blood flow to one leg, 40 s after the onset of exercise in normoxia was 3105  195 mL/min. Brismar et al. [17] measured Yfv during arterial reconstructive surgery on six patients. They concluded that when the leg blood flow in the common femoral artery is less than 200 mL/min, Y will be below 70%. As flow increases above 200 mL/min, Yfv will increase above 70% [17]. Sonnenfeld et al. [18] did similar research in 23 patients and showed that if the femoral artery blood flow was greater than 200 mL/min, then femoral venous oxygen saturation was 70% or greater [18]. We have actually measured the flow in a number of volunteers supine with their leg in a head coil or knee coil and found independent of the velocity encoding value (Venc), flow rates often exceeded 900 mL/min (as would be expected). The correct choice of wdo is critically important for predicting the forward problem, that is, measuring the oxygen saturation from the phase of blood vessels once wdo is known with certainty. In principle, the SWI sequence can be used as a means to measure oxygen saturation throughout the body once the geometry of the vessel is taken into account. In the case of changes in blood oxygen saturation, a relative value can be found even without

REFERENCES

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knowing the geometrical correction factors [19]. For example, Haacke et al. [9] quoted a 55% oxygenation in the pial veins in the brain during resting state and 70% during activation. If A ¼ 1.5, that is, wdo ¼ 0.27 ppm, these numbers would change to 70% during resting state and 80% during activation. This also makes sense given the measured jugular vein oxygen saturations in normal young people as being roughly 70%. Since all the veins in the brain drain to the jugular, it would not make sense that they would all have a resting state oxygen saturation at the 55% level. As discussed above, predicting A can be accomplished if T2* (Y) is known for blood. Given the T2* , Y can be found. Given Y, A can be predicted. Two recent papers give values for T2* for venous blood under very similar conditions [20, 21]. In Ref. 20, they show a venous equivalent R*2 of roughly 50 s1 for Y ¼ 0.7 at 3 T with Hct ¼ 0.435 (see Figure 2 in that paper). In Ref. 21, they show a venous equivalent R*2 of roughly 40 s1 for Y ¼ 0.7 at 3 Twith Hct ¼ 0.44 (see Figure 2 in that paper). We have measured R*2 of venous blood in the leg at 3 T for a male volunteer (Hct unknown but males are often around 0.45) to be 24.3 ms  2.3 ms (giving an R*2 of 41.2  3.6 s1). The higher the predicted R*2 , the lower the oxygen saturation, so from Ref. 20 we might predict Y to be greater than 0.7 while from Ref. 21 we would predict Y to be close to 0.7. Using Figure 27.4, and Y ¼ 0.7, we have no choice but to conclude that A ¼ 1.5 and Dxdo ¼ 0.27 ppm. The change in presumed value of Dwdo ¼ 0.18 ppm versus Dwdo ¼ 0.27 ppm will have important ramifications on the absolute estimates of oxygen saturation in the brain [7, 9] changing in the upward direction most estimates of oxygen saturation and, therefore, changing downward the cerebral metabolism. Consider the simple case of activation where the change in blood flow is 50%. If A ¼ 1, then Y ¼ 0.55, and the activated state will lead to a DY ¼ (1  Y)f/ (1 þ f) ¼ 0.15, where f is the increase in flow in the activated state (Ref. 22). That is, Y increases from 0.55 in the resting state to 0.70 in the activated state. If A ¼ 1.5, then Y ¼ 0.70, and the activated state will lead to a DY ¼ (1  Y)f/(1 þ f) ¼ 0.10, where f is the increase in flow in the activated state. That is, Y increases from 0.70 in the resting state to 0.80 in the activated state. These rather large starting values of Y for the veins in the brain completely change the perspective of oxygen utilization in the brain both in the resting and in the activated states. In summary, if the determination of A was based on the dependence of A on Y extracted from in vivo T2* measurements, the conclusion would be that A ¼ 1 and Dx do ¼ 0.18 ppm. However, given the difficulties in measuring a uniform signal, especially in a series of TE measurements over time where settling of blood may occur in human volunteers, a lower than expected T2* may have been measured. Therefore, given the in vitro T2* results presented above, and the physiological evidence supporting a resting, supine femoral oxygen saturation of 70% or higher, the conclusion can only be that A ¼ 1.5 and that Dx do ¼ 0.27 ppm. In any future attempts to validate these findings in humans, caution should be taken to ensure rapid flow and no settling of the blood when making these measurements.

REFERENCES 1. Weisskoff RM, Kiihne S. MRI susceptometry: image-based measurement of absolute susceptibility of MR contrast agents and human blood. Magn. Reson. Med. 1992;24(2):375–383. 2. Spees WM, Yablonskiy DA, Oswood MC, Ackerman JJ. Water proton MR properties of human blood at 1.5 Tesla: magnetic susceptibility, T(1), T(2), T (2), and non-Lorentzian signal behavior. Magn. Reson. Med. 2001;45(4):533–542. 3. Pauling L, Coryell CD. The magnetic properties and structure of hemoglobin, oxyhemoglobin and carbonmonoxyhemoglobin. Proc. Natl. Acad. Sci. USA 1936;22(4):210–216.

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4. Chien D, Levin DL, Anderson CM. MR gradient echo imaging of intravascular blood oxygenation: T2* determination in the presence of flow. Magn. Reson. Med. 1994;32(4):540–545. 5. Li D, Wang Y, Waight DJ. Blood oxygen saturation assessment in vivo using T2* estimation. Magn. Reson. Med. 1998;39(5):685–690. 6. Haacke EM, Prabhakaran K, Elangovan I, Hu J, Xuan Y, Morton P. Verification of the susceptibility value of deoxyhemoglobin in the blood using susceptibility weighted imaging (SWI). Proc. Intl. Soc. Magn. Reson. Med. 2005;13. 7. Fernandez-Seara MA, Techawiboonwong A, Detre JA, Wehrli FW. MR susceptometry for measuring global brain oxygen extraction. Magn. Reson. Med. 2006;55:967–973. 8. Reichenbach JR, Venkatesan R, Yablonskiy DA, Thompson MR, Lai S, Haacke EM. Theory and application of static field inhomogeneity effects in gradient-echo imaging. J. Magn. Reson. Imaging 1997;7(2):266–279. 9. Haacke EM, Lai S, Reichenbach JR, Kuppusamy K, Hoogenraad FGC, Takeichi H, Lin W. In vivo measurement of blood oxygen saturation using magnetic resonance imaging: a direct validation of the blood oxygen level-dependent concept in functional brain imaging. Hum. Brain Mapp. 1997;5:341–346. 10. Bloos F, Reinhart K. Venous oximetry. Intensive Care Med. 2005;31(7):911–913. 11. Haacke EM, Prabhakaran, KP, Elangovan I, Hu J, Xuan Y, Morton P. Verification of the susceptibility value of de-oxy-hemoglobin in the blood using susceptibility weighted imaging (SWI). Proc. Intl. Soc. Magn. Reson. Med. 2005;13. 12. Haacke EM, Ayaz M, Khan A, Manova ES, Krishnamurthy B, Gollapalli L, Ciulla C, Kim I, Petersen F, Kirsch W. Establishing a baseline phase behavior in magnetic resonance imaging to determine normal vs. abnormal iron content in the brain. J. Magn. Reson. Imaging 2007;26(2):256–264. 13. Ilayaraja Elangovan. Verification of magnetic susceptibility value of de-oxy-hemoglobin of blood using susceptibility weighted imaging (SWI). Master’s Thesis (January 1, 2006). ETD Collection for Wayne State University. Paper AAI1433365. 14. Esaki K, Hamaoka T, Ra˚degran G, Boushel R, Hansen J, Katsumura T, Haga S, Mizuno M. Association between regional quadriceps oxygenation and blood oxygen saturation during normoxic one-legged dynamic knee extension. Eur J Appl Physiol. 2005;95(4):361–370. 15. Costes F, Barthelemy JC, Feasson L, Busso T, Geyssant A, Denis C. Comparison of muscle nearinfrared spectroscopy and femoral blood gases during steady-state exercise in humans. J. Appl. Physiol. 1996;80(4):1345–1350. 16. MacDonald MJ, Tarnopolsky MA, Green HJ, Hughson RL. Comparison of femoral blood gases and musclenear-infrared spectroscopyatexerciseonset inhumans. J.Appl.Physiol.1999;86(2):687–693. 17. Brismar B, Cronestrand R, Jorfeldt L, Juhlin-Dannfelt A. Estimation of femoral arterial blood flow from femoral venous oxygen saturation. Acta Chir. Scand. 1978;144(3):125–128. 18. Sonnenfeld T, Nowak J, Cronestrand R, Astrom H, Euler CV. LEg venous oxygen saturation in the evaluation of intra-operative blood flow during arterial reconstructive surgery. Scand. J. Clin. Lab. Invest. 1979;39(6):577–584. 19. Shen Y, Kou Z, Kreipke CW, Petrov T, Hu J, Haacke EM. In vivo measurement of tissue damage, oxygen saturation changes and blood flow changes after experimental traumatic brain injury in rats using susceptibility weighted imaging. Magn. Reson. Imaging 2007;25(2):219–227. 20. Blockley NP, Jiang L, Gardener AG, Ludman CN, Francis ST, Gowland PA. Field strength dependence of R1 and R*2 relaxivities of human whole blood to ProHance, Vasovist, and deoxyhemoglobin. Magn. Reson. Med. 2008;60(6):1313–1320. 21. Zhao JM, Clingman CS, Narvainen MJ, Kauppinen RA, van Zijl PC. Oxygenation and hematocrit dependence of transverse relaxation rates of blood at 3 T. Magn. Reson. Med. 2007;58(3):592–597. 22. Haacke EM, Brown RW, Thompson MR, and Venkatesan R, Magnetic Resonance Imaging: Physical Principles and Sequence Design. Wiley, New York, 1999.

28 Quantification of Oxygen Saturation of Single Cerebral Veins, the Blood Capillary Network, and Its Dependency on Perfusion Jan Sedlacik, Song Lai, and Ju¨rgen R. Reichenbach

INTRODUCTION MRI, in particular SWI, has the potential to estimate the oxygenation level of blood due to the difference of its magnetic property in the oxygenated and deoxygenated state. Oxygenated blood is diamagnetic with a magnetic susceptibility near to water and to the blood vessel surrounding tissue (the parenchyma). Deoxygenated blood is less diamagnetic than oxygenated blood or water, that is, its magnetic property differs from the parenchyma, which makes it possible to detect venous vessels with SWI. The knowledge of the oxygen saturation of venous blood is important to characterize the physiological or pathological state of blood supply or oxygen consumption in tissue. Especially in the human brain there is a demand for noninvasive and reliable oxygenation quantification that can help to better understand the changes in cerebral hemodynamics due to neuronal activation or to improve the characterization and monitoring of treatment of cerebral pathologies, such as stroke or tumors. There are several methods for the quantification of blood or tissue oxygenation available. These methods, however, are invasive by inserting an oxygen microelectrode directly into the tissue or a catheter into the jugular vein Susceptibility Weighted Imaging in MRI, By E. Mark Haacke and J€urgen R. Reichenbach Copyright
2011 by Wiley-Blackwell

529

530

QUANTIFICATION OF OXYGEN SATURATION OF SINGLE CEREBRAL VEINS

and produce only punctual or global measures of the cerebral oxygenation status, respectively. Near-infrared spectroscopy (NIRS), a noninvasive optical technique, suffers from limited penetration of the light into the tissue, which allows to access only cortical structures of the brain. Positron emission tomography (PET) with the oxygen-15 isotope (15 O) is able to generate maps of the oxygen saturation as cross sections of the human brain. Since 15 O has a short half-life, it has to be produced onsite with a cyclotron, which makes this technique quite expensive and not ubiquitously available. In contrast to these methods, MRI has the potential to noninvasively obtain blood oxygenation levels of local venous vessels or to generate cross sections of tissue oxygenation similar to PET.

BRIEF THEORY The model of an infinitely long, homogeneous magnetic cylinder was used to describe a straight section of a single vessel. Due to the measurement of microscopic spins with MRI, we have to consider the local magnetic field that is experienced by these spins. This local field can be obtained by applying the concept of the sphere of Lorentz that corrects the field equations known from magnetostatics [1]. The local magnetic field generated by the cylinder is then given by

B int ¼

8 < :

1þ

9 =

x e Dx  ð3 cos2 u1Þ  B 0 þ ; 6 3

8
a

Here, the field is split into an internal B int and external B ext field of the cylinder. The transition between these both compartments is defined by the cylinder radius (a). The local field depends further on the orientation of the cylinder with respect to the main magnetic field given by the angle (u) between the long cylinder axis and B 0 . Also the magnetic susceptibility difference ðDx ¼ x int x ext Þ between the cylinder and its surrounding influences the resulting generated field. The extravascular field is additionally defined by the location of the surrounding spins, and is determined by cos 2F=r2, the polar coordinates originating from the cylinder’s long axis (Figure 28.1). The susceptibility difference (Dc) between a blood vessel and its surroundings is characterized by its blood oxygen saturation (Y) and the hematocrit (Hct): Dx ¼ Dx do  Hct  ð1Y Þ

ð28:2Þ

The absolute difference in the magnetic susceptibility between fully oxygenated and deoxygenated red blood cells (Dcdo) is essential for calculating Dc of the blood by using equation (28.2). Early in the twentieth century, Pauling and Coryell [2] reported an effective magnetic moment for independent hemes of about 5.46 Bohr magnetons per heme, which is equivalent to Dcdo ¼ 0.264 ppm (cgs). This value was confirmed by a more recent study of Spees et al. [3] who reported 0.27 ppm (cgs). However, there were other values found in the literature for Dcdo. For instance, Weisskoff and Kiihne [4] reported 0.18 ppm (cgs) and

PHASE INFORMATION OF A SINGLE VEIN

531

FIGURE 28.1 Scheme of the cylinder model. The vessel orientation is given by u, the angle between ~ B 0 and the long cylinder axis. The polar coordinate system has its origin in the center of the cylinder with r always perpendicular to the cylinder axis and F denotes the angle between r and the projection of the main magnetic field B00 on the cylinder cross section.

Thulborn et al. [5] 0.2 ppm (cgs). Since the reported Dcdo values vary distinctly, the resulting blood oxygenation level (Y) by solving equation (28.2) is subject to a large range. Because of this, the actual Dcdo value, which was used for calculating the oxygen saturation of blood, has to be considered when comparing Y of different MR studies. All Dcdo values reported so far were determined by in vitro measurements. Haacke et al. [6] tried to get a reliable estimate of Dcdoin vivo by using the phase information from SWI scans (see Chapter 27). Unfortunately, their independent measurements of the blood oxygen saturation by using a blood gas analyzer or an oximeter were very inconsistent and did not allow to answer the question for the most correct Dcdo value in vivo. Thus, in this chapter, we will use both the highest (0.27 ppm) and lowest (0.18 ppm) reported Dcdo values for calculation and denote the resulting blood oxygenation levels with Y0.27 and Y0.18, respectively.

PHASE INFORMATION OF A SINGLE VEIN SWI provides background field corrected, flow insensitive, high-resolution phase information that makes it possible to directly measure the intravascular field from even small cerebral veins. However, aliasing of the measured phase inside veins is still possible, which has to be kept in mind and corrected manually if necessary. Otherwise, the phase offset (Dj) directly corresponds to an offset in the magnetic field (DB): Dj ¼ g  DB  TE

ð28:3Þ

where g ¼ 2:675  108 rad T1 s1 is the gyromagnetic ratio of protons and TE is the echo time of the SWI scan. Since the phase information of the MR signal is corrected for any

532

QUANTIFICATION OF OXYGEN SATURATION OF SINGLE CEREBRAL VEINS

FIGURE 28.2 Determination of a voxel that is located completely inside a vein, exemplarily shown for an SWI scan at 3 T with TE ¼ 25 ms and a vein with Y0.18 ¼ 55%, Hct ¼ 0.45, u ¼ 0  . In this example, the phase difference of the blood magnetization is nearly p and the spins in the blood point in the opposite direction compared to the spins in the surrounding. The magnetization of blood and the vessel surrounding tissue (a) contribute with different amounts to the net magnetization of neighboring voxels (b). Due to this partial volume effect, voxels that contain blood and parenchyma appear dark in the magnitude image (c). Only the phase value of voxels that are located completely inside the blood vessel can be used for blood oxygenation quantification (d).

slowly varying macroscopic field gradient by homodyne filtering (see Chapter 6), the intravascular magnetic field is measured as a magnetic field offset: DB ¼

Dx  ð3 cos2 u1Þ  jB 0 j 6

ð28:4Þ

The determination of vessel orientation (u) with respect to B 0 is straightforward due to the known orientation of the 3D slab of the SWI scan. Now, the blood oxygenation level (Y) can be calculated by solving equations (28.3), (28.4), and finally equation (28.2). Special care has to be taken by determining the intravascular phase value. Only voxels that are completely located inside the vessel (Figure 28.2) can be used for the calculation because of the partial volume effect that causes an incorrect measure of Df and thus Y. Furthermore, the observer has to be aware of insufficient phase corrections that mainly occur near tissue/air or bone boundaries. If for any reason the shimming procedure has been carried out insufficiently, the phase correction could also fail, even for smooth brain tissue. In such cases, it is not possible to determine reliable phase and thus Y values. Exemplary results of this method are shown in Table 28.1, where the measured phase offset and all other calculated parameters (e.g., blood oxygen saturation) are listed for several cerebral veins in three healthy volunteers [7]. The obtained mean blood oxygenation was very consistent across several veins and subjects with Y0.18 ¼ 53  3% and Y0.27 ¼ 67  2%, respectively. The phase maps necessary for calculation were obtained from a SWI scan at B0 ¼ 1.5 T with TE ¼ 40 ms and an in-plane resolution of 0.5  0.5 mm2. The slice thickness was 2 mm and the imaging slab was axially oriented. Thus, the oblong voxels of the SWI scan are located inside a vein only for those vessels that are running in a cranial–caudal direction, that is e.g. Vv. centrales. An earlier work of Haack et al. [8] also measured blood oxygen saturation values from the signal phase of single cerebral veins. However, at that time the well-sophisticated SWI sequence and postprocessing algorithms were not yet established and the authors had to measure at least three gradient echo scans with different echo times to

SPIN DEPHASING IN PRESENCE OF A SINGLE VEIN

533

TABLE 28.1 Blood Oxygenation (Y), Magnetic Field (DB), and Susceptibility Offset (Dx) Calculated from the Phase Offset (Df) of Single Veins (i.e., Vv. centrales) that Were Oriented Parallel to the Main Magnetic Field (u ¼ 0 ) Vein

Df (rad)

DB (mT)

Dx (ppm) (SI)

Y0.18 (%)

Y0.27 (%)

A: Hct ¼ 0.42

V. centralis 1 V. centralis 2 V. centralis 3

0.76p 0.86p 0.80p

0.22 0.25 0.23

0.45 0.51 0.47

52.9 46.7 50.8

68.6 64.5 67.2

B: Hct ¼ 0.43

V. centralis 1 V. centralis 2 V. centralis 3

0.70p 0.78p 0.77p

0.21 0.23 0.23

0.41 0.46 0.45

57.7 52.9 53.4

71.1 67.9 68.2

C: Hct ¼ 0.46

V. centralis 1 V. centralis 2 V. centralis 3

0.84p 0.83p 0.83p

0.25 0.25 0.24

0.49 0.49 0.49

52.8 52.9 53.2

65.5 65.6 65.8

(0.80  0.05)p

0.23  0.01

0.47  0.03

53  3

67  2

Subject

Mean  SD

correct the obtained phase values for flow and background gradients. Nevertheless, they were able to measure the blood oxygenation of small cerebral veins in five healthy volunteers. They reported Y0.18 ¼ 54.4  2.9% that is in excellent agreement with our results. If we recalculate their result with Dcdo ¼ 0.27 ppm (cgs), as reported by Spees et al. [3] we obtain Y0.27 ¼ 70% which is again equivalent to our findings (see Table 28.1).

SPIN DEPHASING IN PRESENCE OF A SINGLE VEIN Due to the partial volume effect, it is possible to detect venous vessels that are even smaller than the image resolution of the actual SWI scan. The net magnetization of a voxel that contains a vein is affected by the contributions of the intra- and extravascular magnetization, originating from venous blood inside the vessel and its surrounding tissue. A scheme of this superposition is shown in Figure 28.3. Cylinder oriented parallel to B 0 (u ¼ 0 ), the voxel’s

FIGURE 28.3 Visualization of the magnetization superposition within a square voxel in the presence of a single vessel oriented perpendicular to the main magnetic field (u ¼ 90 ). Small spin packages (arrows) precess with their local resonance frequency, causing constructive and destructive interference that modulates the net magnetization (Mnet) of the voxel as time goes on. Adapted from Ref 12, with permission from Elsevier Science.

534

QUANTIFICATION OF OXYGEN SATURATION OF SINGLE CEREBRAL VEINS

net magnetization (M net ) oscillates as a function of time due to the constructive and destructive interference of the intravascular (M int ) and extravascular (M ext ) magnetization. With perpendicular orientation (u ¼ 90 ), field inhomogeneities around the cylinder cause additional spin dephasing that lowers M ext . Thus, the net magnetization of the voxel is decaying without such prominent oscillations. However, due to the high symmetry of the field inhomogeneity and the still existent intravascular magnetization, the net magnetization decay is not monoexponential but still shows some recovery due to partial constructive spin superposition. The time course of the net magnetization and, thus, the measured MR signal of the voxel are characteristic for the magnetic difference between the cylinder and its surrounding (Dx) as well as the volume fraction of the cylinder on the total voxel volume (l). MR signal simulations of voxels that are affected by single magnetized cylinders were first performed by Yablonskiy and Haacke [9] and can be expressed as follows: Svox ðtÞ ¼ l  Sint  ei  g  DB  t  et=T2int þ ð1lÞ  Sext  et=T2ext  h

ð28:5Þ

where Sint/ext denotes the intra- and extravascular signal intensity directly after excitation (t ¼ 0) that further depends on the specific spin density, T1 relaxation time, and the sequence’s flip angle and repetition time. The transverse relaxation times of the intra- and extravascular compartment are given by T2int/ext. The frequency shift, gDB, between the intra- and extravascular signal component follows directly from equation (28.4). The additional extravascular signal loss, due to spin dephasing caused by the static field inhomogeneity around the vessel, is given by h with h ¼ 1f ðdv  tÞ 

l 1 þ f ðl  dv  tÞ  1l 1l

ð28:6Þ

where dv is the extravascular frequency shift induced by the cylinder dv ¼ g 

Dx  B0  sin2 u 2

ð28:7Þ

and f(x) is given by ð1 f ðxÞ ¼

1J0 ðxuÞ du u2

ð28:8Þ

0

However, this analytical solution for the voxel signal is only valid for a cylindrical vessel coaxial in a cylindrical voxel. Due to the fact that the extravascular field inhomogeneity also affects the net magnetization of the voxel, the real voxel shape of the particular MR scan has to be considered in the signal simulation. The voxel shape depends on the k-space sampling scheme of the actual MRI sequence. Usually, an MR image is reconstructed from a Cartesian sampled k-space that results in square voxels convolved with the sampling point spread function (sPSF) [10]. We accomplished this requirement to consider the voxel shapes by developing a numerical simulation where the signal of arbitrarily shaped voxels can be calculated [7]. Numerical calculations were carried out on a 2D matrix with 210  210 complex numbers. A two-dimensional simulation is sufficient due to 2D nature of the infinite long cylinder model. The voxel signal then results by adding up all these complex

SPIN DEPHASING IN PRESENCE OF A SINGLE VEIN

535

FIGURE 28.4 Simulation of the signal decay for a voxel containing a magnetized cylinder with l ¼ 0.3, Dx ¼ 1 ppm, u ¼ 90 , B0 ¼ 1.5 T for different voxel shapes. Their corresponding weighting function Wn is visualized in the right column.

numbers, each representing a small spin packet (n) with its own signal magnitude (Sn), phase (w ¼ gBnt), and transverse relaxation time (T2n): X Svox ðtÞ ¼ Wn  Sn  ei  g  Bn  t  et=T2n ð28:9Þ n

Here, the weighting function Wn represents the shape of the voxel. Wn is zero for matrix points outside the voxel or unity for points inside. Wn can also become negative, for instance, for the negative lobes of the sampling point spread function. Figure 28.4 exemplarily shows the numerically simulated signal decay for a cylinder oriented perpendicular to B0 within three voxels of different shapes. The initial signal decay is similar for all three voxel shapes, whereas later the partial signal recovery varies dramatically. The signal–time course of the sPSF shaped voxel is quite different from a square or cylindrical voxel, which makes it clear that we have to consider the real voxel geometry to correctly describe the measured signal decays. This numerical method has also been used by Deistung et al. [11] to optimize SWI imaging parameters at ultrahigh-field strengths and different aspect ratios of the imaging voxels. We applied this numerical simulation to three healthy volunteers and measured signal decays of voxels affected by a single vein in vivo [7]. The signal decay was acquired with a multi-echo gradient echo sequence that sampled the MR signal from TE ¼ 4  172 ms in steps of DTE ¼ 7 ms. The in-plane resolution was 1.5  1.5 mm2 with 3 mm slice thickness. Though the numerical simulation is able to simulate the signal of a real measured sPSF voxel, the position of the vein has still to be in the center of the voxel. This was achieved by subvoxel shifts put into effect by adding phase gradients in k-space. Furthermore, the imaged slice had to be oriented perpendicular to the investigated vein so that the 2D approach of the simulation holds. Background field gradients that also have an influence on the evolution of the voxel’s net magnetization were eliminated by carefully shimming the local region around the vessel. Figure 28.5 exemplarily shows the measured and simulated signal decays of a parallel to B 0 oriented V. centralis and a perpendicular oriented V. thalamostriata for one subject. The signal simulation fits the measurement very well with r2

536

QUANTIFICATION OF OXYGEN SATURATION OF SINGLE CEREBRAL VEINS

FIGURE 28.5 Left and right: MR signal decay shown exemplarily for one subject. The measured decay (symbols) of both vessels (V. centralis, u ¼ 0 ; V. thalamostriata, u ¼ 90 ) is well fitted by the signal simulation (solid line). The dotted lines represent the signal of homogeneous tissue surrounding the vein. The error bars denote the standard deviation determined over all voxels in the homogeneous ROI. Middle: Schematic location of the measured voxels that are traversed by the investigated veins. Images adapted from Ref 12, with permission from Elsevier Science. TABLE 28.2 Blood Oxygenation (Y) and Vessel Radius (a) of Single Veins (i.e., Vv. centrales, u ¼ 0 ; V. thalamostriata and V. septi pellucidi, Both u ¼ 90 ) Calculated from Susceptibility Offset (Dx) and Volume Fraction (l) that Were Obtained by Fitting the Numerical Signal Simulation on the Measures Signal Decay (r2) Subject

Vein

r2

l (%)

a (mm) Dx (ppm) (SI) Y0.18 (%) Y0.27 (%)

V. V. A: Hct ¼ 0.42 V. V.

centralis 1 centralis 2 centralis 3 thalamostriata right

0.996 0.947 0.990 0.999

0.49 0.44 0.28 0.25

0.59 0.56 0.45 0.42

0.42 0.40 0.44 0.45

56.7 58.2 54.1 53.1

71.13 72.13 69.40 68.73

V. V. B: Hct ¼ 0.43 V. V.

centralis 1 centralis 2 centralis 3 septi pellucidi left

0.960 0.980 0.998 0.999

0.42 0.57 0.44 0.21

0.55 0.64 0.56 0.39

0.42 0.45 0.44 0.40

55.9 52.5 54.2 57.8

70.60 68.33 69.47 71.87

V. V. C: Hct ¼ 0.46 V. V.

centralis 1 centralis 2 centralis 3 thalamostriata right

0.995 0.993 0.996 0.999

0.51 0.23 0.18 0.27

0.60 0.41 0.36 0.44

0.46 0.48 0.48 0.47

55.4 54 53.7 54.9

70.27 69.33 69.13 69.93

0.44  0.03

55  2

70  1

Mean  SD

0.99  0.02 0.36  0.13 0.5  0.1

values close to unity. The results of all three subjects are summarized in Table 28.2. The blood oxygenation level and vessel radius of a vein were calculated from the susceptibility offset (Dx) and volume fraction (l) of the numerical simulation, which were obtained by fitting the simulated signal to the measured curve. The capability of this method to detect and quantify changes in the venous oxygen saturation was demonstrated in single subjects while breathing air and carbogen or ingesting caffeine [7, 12]. Since carbogen (5%CO2, 95%O2) is known to increase CBF [13], it increases the venous blood oxygenation. For demonstration in one subject, air was applied first followed by carbogen using a continuous positive airway pressure system (CPAP-CF 800, Dr€ager Medical, L€ ubeck, Germany) with a gas flow rate of about 25 L/min for both breathing gases. The signal decays of single venous vessels with

MR SIGNAL RELAXATION IN A VASCULAR NETWORK

537

different orientation to B 0 (V. centralis, V. thalamostriata) were sampled for both breathing conditions. We found a consistent increase of Y in both veins from Y0.18 (air) ¼ 0.5 to Y0.18(carbogen) ¼ 0.7. In contrast to this breathing experiment, CBF and thus the venous blood oxygenation were lowered in another subject when ingesting caffeine [14]. Two hundred milligrams (200 mg) of caffeine (Coffeinum N 0.2 g; Merck dura GmbH, Darmstadt, Germany) dissolved in 0.1 L water was administered orally. Caffeine acts as an adenosine antagonist and inhibits A2A receptors that cause vasoconstriction of cerebral vessels, thereby decreasing CBF [15]. Again the signal decays of different cerebral veins were measured before and about 45 min after ingestion of caffeine. The blood oxygenation level in these veins was found to fall from Y0.18 (native) ¼ 0.55 to Y0.18 (caffeine) ¼ 0.42 for this particular subject (see Chapter 26).

MR SIGNAL RELAXATION IN A VASCULAR NETWORK The single cylinder model was further extended to a cylinder network by Yablonskiy and Haacke [9], which was formed by infinitely long, randomly orientated and positioned cylinders to simulate the blood capillary network. Due to the macroscopically apparent uniform network, the actual voxel shape plays no role with respect to signal formation and the later it can be computed completely analytically. Furthermore, the method is not restricted to single vessels and, thus, cross-sectional blood oxygenation maps can be obtained from the whole brain. For a low volume fraction of deoxygenated blood in the capillary network (l < 5%), the signal of the blood itself can be neglected and the network signal is then formed by the extravascular signal only: Snet ðtÞ ¼ ð1lÞ  Sext  el  f ðdv  tÞ  e

T

t 2ext

ð28:10Þ

where dv is the extravascular frequency shift induced by the capillaries, dv ¼ g 

Dx  B0 3

ð28:11Þ

and f(x) is given by ð1 pffiffiffiffiffiffiffiffiffi 1J0 ðð3=2Þ  xuÞ 1 du f ðxÞ ¼  ð2 þ uÞ  1u  3 u2

ð28:12Þ

0

This theoretically derived signal formation was first verified in phantom experiments by Yablonskiy [16] and later applied in vivo by An and Lin [17]. The latter work demonstrated that it is essential to correct for the signal loss caused by macroscopic field gradients in the voxel. Otherwise, this effect will be ascribed to the capillary network which in return leads to substantial overestimation of the volume fraction and underestimation of the oxygenation level. The authors also applied their method to carbogen-induced changes of the cerebral physiology [18]. In a recent study, He and Yablonskiy [19] further extended this model by the intravascular signal of the blood and the signal from extracellular water. The final resulting parameters of the blood capillary network of all the three referenced works are summarized in Table 28.3 and an exemplary map of the venous blood volume fraction and oxygenation is shown in Figure 28.6.

538

QUANTIFICATION OF OXYGEN SATURATION OF SINGLE CEREBRAL VEINS

TABLE 28.3 Blood Oxygenation (Y ) Levels Calculated from Values of the Oxygen Extraction Fractions that Were Obtained by Investigating the MR Signal Relaxation in a Vascular Network References

Y0.18 (%)

Y0.27 (%)

An and Lin [17] An and Lin [18] (Normocapnia) An and Lin [18] (Hypercapnia) He and Yablonskiy [19]

52–55 53.5 75 42.6

68–70 69 83.3 61.7

l (%) 2.7–3.0 3 4.6 0.6–1.75

FIGURE 28.6 Maps of the venous blood volume fraction (l) and oxygenation extraction fraction (OEF). OEF can be calculated by Y ¼ (100% OEF) provided that the arterial blood is completely oxygenized. Images were adopted from He and Yablonskiy [19]. Reprinted with permission from John Wiley & Sons. Image quality and contrast may not be optimal due to conversion from color to grayscale display. Please see the color plates section for the original version of this figure.

CLINICAL APPLICATION OF SWI IN STROKE Application of SWI in stroke may offer important insight into the pathophysiology of the disease. Figure 28.7 shows an example of SWI obtained pre- and postcontrast injection. The

FIGURE 28.7 SWI application in an ischemic stroke patient. Significantly reduced oxygenation in draining veins is seen in the mIP images, due to largely suppressed perfusion to the ischemic lesion region.

CLINICAL APPLICATION OF SWI IN STROKE

539

FIGURE 28.8 SWI application in an acute ischemic stroke patient. Low SWI signals of tissue surrounding the infarct lesion (small arrows) combined with significantly reduced perfusion, suggest that these regions might be ischemic penumbra (i.e., at risk of infarction). In addition to the ischemic lesion, this patient also presented with a bleeding-like lesion that is clearly shown in the SWI images (arrow head).

draining veins revealed abnormally low signals, in consistency with the greatly reduced perfusion in the ischemic lesion. We further postulate that when combined with perfusion MRI, SWI may provide one more piece of information to detecting tissue at risk of infarction (i.e., ischemic penumbra). Figure 28.8 shows images of an acute stroke patient, where arterial spin labeling-based perfusion MRI and conventional DWI images clearly demonstrated the infarct lesion. Some tissue surrounding the infarct lesion showed low SWI signal, which, when taking into consideration the low perfusion signal, suggested this tissue being at risk of developing subsequent infarction. A possible explanation would be that in the ischemic penumbra, perfusion is greatly reduced (30–50% to that in normal tissue), while oxygen utilization is also reduced (60–80% to that in the normal tissue) but not as much

540

QUANTIFICATION OF OXYGEN SATURATION OF SINGLE CEREBRAL VEINS

reduced as perfusion, leading to increased deoxyhemoglobin in the penumbra, with concomitant low signal in SWI is. More research is necessary along these lines, and in this regard, multi-echo SWI sequences such as the 3D FLASH sequence with SENSE, as described in Chapter 31, will be very useful by providing the ability of mapping T2* . DISCUSSION Blood oxygenation saturation in cerebral veins, extracted by MRI and in particular by SWI, is in excellent agreement with values known from the literature. For instance, Vovenko [20] measured a partial oxygen pressure of pO2 ¼ 38  12 mmHg in cerebral venules of rats that is equivalent to Yrat vein ¼ 54  18%. Grote et al. [21] also applied oxygen microelectrode measurements in the rat brain and obtained pO2  30 mmHg in the cortex, which is equivalent to a blood oxygenation of Yrat cortex  50%. In vivo measurements of the human brain with 15 O-PET yielded mean cerebral oxygenation extraction fraction (OEF) of 0.44  0.06 that is equivalent to YPET  56% [22]. Although the cerebral blood oxygenation levels measured with methods other than MRI were closer to the blood oxygen saturation calculated with Dxdo ¼ 0.18 ppm (cgs) [4], we cannot comment on the true value of the blood susceptibility. To be able to give a valid estimation of Dxdo, the methods proposed in this chapter have to be calibrated with well-defined in vitro measurements where the oxygen saturation of blood samples is exactly adjusted. The fact that these methods are sensitive to the susceptibility difference between blood and its surrounding tissue and not to the blood oxygen saturation itself gives rise to other limitations. For example, iron depositions in the parenchyma or paramagnetic contrast agents in the blood pool bias the susceptibility difference and, thus, could falsify the estimation of the blood oxygenation level.

CONCLUSION In this chapter, we demonstrated the possibility to estimate the blood oxygenation level due to the dependency of its magnetic susceptibility on oxygen saturation. These methods are based on the measurement of the phase offset of cerebral veins or the evolution of the net magnetization in voxels that are traversed by single veins or a network of blood capillaries. Whereas the latter method is able to obtain cross-sectional oxygenation maps of the brain, the others are focused on single veins. Nevertheless, all three methods may help to better understand the changes in cerebral hemodynamics due to neuronal activation or may improve the characterization and monitoring of treatment of cerebral pathologies, such as stroke or tumors.

REFERENCES 1. Springer CS. Physicochemical principles influencing magnetopharmaceuticals. In: Gillies RJ, editor. NMR in Physiology and Biomedicine, Academic Press, San Diego, 1994, pp. 75–99. 2. Pauling L, Coryell CD. The magnetic properties and structure of hemoglobin, oxyhemoglobin and carbonmonoxyhemoglobin. Proc. Natl. Acad. Sci. USA 1936;22(4):210–216.

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3. Spees WM, Yablonskiy DA, Oswood MC, Ackerman JJ. Water proton MR properties of human blood at 1.5 Tesla: magnetic susceptibility, T(1), T(2), T (2), and non-Lorentzian signal behavior. Magn. Reson. Med. 2001;45(4):533–542. 4. Weisskoff RM, Kiihne S. MRI susceptometry: image-based measurement of absolute susceptibility of MR contrast agents and human blood. Magn. Reson. Med. 1992;24(2):375–383. 5. Thulborn KR, Waterton JC, Matthews PM, Radda GK. Oxygenation dependence of the transverse relaxation time of water protons in whole blood at high field. Biochim. Biophys. Acta 1982; 714(2):265–270. 6. Haacke EM, Prabhakaran K, Elangovan I, Hu J, Xuan Y, Morton P. Verification of the susceptibility value of deoxyhemoglobin in the blood using susceptibility weighted imaging (SWI). Proc. Int. Soc. Magn. Reson. Med. 2005;13:1557. 7. Sedlacik J, Rauscher A, Reichenbach JR. Obtaining blood oxygenation levels from MR signal behavior in the presence of single venous vessels. Magn. Reson. Med. 2007;58(5):1035–1044. 8. Haacke EM, Lai S, Yablonskiy DA, Weili L. In vivo validation of the BOLD mechanism: a review of signal changes in gradient echo functional MRI in the presence of flow. Int. J. Imaging Syst. Technol. 1995;6:153–163. 9. Yablonskiy DA, Haacke EM. Theory of NMR signal behavior in magnetically inhomogeneous tissues: the static dephasing regime. Magn. Reson. Med. 1994;32(6):749–763. 10. Haacke EM. The effects of finite sampling in spin-echo or field-echo magnetic resonance imaging. Magn. Reson. Med. 1994;4:407–421. 11. Deistung A, Rauscher A, Sedlacik J, Stadler J, Witoszynskyj S, Reichenbach JR, Susceptibility weighted imaging (SWI) at ultra high magnetic field strengths: theoretical considerations and experimental result. Magn. Reson. Med. 2008;60(5):1155–1168. 12. Sedlacik J, Rauscher A, Reichenbach JR. Quantification of modulated blood oxygenation levels in single cerebral veins by investigating their MR signal decay. Z. Med. Phys. 2009; 19(1):48–57. 13. Brian JE, Jr. Carbon dioxide and the cerebral circulation. Anesthesiology 1998;88:1365–1386. 14. Field AS, Laurienti PJ, Yen YF, Burdette JH, Moody DM. Dietary caffeine consumption and withdrawal: confounding variables in quantitative cerebral perfusion studies? Radiology 2003;227:129–135. 15. Nehlig A, Daval JL, Debry G. Caffeine and the central nervous system: mechanisms of action, biochemical, metabolic and psychostimulant effects. Brain Res. Brain Res. Rev. 1992; 17:139–170. 16. Yablonskiy DA. Quantitation of intrinsic magnetic susceptibility-related effects in a tissue matrix. Phantom study. Magn. Reson. Med. 1998;39(3):417–428. 17. An H, Lin W. Cerebral oxygen extraction fraction and cerebral venous blood volume measurements using MRI: effects of magnetic field variation. Magn. Reson. Med. 2002;47(5):958–966. 18. An H, Lin W. Impact of intravascular signal on quantitative measures of cerebral oxygen extraction and blood volume under normo- and hypercapnic conditions using an asymmetric spin echo approach. Magn. Reson. Med. 2003;50(4):708–716. 19. He X, Yablonskiy DA, Quantitative BOLD: mapping of human cerebral deoxygenated blood volume and oxygen extraction fraction: default state. Magn. Reson. Med. 2007;57(1): 115–126. 20. Vovenko E. Distribution of oxygen tension on the surface of arterioles, capillaries and venules of brain cortex and in tissue in normoxia: an experimental study on rats. Pflugers Arch. 1999;437(4): 617–623. 21. Grote J, Laue O, Eiring P, Wehler M. Evaluation of brain tissue O2 supply based on results of PO2 measurements with needle and surface microelectrodes. J. Auton. Nerv. Syst. 1996;57(3): 168–172.

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22. Ito H, Kanno I, Kato C, Sasaki T, Ishii K, Ouchi Y, Iida A, Okazawa H, Hayashida K, Tsuyuguchi N, Ishii K, Kuwabara Y, Senda M. Database of normal human cerebral blood flow, cerebral blood volume, cerebral oxygen extraction fraction and cerebral metabolic rate of oxygen measured by positron emission tomography with 15 O-labelled carbon dioxide or water, carbon monoxide and oxygen: a multicentre study in Japan. Eur. J. Nucl. Med. Mol. Imaging 2004;31(5):635–643.

29 Integrating Perfusion Weighted Imaging, MR Angiography, and Susceptibility Weighted Imaging Meng Li and E. Mark Haacke

INTRODUCTION The ability to image perfusion remains an important topic in the neuroimaging arena. Perfusion can be used to determine the energy consumption status of the tissue at the capillary level. The ability to accurately measure cerebral perfusion has several clinical applications such as in acute ischemic stroke, cancer, and multiple sclerosis (MS). In the former case, information about the severity of brain tissue ischemia is helpful in the assessment of the risk to benefit ratio when considering thrombolytic therapy [1, 2] as well as predicting final infarct volume [3–5]. For cancer, blood flow measurements are of interest in tumor characterization, assessment of prognosis, and monitoring of cancer therapy [6–8]. And more recently, PWI has shown that there is a significant reduction in perfusion in severe MS patients [9]. Some other disorders for which accurate measurement of cerebral perfusion might be important include chronic cerebral ischemia [10], vasospasm after subarachnoid hemorrhage [11], arteriovenous malformation

Susceptibility Weighted Imaging in MRI, By E. Mark Haacke and J€urgen R. Reichenbach Copyright
2011 by Wiley-Blackwell

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(AVM) or fistula (AVF) [12], moyamoya disease [13], trauma [14], dementia [15], and schizophrenia [16]. Cerebral perfusion can be measured by several imaging modalities [17], such as positron emission tomography (PET) [18], single photon emission computed tomography (SPECT) [19], xenon-enhanced CT (Xe-CT) [20], dynamic computed tomography (CT) perfusion [21], and magnetic resonance imaging (MRI) [22–24]. Among these techniques, PET and SPECT have been used to measure cerebral perfusion in vivo for decades. PET is accepted as the gold standard for the in vivo assessment of cerebral blood flow (CBF) and brain metabolism. However, the high cost and limited accessibility have restricted the widespread clinical use of PET. Perfusion imaging is more commonly done using Xe-CT but this requires specific instruments for inhalation of Xe gas. Dynamic CT and MRI have several clinical advantages. Both can be performed immediately, with considerably shorter scan time and higher spatial resolution than the other methods. Similar to CT, MRI is also noninvasive, but unlike CT, MRI does not require any radiation exposure. MR perfusion weighted imaging (PWI) using dynamic susceptibility contrast (DSC) is a useful tool to evaluate various neurovascular disorders of the brain. Cerebral vasculature, regional blood flow, and hemodynamic status can be quickly evaluated with PWI data for cerebral blood flow (CBF), cerebral blood volume (CBV), and mean transit time (MTT). However, there are several problems associated with such parametric maps, particularly the lower resolution usually used with PWI; this reduces the sensitivity to small regions with abnormal perfusion. Further, partial volume effects associated with low resolution PWI will lead to poor quantification of the actual CBF and CBV as well. On the other hand, susceptibility weighted imaging (SWI) offers high resolution MR venography (MRV) and also the information about regional oxygen saturation [25], and MR angiography (MRA) gives us information about the arterial vasculature [26]. By combining information from PWI, SWI, and MRA, one can obtain more accurate information about macro-circulation (arterial and venous blood flow), micro-circulation (capillary blood flow), and oxygen consumption. Our goals were to compare the quantification ability of the routine clinically used low resolution PWI (LR PWI) sequence (2
2
4 mm3) with a high spatial resolution PWI (HR PWI) sequence (1
1
4 mm3), and to assess regional cerebral perfusion after accounting for large vessel effects with SWI and MRA. By incorporating the macro-vessel information into the PWI data, we expect to be able to remove the effects of major arteries and veins and focus more accurately on perfusion in parenchyma.

MATERIALS AND METHODS Subjects Ten normal, healthy volunteers aged from 23 to 53 years old were enrolled in this study. There were seven males and three females; the mean and standard deviation of the age was 40.3 and 10.2, respectively. HR PWI was done on all subjects. The standard LR PWI was acquired on three subjects. HR PWI with a 6/8 partial Fourier factor was obtained on one subject. Informed consent was obtained from all subjects, and all protocols were approved by the institution’s review board.

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MR Imaging All MR imaging was performed on a 1.5 T magnet (Siemens Sonata, Erlangen, Germany) with an eight-channel head coil. Parallel imaging was used with GRAPPA (generalized autocalibrating partially parallel acquisitions) and an acceleration factor of 2. The contrast agent gadolinium-DTPA (Magnevist, Berlex, USA) was administered with a dose of 0.1 mmol/kg of body weight and injected in a peripheral arm vein using a power injector (Medrad, Spectris MR Injection System, Pittsburgh, PA, USA) at a rate of 2 ml/s. The injection of contrast agent started when the seventh measurement of PWI was acquired, followed immediately by a 20 ml saline flush. The high resolution PWI data were obtained using a two-dimensional, single-shot, gradient echo EPI sequence with repeat time (TR) ¼ 2200 ms, flip angle (FA) ¼ 60 , slice thickness (TH) ¼ 4 mm, and an interslice gap ¼ 4 mm. The field of view (FOV) was 256 mm
256 mm, and the acquisition matrix was 256
256 but was interpolated to 512
512 for display purposes. Fifty measurements were acquired over 110 s. We acquired HR PWI data first with echo time (TE) ¼ 98 ms and again with TE ¼ 52 ms by using a partial Fourier factor of 6/8 in the phase encoding direction in an attempt to obtain a better arterial input function (AIF) and better signal to noise ratio (SNR). Another two LR PWI data sets were obtained using the same sequence and parameters as the HR PWI except for the TE and resolution. We used echo times of 52 and 98 ms for these two LR PWI scans, and an acquisition matrix of 128
128 with no interpolation. The purpose of using different echo times and different resolutions in the PWI scans was to see how the echo time and spatial resolution influence the hemodynamic quantification and to compare these results with HR PWI with an echo time of 98 ms. MRA and SWI data were also acquired. MRA data were obtained precontrast, using a 3D-TOF approach with TE/TR ¼ 7/37 ms, FA ¼ 25 , TH ¼ 0.8 mm, and an acquisition matrix ¼ 512
384. The SWI sequence used was a fully velocity compensated, threedimensional, gradient echo sequence, with the following parameters: TE/TR ¼ 40/49 ms, FA ¼ 20 , TH ¼ 2 mm, and an acquisition matrix ¼ 512
448. High-pass filtering and phase processing were applied after image acquisition using a central matrix size of 64
64 [25]. Data Analysis After the acquisition, the PWI source data were postprocessed using SPIN (Signal Processing In NMR) software (Detroit, Michigan) to create perfusion maps. Deconvolution with singular value decomposition (SVD) was used to create quantitative maps of rCBF, rCBV, and MTT. The following five processing steps were performed: (1) The position of the arterial input function, which was needed for deconvolution, was automatically determined by using the maximum concentration (Cmax), time to peak (TTP), and first moment MTT (fMTT). The concentration time curve for arteries has short fMTT, short TTP, and high Cmax. Twenty voxels that best fit these properties were selected. Then the concentration time curves of these voxels were averaged, smoothed, and truncated to avoid the signal from the second pass of the tracer. (2) rCBV was calculated from the area under the concentration time curve. SVD [23, 24] was used to determine rCBF. MTT was obtained from the ratio of rCBV/rCBF.

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FIGURE 29.1 Eight ROIs of GM and WM were chosen to measure the signal intensity–time curve s(t) and the relevant hemodynamics.

(3) Regional mean values of rCBV, rCBF, MTT of white matter (WM) and gray matter (GM) were measured for the four different kinds of PWI acquisition. Eight ROIs were chosen in the WM, including regions in the frontal, occipitoparietal, and subcortical WM for bilateral cerebral hemispheres. Eight ROIs were chosen in the GM including head of the caudate, putamen, and thalamus, which crossed two to three slices, also bilaterally (Figure 29.1). The average signal intensity curves for the arteries were obtained from selected AIF pixels. All ROIs were chosen with minimized partial volume effects. (4) MRA images were used to exclude voxels that corresponded to a major artery (i.e., what is seen in MRA). (5) Similarly, the SWI venographic information was used to nullify those pixels in the PWI images that corresponded to veins. The latter two steps were performed with the idea that the parenchyma would no longer be corrupted by signal from major vessels so that the gray matter would become more clearly depicted in the processed PWI data.

RESULTS The HR PWI data were of sufficient signal to noise and image quality to reveal the following: clear GM/WM differentiation in the sulci without the deleterious effects from major arteries and veins; other GM structures such as the putamen, caudate nucleus, and thalamus; and deep medullary veins. These images portrayed a major visual improvement over the usual LR PWI data (see Figure 29.2). In order to assess quantitatively the HR versus LR PWI data, we acquired both HR PWI and LR PWI from one subject with an echo time of 98 ms. The mean signal intensity–time curves of arterial blood (from selected AIF pixels), GM, and WM are shown in Figure 29.3. The resolution did not affect the signal intensity curves if the same echo time were used in each scan. Figure 29.4 shows the concentration time curve of GM and WM. As expected, they too are in reasonable agreement with each other.

RESULTS

547

FIGURE 29.2 Comparison between low and high resolution PWI images for a single subject on rCBV maps (left column), rCBF maps (middle column), and rMTT maps (right column). (a–c) High resolution, long TE (1
1
4 mm3, TE ¼ 98 ms); (d–f) low resolution, long TE (2
2
4 mm3, TE ¼ 98 ms); (g–i) high resolution, short TE (1
1
4 mm3, TE ¼ 52 ms, 6/8 partial Fourier); (j–l) low resolution, short TE (2
2
4 mm3, TE ¼ 52 ms). Note the blooming effect in the Sylvian fissures (images d, e and j, k) in the low resolution PWI image compared with high resolution. Image quality and contrast may not be optimal due to conversion from color to grayscale display. Please see the color plates section for the original version of this figure.

Shown in Figure 29.5 are HR PWI and LR PWI data from a same subject with an echo time 98 ms for the HR PWI, 52 ms for the HR PWI with 6/8 partial Fourier factor, and 52 ms for the LR PWI, respectively. We found that the signal intensity vs. time curves changed with the echo time. The baselines of GM and WM at the 52 ms echo time were approximately double of those at 98 ms. However, the signal intensity vs. time curve of the artery was not affected (Figure 29.6). This could be because the T2* of the artery is much longer than that of the gray matter. The resultant concentration vs. time curves of GM and WM for the two scans were almost identical (Figure 29.7). This invariance of the AIF led

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FIGURE 29.3

The signal intensity curves from the one subject for both the HR and LR data collected with the same echo time. Despite being scanned on different days, the signal responses for WM, GM, and the arterial information are consistent for both data sets.

FIGURE 29.4 The concentration–time curves from one subject with different resolutions (HR: 1
1
4 mm3, LR: 2
2
4 mm3) and the same echo time (TE ¼ 98 ms) for PWI. The curves of gray matter (GM) and white matter (WM) are acquired from the mean signal intensity curves shown in Figure 29.3 that are obtained from 8 ROIs of GM and 8 ROIs of WM.

RESULTS

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FIGURE 29.5 The signal intensity curves from one subject with different resolutions (HR: 1
1
4 mm3, LR: 2
2
4 mm3) and different echo times (TE ¼ 98 ms and TE ¼ 52 ms) from the PWI scans. The curves of gray matter (GM) are acquired from 8 ROIs, and the curves of white matter (WM) are acquired from 8 ROIs as shown in Figure 29.1. The error bars represent standard error of mean.

FIGURE 29.6

The AIF signal intensity curves from one subject with different resolutions (HR: 1
1
4 mm3, LR: 2
2
4 mm3) and different echo times (TE ¼ 98 and TE ¼ 52 ms) for the PWI scans. The curves for arterial blood are the mean of the selected AIF pixels, the error bars represent the standard error of the mean.

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FIGURE 29.7 The concentration vs. time curves from one subject with different resolutions (HR: 1
1
4 mm3, LR: 2
2
4 mm3) and different echo times (TE ¼ 98 ms and TE ¼ 52 ms) for the PWI scans. The curves of gray matter (GM) and white matter (WM) were acquired from the mean signal intensity curves shown in Figure 29.6 that were measured from 8 ROIs of GM and 8 ROIs of WM.

TABLE 29.1 Mean and Standard Deviation of Each Perfusion Measure for the Four Different Acquisitions PWI Acquisition HR PWI (TE ¼ 98 ms) HR PWI 6/8 (TE ¼ 52 ms) LR PWI (TE ¼ 98 ms) LR PWI (TE ¼ 52 ms)

rCBV (mL/100 g)

rCBF (mL/min/100 g)

GM

WM

GM

WM

12.63  0.86 6.09  0.55 13.27  0.61 6.84  1.03

5.55  0.9 2.35  0.29 6.25  0.85 3.17  0.25

133.63  35.74 69.27  4.69 117.93  23.82 70.77  3.73

55.37  17.08 30.19  2.14 44.51  6.14 25.19  5.49

to rCBV values for the 98 ms echo time data twice of those of the 52 ms data. This suggests that the AIF is not properly determined in either experiment, likely due to the rapid flowing blood and its inconsistent signal compared to stationary signal. Table 29.1 summarizes the rCBV and rCBF results. The rCBV values for TE ¼ 98 ms are unrealistic for GM and WM as they are about twice of what one would expect and twice of what are shown in the TE ¼ 52 ms data. The HR PWI data (Figure 29.8c) have sufficient resolution to visualize major blood vessels and make it possible to remove them. This is accomplished by using both the MRA (Figure 29.8a) and SWI data (Figure 29.8b). The major vessels were then removed from the HR PWI data in an attempt to create a segmented vessel free image (Figure 29.8d). This

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FIGURE 29.8 (a) MRA-pre-Gd, (b) SWI-post-Gd phase processed, (c) HR PWI-rCBV map, (d) overlay of MRA and SWI on HR PWI-rCBV.

makes it possible to focus only on GM or WM and easier to filter the GM data without interference from major vessels.

DISCUSSION Our results show that concentration time course c(t) for GM or WM remains reasonably consistent from short to long echo times and from low to high resolution (see Figures 29.4

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and 29.7). The high resolution approach makes it possible to reduce partial volume effects in specific tissue measurements. Imaging at a longer echo time tends to exacerbate the T2* broadening effect of arteries and veins in the presence of a contrast agent. This is dealt with in part by removing those signals from major vessels as determined from MRA and SWI data. Another limitation of the HR PWI data is that we obtain fewer slices when the repeat time is kept the same as that for the LR PWI data. However, parallel imaging developments may increase the potential coverage by reducing the TE. As the echo time is decreased from 98 to 52 ms, there is a drop in the change in peak signal by nearly a factor of 2 for both GM and WM, which can be predicted by the T2* values of each tissue. Specifically, we predicted a drop of 1.7 for GM and 2.0 for WM by using the T2* values of 50 ms for WM and 60 ms for GM [27, 28], while the measured drop being 1.9 for GM and 2.1 for WM. The fact that the signal drops by a factor of 2 due to the longer echo times does not change the predicted c(t), although the individual pixel measurements will be noisier. Some of this noise can be removed by temporally smoothing the signal over time. Once the vessels have been removed, the images can then be smoothed spatially, ideally best done after segmenting GM from WM. Although c(t) of GM and WM does not change for short or long echo times, the AIFs varied considerably in our study. The maximum concentration value of the short echo time is almost double of that of the long echo time data. Partial volume effects on the AIF can lead to an overestimation or underestimation of the contrast agent concentration [29, 30]. Long echo times reduce the SNR and distort the arterial signal further. Using partial Fourier and parallel imaging techniques to reduce the echo times could help improve the AIF, and high spatial resolution can also lead to less blurring than related error making the extraction of major veins even easier. As shown in Table 29.1 for the TE ¼ 52 ms data, the lower CBV values for GM (near 6%) and WM (near 2.5–3%) are much more realistic as are the rCBF values near 70 mL/100 gm tissue per minute for GM and 25–30 mL/100 gm tissue per minute for WM. Nowadays many tumor researchers have used lesion rCBV data against the contralateral normal appearing white matter to evaluate tumor grading and monitor treatment effects [31, 32]. This approach avoids the need for an absolute CBV calculation. We propose that the combined use of high-resolution PWI, SWI, and MRA may be an ideal approach to studying perfusion and vascular changes in such studies.

CLINICAL APPLICATION OF COMBINING SWI, PWI AND MRA Combination of SWI, MRA and PWI can provide us with a more complete picture of the brain’s vasculature. MRA shows us if there are any stenoses or occlusions in the major brain arteries. SWI allows us to assess the conditions on the venous side such as changes in oxygen saturation or the presence of blood products such as hemorrhages. Finally, the rest of the hemodynamic story is given by PWI that reveals the information at the capillary level, for example, cerebral blood flow, cerebral blood volume, and mean transit times. The information incorporated from SWI, MRA and PWI may become an important tool to be used clinically for disease diagnosis and overall evaluation of the patient’s condition.

CLINICAL APPLICATION OF COMBINING SWI, PWI AND MRA

553

Multiple sclerosis (MS) is a neurodegenerative disease often referred to as an inflammatory demyelinating disease although it is also known to have a major perivascular component [33, 34]. More recent data suggest that it is caused, in part, by an autoimmune inflammatory response mediated by macrophage activity originating in the venous system. Conventional MR T2-weighted imaging and FLAIR are used to detect hyperintense MS lesions in white matter. However, T2-weighted imaging and FLAIR cannot by themselves discriminate acute from chronic lesions [35, 36]. Gadolinium enhancement on T1-weighted imaging suggests the presence of acute active lesions [37]. Newer MRI techniques including SWI [38, 39], PWI, diffusion tensor imaging (DTI), and myelin water imaging [40] are applied in MS to detect changes of iron, cerebral hemodynamics, and integrity of axons in the affected area. Many studies show that iron is enriched within oligodendrocytes compared to neurons and other glial cells [41–43]. In addition, brain iron accumulation has been shown histologically in neurodegenerative diseases, including MS [44, 45]. SWI is shown to be very sensitive to iron in the form of hemosiderin, ferritin, and deoxyhemoglobin, and offers the ability to measure iron on the order of just 1 mg/g of tissue in vivo [46]. PWI also plays an important role in MS pathogenesis and lesion development since vascular pathology is usually involved [47]. Hemodynamic abnormalities are associated with inflammatory activity, lesion reactivity, and inflammation-mediated vasodilatation. Acute MS lesions have increased CBF and CBV indicating inflammatory reactivity. They show gadolinium enhancement on T1-weighted imaging (Figure 29.9). Most nonenhancing MS lesions show low perfusion suggesting microvascular abnormalities with hemodynamic impairment. An example of an MS case is shown in Figure 29.10. A number of MS plaques can be seen on the FLAIR imaging. SWI phase imaging shows hypointense lesions matched with FLAIR indicating iron involvement. On PWI, some of the lesions have lower CBV in comparison to the normal white matter. This may be a feature of chronic lesions with tissue damage and a reduction in the local blood supply. Stroke is an interruption in the blood supply of the brain. Around 80% of strokes are ischemic strokes. The remaining 20% are associated with hemorrhage. If hypoperfusion persists for too long, then the ischemic brain tissue will progress into irreversible infarction. Deoxyhemoglobin exhibits paramagnetic properties relative to oxygenated hemoglobin and surrounding tissue. In ischemic stroke, changes in cerebral blood flow and cerebral metabolic rate affect the relative levels of oxyhemoglobin and deoxyhemoglobin. Due to the phase difference between deoxyhemoglobin containing veins and

FIGURE 29.9 A multiple sclerosis case showing an acute lesion with contrast:(a) FLAIR, (b) postcontrast T1-weighted imaging, (c) SWI magnitude image, (d) SWI filtered phase, and (e) highresolution PWI-rCBV. FLAIR shows many lesions in this slice but only one lesion (in circle) shows enhancement in the postcontrast T1-weighted imaging. This lesion shows an increase in rCBV of the PWI data. Image quality and contrast may not be optimal due to conversion from color to grayscale display. Please see the color plates section for the original version of this figure.

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FIGURE 29.10 A multiple sclerosis case showing that some lesions (perhaps chronic) have a reduced CBV and increased iron content. (a) FLAIR, (b) precontrast SWI magnitude, (c) SWI filtered phase precontrast, and (d) PWI-CBV. The bright areas in the FLAIR correspond with the dark gray in the PWI scan indicating reduced CBV. Both the SWI magnitude and phase images show iron deposition in the larger lesion (arrow). Image quality and contrast may not be optimal due to conversion from color to grayscale display. Please see the color plates section for the original version of this figure.

the surrounding tissue [48], SWI presents a useful tool to measure blood oxygen content. The occlusion of an artery typically yields a decrease in CBVand CBF in the affected area, as well as a prolonged TTP and MTT [49]. An example of ischemic stroke is shown in Figure 29.11. In this case, the left middle cerebral artery (MCA) is blocked. However, the collateral circulation carries blood to the tissue to keep the tissue viable. SWI data show that, in the affected area, the deoxyhemoglobin level increases in some vessels. PWI

CLINICAL APPLICATION OF COMBINING SWI, PWI AND MRA

555

FIGURE 29.11 A stroke case with left middle cerebral artery occlusion. (a) Postcontrast T1weighted image, (b) SWI magnitude image, (c) SWI filtered phase image, (d) MR angiogram, (e) PWI-CBF, (f) PWI-CBV, (g) PWI-MTT, and (h) PWI-TTP. The hypointense spots on the SWI magnitude image (b) and phase image (c) indicate that there are hemorrhages in the affected area (arrow), and also SWI shows a decrease in signal intensity of the blood vessel in the affected region likely indicative of reduced oxygen saturation. The perfusion shows a reduced CBF and prolonged MTT and TTP values on the left-side MCA territory, while CBV in the same area maintains normal values.

hemodynamic maps, on the other hand, give relative tissue information. Here, CBF is slightly decreased; CBV is maintained in the affected area, while both MTT and TTP are prolonged. Most pathological characteristics of a tumor are related to tumor vascularity. Therefore, the ability to image the vasculature and to differentiate between vascular sources of signal change in tumors is a key component in diagnosing tumor presence, characterizing the stage of development and assessing tumor progression. The conventional approach has been to use T1-weighted imaging pre- and postcontrast. Contrast enhancement within the tumor helps to detect differences in signal between normal structures and tumors. However, it does not reveal the inner structure of the tumor. Tumor characterization is partly reliant on understanding angiogenesis and hemorrhage. SWI is able to detect some components of the tumor vascularity. First, SWI is very sensitive to the presence of hemorrhage in tumor. Second, SWI can show the changes in oxygen saturation level of brain tumor tissue. Third, SWI shows the draining veins that can be very important for the neurosurgeon. Finally, SWI can indirectly show the breakdown of BBB (blood–brain barrier), sometimes even without the use of a contrast agent [50]. Perfusion imaging offers another approach to quantify relative CBV, CBF, and MTT, all of which are important in determining the extent of tumor angiogenesis and capillary permeability. Perfusion imaging can show that there is up to a fivefold increase in CBV relative to white matter in high-grade tumors [51]. Figure 29.12 shows a major increase in CBV in different parts of a glioma and compares the PWI and SWI available in this case.

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INTEGRATING PERFUSION WEIGHTED IMAGING

FIGURE 29.12 A patient with a brain glioma. (a) Postcontrast T1-weighted image, (b) FLAIR, (c) T2-weighted image, (d) SWI magnitude, (e) SWI phase, and (f) PWI-CBV map. Each image reveals different information. The SWI magnitude (d) and phase data (e) show clearly the change in susceptibility caused by angiogenesis and microbleeding within the tumor lesion (small arrow). The CBV map shows a region of enhanced blood volume that is of good match with T1-weighted scan. The SWI phase image (e) also shows vasculature within the tumor that also appears in the CBV map (big arrow).

CONCLUSIONS HR PWI is a better means to accurately measure microcirculation in the brain. Combined with MRA and SWI data, it is possible to remove most of the major vessel blurring effects shown in low-resolution PWI, thereby presenting a better image for gray matter quantification. SWI plays a key role in complementing PWI which is unable to ascertain the presence of blood products or the amount of oxygen saturation. SWI helps on both these counts.

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30 Functional Susceptibility Weighted Magnetic Resonance Imaging Markus Barth and Daniel B. Rowe

INTRODUCTION Functional magnetic resonance imaging (fMRI) based on the blood oxygenation leveldependent (BOLD) effect has found widespread applications in neuroscience and medicine since its detection in the early 1990s [1, 2] for its powerful ability to map brain regions that are ‘‘activated’’ during performance of a specific task. The functional contrast of fMRI is obtained by dynamically measuring the BOLD signal changes, using a time series of images to assess the hemodynamic response (e.g., blood flow, blood volume, and blood oxygenation). This is possible because changes in hemodynamics are linked to neural activity [3]. When neuron cells are active, oxygen consumption is increased, initially decreasing the oxygenation level in local capillaries. More importantly, this local increase in oxygen consumption leads to an increase in blood flow, delayed by approximately 1–2 s. Then as the increased blood flow is usually overcompensating the oxygen consumption with more than needed fresh blood, the oxygenation level will gradually increase again. This hemodynamic response reaches a peak after 4–5 s and then falls back to baseline (and typically forming an undershoot before returning to the baseline state). Consequently, the local concentrations of oxyhemoglobin and deoxyhemoglobin change dynamically due to the interaction between cerebral blood flow (CBF) and cerebral blood volume (CBV) [4].

Susceptibility Weighted Imaging in MRI, By E. Mark Haacke and J€urgen R. Reichenbach Copyright
2011 by Wiley-Blackwell

561

562

FUNCTIONAL SUSCEPTIBILITY WEIGHTED MAGNETIC RESONANCE IMAGING

The BOLD signal change amounts to

where



 ! DBOLD CMRO2 b CBF ab ¼ M  1  BOLD CBF0 CMRO2 j0

ð30:1Þ

M  TE  A  CBV0  ½dHBbv0

ð30:2Þ

and CBV ¼ CBV0




CBF CBF0

a

ð30:3Þ

where a is a constant that relates CBF changes to CBV changes, and CBF0 and CBV0 are the corresponding values at resting state. The parameter a has been determined experimentally as 0.38 [5] or 0.5 [6]. The parameter A is a field strength and sample-specific constant, and b is a constant in the range of 1–2 depending on the average blood volume [4]. Because oxyhemoglobin is diamagnetic while deoxyhemoglobin is paramagnetic, the interplay of the aforementioned hemodynamic processes results in a change in the magnetic susceptibility of blood, which in turn leads to a slight change in the local magnetic field and hence in the MR signal intensity. The MRI signal of blood is therefore dependent on the level of oxygenation that can be detected using an appropriate MR pulse sequence. The BOLD effect is commonly measured using the rapid acquisition of a series of 2D images with a contrast heavily weighted by the local field inhomogeneities, also known as T2* -weighted images. The most commonly used technique is called echo planar imaging (EPI), which is based on gradient echo acquisition. The EPI technique offers moderately good spatial and temporal resolution, covering the whole brain with a spatial resolution of about 3 mm and a temporal resolution of about 2–3 s. Recent technical advancements, such as the use of high magnetic fields (3 T) and advanced ‘‘multichannel’’ RF reception, have increased the spatial resolution to the millimeter scale. Although the hemodynamic response takes several seconds, BOLD responses to temporally close stimuli (as close as 1–2 s) can be distinguished from one another, using experimental paradigms known as event-related fMRI. Using specifically designed MR pulse sequences, changes in CBF or CBV can also be measured.

THE VENOUS INFLUENCE ON THE FUNCTIONAL SPECIFICITY OF BOLD fMRI The BOLD signal is mainly composed of signal contributions from larger veins, smaller venules, and capillaries, that is, where deoxyhemoglobin concentration change significantly. It has been shown that larger venous vessels give rise to a significant portion of the observed BOLD activation in both gradient echo [7–13] and spin echo fMRI [14]. This can lead to spurious activations and an intrinsic ambiguity of the actual localization of the neuronal activation and as a result reduce the functional specificity of fMRI. Using BOLD fMRI this problem cannot be solved by simply increasing the imaging spatial resolution [11]. However, experimental results indicate that the BOLD signal can be weighted

THE VENOUS INFLUENCE ON THE FUNCTIONAL SPECIFICITY OF BOLD fMRI

TABLE 30.1

563

Blood velocity in vessels of various diameters

Type of Vessels Capillaries Venules Intracortical veins Pial veins

Velocity (mm/s)

Diameter (mm)

0.26–1.1 0.18–4.2 >5 –

60 25–250

Data are taken from measurements of cat cortex [17] and are consistent with estimates for human brain vessels given in physiology textbooks [47].

more toward the smaller vessels at higher magnetic fields [15], and hence closer to the activation sites. It has been estimated that about 70% of the BOLD signal arises from larger vessels at 1.5 T, while about 70% arises from smaller vessels at 7 T. Furthermore, the portion of the BOLD signal originating from the capillaries increases roughly as the square of the magnetic field strength, making higher field scanners favorable for improving fMRI on both localization and sensitivity. As the venous part of the vasculature is relevant for BOLD fMRI, knowledge about venous vasculature is very important. From an anatomical point of view, venous vessels in the brain can be classified into several categories [16]: the large cortical cerebral veins that drain the hemispheres, the (extracortical) pial venous network that drains the lobules, and the intracortical vascular network. The diameters of venous vessels span a vast range, from the very small venules (10 mm diameter) to the large sagittal sinus (diameter >10 mm; see Table 30.1 for a summary of some vessel properties [17]). The venules that drain the capillary bed and run approximately parallel to the cortical surface are part of the intracortical vascular network. The venules in turn are connected to intracortical veins that can be divided into several groups depending on from which cortical layer they are draining (Figure 30.1) [16]. For fMRI it is important that, these intracortical veins (diameter 80 mm) emerge from the cortex roughly at a right angle to the pial vein (of diameter 200–500 mm) to which they then join. From the point of view of venous blood flowing, this means that

FIGURE 30.1 Vascular architecture of the cortex. (a) The classification of the cortical layers (I–VI) is given on the left-hand side and the vascular layers (1–4) on the right-hand side. (b) View on the cortical surface depicting the extracortical pial vein network. Reprinted from Ref. [16].

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FUNCTIONAL SUSCEPTIBILITY WEIGHTED MAGNETIC RESONANCE IMAGING

venous blood is first drained within a layer to an intracortical vein that connects the vascular layers and leads to the cortical surface (Figure 30.1a). The venous blood then flows along the cortical surface draining away from the corresponding cortical area (Figure 30.1b). From this anatomical argument, it becomes clear that functional signal changes detected in large extracortical veins can severely compromise functional localization and specificity. The same argument explains why a layer-specific activation can be found in BOLD fMRI once the resolution is sufficiently high [18]. Duvernoy et al. [16] also define a vertical vascular unit that is centered with a large intracortical vein (also called principal intracortical vein) and surrounded by a ring of arteries, and both together form a column-like appearance. From the seminal papers of Ogawa that triggered the use of the BOLD effect in fMRI [1, 2], as well as from previous chapters (Chapters 1 through 5), we know that a large venous vessel will have heavily T2* -weighted signals. Therefore, it was thought that a certain amount of the functional signal change (i.e., ‘‘activation’’) could originate from large venous vessels. The problem is that the larger the vein, the farther away it is located from the brain area where the neuronal activation occurs. The estimates for the distance where ‘‘spurious activation’’ can still be detected range from roughly 4 mm [19] to three times that amount [20]. By using Monte Carlo simulations with a cylindrical vein model, Boxerman et al. [21] showed that a spin echo sequence is primarily susceptible to capillaries whereas a gradient echo sequence is most sensitive to larger veins (diameter >10 mm, see Figure 30.2). However, because of the influence of the vascular geometry (e.g., vessel size, vessel distribution, and orientation of the vessel to B0) on the venous signal, it is still difficult to estimate the exact amount of extracortical vein contribution. One could argue that spin echo sequences should be used in fMRI because they are more susceptible to the capillary bed, but this increase in specificity comes with a greatly reduced sensitivity (about a factor of 3) that is normally not favorable for fMRI experiments.

–In(S)/TE (1/s)

4.0

GE, TE = 60 ms

3.0

2.0

SE, TE = 100 ms

1.0

0.0 1.0

10.0

100.0

Radius (μm)

FIGURE 30.2 from Ref. [21].

Gradient and spin echo signals as a function of vessel radius. Reprinted with permission

FUNCTIONAL SWI (fSWI)

565

FUNCTIONAL SWI (fSWI) To get a clearer view on the influence of veins on the BOLD fMRI signal, one can use the SWI technique to directly depict the venous vasculature in a functional experiment. Due to significant improvements in scanner hardware (e.g., high-field scanners, coil arrays) and imaging methods (e.g., parallel imaging), it is now possible to achieve very high isotropic resolution in functional MRI where veins can be identified and their contribution be estimated based on their spatial location rather than merely on model calculations [12]. As described in previous chapters, SWI can visualize very small veins (down to a diameter of 50 mm in human brain depending on field strength, see also Chapter 7) using very highresolution 3D gradient echo imaging [22–24]. However, a very high spatial resolution is normally detrimental to fMRI experimental design and is difficult to implement. First, it will further increase the geometric distortion, making the registration of EPI data sets onto the anatomical or, in this case, the venographic data sets problematic. Second, the contrast of veins in high-resolution EPI is lower than in corresponding SWI data sets, most probably due to T2* blurring effects related to the long EPI readout. Nevertheless, some studies have attempted to identify veins [25–27] based on a rather coarse resolution at least in the slice direction (typically 3–5 mm). This leads to significant partial volume effects limiting the identification of small veins. However, once the functional signal characteristics (both magnitude and phase) are established in high-resolution studies, one can go back to lower resolution and try to use this information to reduce the influence of veins in a standard fMRI experiment. Therefore, attempts can be made to account for large vein effects by making use of their functional properties, for example, setting a threshold for the functional signal change [28] or using their phase behavior [29–32]. Other studies tried to reduce their influence by using diffusion weighting to at least remove the intravascular effects [33–35]. The SWI data were acquired at 3 T (Siemens Magnetom Trio, Siemens, Erlangen, Germany) with the following imaging parameters: TR/TE ¼ 35/28 ms, flip angle ¼ 15 , bandwidth ¼ 100 Hz/pixel, voxel size ¼ 0.75 0.75 0.75 mm3, and GRAPPA with acceleration factor of 2. A custom-built eight-channel array coil (Stark Contrast; MRI Coils, Erlangen, Germany) was used in an fMRI experiment that was confined to the visual cortex (see Figure 30.3a for the positioning of the 3D slab) and was fast enough to be compatible with a block design. The stimulus paradigm consisted of a block showing a black screen with a fixation cross interleaved with a block showing a flickering checkerboard (5 Hz, that is, 200 ms for the full cycle). The block duration was matched to the respective acquisition times per 3D volume. These blocks were repeated between 14 and 37 times resulting in total acquisition times between 15 and 30 min per run. The data were analyzed using the general linear model as implemented in FEAT [36]. FSL MCFLIRT was used for motion correction between the volumes of the functional data set. No spatial or temporal smoothing was used. Figure 30.3b shows one sample image from the functional data set. One can clearly see that the image in Figure 30.3b lacks the geometrical distortion that is common in EPI images, and it is also possible to directly identify venous vessels as dark spots or lines as a result of both dephasing between blood and tissue compartments in a voxel and extravascular effects [37, 38]. Veins could therefore be segmented manually or automatically [39] in the functional data sets based on their appearance. With a block design visual task, the computed activation map clearly shows tubular structures that can be identified as veins by comparison with the venous vascular tree that is

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FUNCTIONAL SUSCEPTIBILITY WEIGHTED MAGNETIC RESONANCE IMAGING

FIGURE 30.3 (a) Positioning of the 3D slab on the sagittal localizer that clearly shows the high sensitivity region of the array coil on the occipital cortex. (b) Single slice out of functional data set (0.75 mm isotropic voxel size). Note the clear depiction of venous vessels (arrows). Reprinted with permission in a modified form from Ref. [13].

segmented from the functional data itself (Figure 30.4a). A region of interest containing these segmented venous vessels is used as a mask to remove the respective voxels in the functional data set. In the second step, the general linear model will be applied again to these data sets with these visible veins removed. Due to the negligible geometric distortion, it is straightforward to overlay the significant activation on the corresponding anatomical slices after removing the venous effects (Figure 30.4b). The visible veins contributing to the activation volume was found to be approximately one quarter. The signal change maps (Figure 30.4c) can show the venous structures clearly. However, the venous vasculature differs significantly from subject to subject, suggesting a relationship and possible explanation to the intersubject variation of functional activation significance and localization that have been observed and confirmed by many studies, see also reference [40]. When analyzing the functional signal changes of the veins compared to cortical regions (Figure 30.5a), one finds that a huge signal change occurs in veins at high spatial resolution and gets closer to that of cortical regions with reduced resolution [11]. The signal changes in cortical regions are essentially independent of resolution. At a commonly used spatial resolution of about 4 mm voxel size, cortical activation and signal changes in veins are not distinguishable. However, with high enough resolution, a signal change threshold can clearly eliminate the majority of vein effects (Figure 30.5b). Such results also enable a rough estimation of how far the ‘‘activation’’ can travel along the draining veins by simply counting the voxels of the long tubular structures. The result of 40–50 mm is 10 times higher than expected from the original estimation of Turner [19] and still a factor of 3 higher than from Lauwers et al. [20]. One factor explaining such discrepancy is that an activated volume of only 1 cm3 was assumed in their model, while the visual task used in the fSWI actually activates a much larger area. When performing a similar experiment at 7 T, one can still see the influence of veins (Figure 30.5c), that is, the appearance of high activation within the sulcus, but also activation in gray matter at the depth of cortical layer 4. This layer specific activation could also be demonstrated at 3 T, however, only by averaging over multiple cortical profiles [18].

SUSCEPTIBILITY-INDUCED PHASE CHANGES

567

FIGURE 30.4 (a) 3D z-map of the occipital lobe: before (left) and after (right) removing veins (middle: venous mask). (b) z-map of a single slice (upper) and its overlay on corresponding anatomical image (lower). (c) 3D signal change map of the same subject (upper: projection on axial plane; lower: projection on coronal plane). For visualization purposes, the resulting z-maps were smoothed; activated volumes are quantified before and after application of the venous mask by using all pixels in the z-maps above a threshold Z ¼ 2 and a cluster threshold of P ¼ 0.005. (a) and (b) reprinted with permission in a modified form from Ref. [13].

SUSCEPTIBILITY-INDUCED PHASE CHANGES Another confirmation of the influence of veins can be demonstrated with Figure 30.6. As discussed previously (see Chapters 2 and 4), venous vessels produce a phase effect due to dephasing between veins and surrounding tissue. This extravascular phase effect around a vessel has a specific cross-shaped pattern with two positive and two negative lobes which results in a dark cross in the magnitude and SWI image (Figure 30.6a and b). If the blood’s susceptibility changes during activation, the extravascular phase distribution would also change accordingly; see, for example, Figure 30.6c where phase changes can be seen for some activated regions that are also seen in the magnitude. This phase information can be used to estimate oxygen saturation and its change during activation. In addition to the extravascular effect, the intravascular dephasing also changes the phase of a voxel containing blood and tissue. In cortical tissue where only small intracortical veins are

568

FUNCTIONAL SUSCEPTIBILITY WEIGHTED MAGNETIC RESONANCE IMAGING

REMOVAL OF THE VEIN CONTRIBUTION IN fMRI USING PHASE INFORMATION

569

present, the extravascular phase effect averages out. Also, the intravascular dephasing effect will be very small, and assuming a random distribution of vessel orientations, it would be about 1/12 of that of a single vessel with the same blood volume. Because the venous blood volume in gray matter is very small (2–3%), a phase change in gray matter is difficult to detect experimentally. However, a very small phase effect has been observed in an animal study [41] and in a whole-brain analysis during breathing challenges [42]. The phase information is generally discarded in fMRI analysis and activations are computed using only the magnitude. However, the phase component of the data has been demonstrated to contain important spatial [22, 43] and temporal information [28, 41, 44] on neuronal activation-induced hemodynamics changes. In voxels containing mainly large veins change in oxygenation level will produce a change in phase assuming all other parameters are held fixed [45-47]. In voxels that contain mainly parenchymal tissue, the vessels are usually small and randomly oriented, and there will be little coherent task-related phase change (TRPC). In voxels that contain venous architecture (several millimeters or more) downstream from the site of neuronal firing, the vessels are usually larger and well oriented, thus producing a coherent task-related phase change [19], and in this way the phase component of the data contains information regarding the venous structure. It should be noted that the phase may also be contaminated by other physiological signals [48]. In fMRI, statistical activation analysis has predominantly utilized only the magnitude portion of the data, but more recently activation methods have been developed to utilize the entire complex-valued (magnitude and phase) data [49, 50]. The goal in fMRI has been to utilize the phase information in order to suppress or bias against determining voxels as active in terms of task-related phase changes, so as to remove spuriously active voxels that are distant from the site of neuronal activation [29–32].

REMOVAL OF THE VEIN CONTRIBUTION IN fMRI USING PHASE INFORMATION A subject was imaged using a standard resolution flow compensated SWI sequence (TR/TE ¼ 46/28 ms, flip angle ¼ 20 , voxel size ¼ 0.5 0.7 1 mm3) at 3 T. A venogram was created by taking a minimum intensity projection (mIP) through several slices [22]. The subject then performed a blocked design visual task of rest/active flickering checkerboard and was scanned with a normal GE-EPI sequence. Activations are computed as described in Ref. 3. Signed z-statistics are generated with an a ¼ 0.05 slicewise Bonferroni adjusted threshold. The results for one slice are presented in Figure 30.7. Figure 30.7a is a mIP venogram through the shown functional slice and its neighboring slices. Figure 30.7b shows the 3

FIGURE 30.5 (a) Relative signal change of a cortical (gray matter) region (open diamonds) and of a venous region (solid squares). Insert shows the enlarged signal change of the cortical ROI. (b) Left: 3D projection of the signal change (DS) map. Middle: venous mask obtained by including only pixels with DS > 4.5%. Right: DS map after applying the venous mask (different scaling). (c) Single slice image of a functional SWI data set acquired at 7 T with an isotropic resolution of 0.75 mm using a surface array (left top). Zoomed region showing a dark stripe (arrows) at the cortical depth of layer 4 (right top). Activation map of the same slice (bottom left) and the corresponding zoomed rectangle showing activation at the site of the stripe (arrows).

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FUNCTIONAL SUSCEPTIBILITY WEIGHTED MAGNETIC RESONANCE IMAGING

REMOVAL OF THE VEIN CONTRIBUTION IN fMRI USING PHASE INFORMATION

571

FIGURE 30.7

(a) Minimum intensity projection of the venogram through the functional slice and its two neighboring slices. (b) Magnitude-only activations from the visual task include regions of activation with a high correspondence to draining veins (arrows). (c) Complex constant phase activations exclude the obvious draining vein activations while preserving a cluster of voxels in which no large draining veins are observed.

magnitude-only activations, while Figure 30.7c presents the complex constant phase activations. Venous activations are indicated with arrows. This shows that the phase component of the data can be used to remove or bias against less desirable voxels that contain larger venous vessels. Statistical methods can be successfully utilized to bias against these larger venous vessels. In the simulation on ideal data (results not shown), the complex constant phase model retains the power of the magnitude-only method at low CNRs when little to no task-related phase changes are present, but can bias against determining voxels that have larger TRPCs but low CNR as active. These are favorable properties to an activation model. As the CNR increases, the complex constant phase model will behave more similarly to the magnitude-only model. However, the complex constant phase model may still include some draining vein activations with large CNR and TRPCs. It should also be noted that additional simulations (not shown) have observed that the larger the SNR, the larger the bias against voxels with taskrelated phase changes. In the experimentally acquired data shown here, the magnitude-only model detects four primary regions of focal activation. Three are identified in the venogram as hypointense areas, denoted by the arrows in Figure 30.7, strongly indicating the existence of large venous structures. The complex constant phase model detects a subset of the magnitude-only activations as has been previously observed [49]. The two of the three activation regions corresponding to hypointense venogram areas are completely eliminated with the complex constant phase model while the third is also nearly eliminated. The single activation region that does not correspond to a hypointense area in the venogram is not eliminated and is strongly believed to be parenchymal in origin. Moreover, it has been reported that magnitude-only and complex constant phase activations in fMRI data utilizing a spin echo pulse sequence are quite similar [50]. This suggests that the spin echo pulse sequence suppresses the BOLD contributions from large 3

FIGURE 30.6 (a) Slice through the occipital cortex showing the cross-shaped pattern around the cross section of small veins (small arrow; resolution: 0.5 mm isotropic, 3 T). Long arrow points to a vein running in-plane. Arrowheads follow the shape of a sulcus. (b) The processed SWI image. (c) Phase changes that accompany magnitude changes in fMRI. From top to bottom: magnitude changes, phase changes, and absolute phase changes.

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FUNCTIONAL SUSCEPTIBILITY WEIGHTED MAGNETIC RESONANCE IMAGING

veins but retains signal from the capillary bed that has constant phase. Therefore, the complex constant phase model results in similar activation as the magnitude-only model. In addition, the complex constant phase model implemented on a gradient echo image yields results similar to both magnitude and complex constant phase model results on spin echo images. This suggests that the complex constant phase model biases against the BOLD activations from larger venous vessels and returns those from the parenchymal capillary bed. In the meantime, the strong correlation of magnitude-only BOLD activations with large draining veins is in agreement with many studies [51]. It is also possible that reduction in non-task-related phase changes is responsible for the decreased volume of parenchymal activation found by the complex constant phase method. This could also be the result of unresolved, well-oriented draining veins within the volume. It should also be noted that a parallel line of research aiming at direct detection of magnetic field changes due to neuronal activation has tried to utilize the time series of phase in addition to the magnitude. At present, magnetic field changes in wire phantoms have been detected [52] while human results are not yet conclusive [53]. To conclude, the biological information contained in the phase of MR data can be used to increase the functional specificity of fMRI activation to the parenchymal tissue [54]. In the future, the use of the phase should become regular practice in MR imaging.

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30. Rowe DB. Modeling both the magnitude and phase of complex-valued fMRI data. Neuroimage 2005;25:1310–1324. 31. Rowe DB, Nencka AS. Complex activation suppresses venous BOLD in GE-EPI fMRI data. Proc. Intl. Soc. Magn. Reson. Med. 2006;14:2834. 32. Nencka AS, Rowe DB. Reducing the unwanted draining vein BOLD contribution in fMRI with statistical post-processing methods. Neuroimage 2007;37:177–188. 33. Song AW, Wong EC, Tan SG, Hyde JS. Diffusion weighted fMRI at 1.5 T. Magn. Reson. Med. 1996;35:155–158. 34. Jochimsen TH, Norris DG, Mildner T, Moller HE. Quantifying the intra- and extravascular contributions to spin-echo fMRI at 3 T. Magn. Reson. Med. 2004;52:724–732. 35. Michelich CR, Song AW, Macfall JR. Dependence of gradient-echo and spin-echo BOLD fMRI at 4 T on diffusion weighting. NMR Biomed. 2006;19:566–572. 36. FSL, FMRIB, Oxford, UK. http://www.fmrib.ox.ac.uk/fsl. 37. Reichenbach JR, Essig M, Haacke EM, Lee BC, Przetak C, Kaiser WA, Schad LR. Highresolution venography of the brain using magnetic resonance imaging. MAGMA 1998;6:62–69. 38. Reichenbach JR, Haacke EM. High-resolution BOLD venographic imaging: a window into brain function. NMR Biomed. 2001;14:453–467. 39. Koopmans PJ, Manniesing R, Norris DG,Viergever M, Niessen WJ, Barth M. MR venography of the human brain using susceptibility weighted imaging at very high field strength. Magn Reson Mater Phys (MagMa) 2008;21: 149–158. 40. Cusack R, Mitchell DJ, Beauregard DA, Salfity MF, Huntley JM. Individual variability in cerebral vein structure and the BOLD signal. In: Proceedings of the Organization for Human Brain Mapping, Florence, Italy, 2006, S99. 41. Zhao F, Jin T, Wang P, Hu X, Kim SG. Sources of phase changes in BOLD and CBV-weighted fMRI. Magn. Reson. Med. 2007;57:520–527. 42. Sedlacik J, Kutschbach C, Rauscher A, Deistung A, Reichenbach JR. Investigation of the influence of carbon dioxide concentrations on cerebral physiology by susceptibility-weighted magnetic resonance imaging (SWI). Neuroimage 2008;43:36–43. 43. Duyn, JH, van Gelderen, P, Li T-Q, de Zewart JA, Koretsky AP, Fukunaga M. High field MRI of brain cortical substructure based on signal phase. PNAS 2007;104:11796–11801. 44. Hoogenraad FG, Reichenbach JR, Haacke EM, Lai S, Kuppusamy K, Sprenger M. In vivo measurement of changes in venous blood-oxygenation with high resolution functional MRI at 0.95 Tesla by measuring changes in susceptibility and velocity. Magn. Reson. Med. 1998;39:97–107. 45. Springer CS, Xu Y. Aspects of bulk magnetic susceptibility in in vivo MRI and MRS. In: Rink PA, Muller, RN, editors. New Developments in Contrast Agent Research, European Magnetic Resonance Forum, Blonay, Switzerland, 1991, pp. 13–25. 46. Weisskoff RM, Kiihne S. MRI susceptometry: image-based measurement of absolute susceptibility of MR contrast agent and human blood. Magn. Reson. Med. 1992;24:375–383. 47. Guyton AC. Textbook of Medical Physiology, W.B. Saunders Company, Philadelphia, PA, 1981, p. 206. 48. Pfeuffer J, Van de Moortele PF, Ugurbil K, Hu X, Glover GH. Correction of physiologically induced global off-resonance effects in dynamic echo-planar and spiral functional imaging. Magn. Reson. Med. 2002;47:344–353. 49. Rowe DB, Logan BR. A complex way to compute fMRI activation. Neuroimage 2004;23:1078–1092. 50. Nencka AS, Rowe DB. Complex constant phase method removes venous BOLD component in fMRI. Proc. Intl. Soc. Magn. Reson. Med. 2005;13:495.

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31 Complex Thresholding Methods for Eliminating Voxels That Contain Predominantly Noise in Magnetic Resonance Images Daniel B. Rowe, Jing Jiang, and E. Mark Haacke

INTRODUCTION There have been a number of excellent studies that have discussed the basic properties of noise in magnetic resonance (MR) imaging [1–12]. Removing noise in magnetic resonance images is important for improving the visualization of phase images and for the quantification of, for example, parametric maps such as the T2 map [13–19]. Once noise is removed, it is also possible to revisit the data and extract boundary information, for instance. The simplest and most effective means to date to remove noise is to use a simple threshold on the magnitude images, which is to set voxels whose intensity fall below a certain threshold to zero. However, this approach has its limitations and can lead to the loss of signal information in the image and an incomplete removal of noise. In this chapter, we show that it is possible to achieve ‘‘better’’ results using information from both magnitude and phase images by applying a connectivity constraint [20, 21] or using a local neighborhood of voxels [22]. The motivation behind this work stems from susceptibility weighted imaging (SWI) [23] where it has been found that the tissue contrast was enhanced and the noise evidently reduced throughout Susceptibility Weighted Imaging in MRI, By E. Mark Haacke and J€urgen R. Reichenbach Copyright
2011 by Wiley-Blackwell

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the image [24] using both magnitude and phase data. This work builds upon the feature of SWI to create a rapid means to remove as much noise from the image with as little effect on the object as possible. We are interested in the noise behavior for the magnitude and phase images, specifically in complex-valued MR images. We assume that the original real and imaginary channels generate independent noise that is Gaussian distributed with mean zero and standard deviation s. With the Gaussian distributed noise assumption, the real and imaginary channels are yR ¼ A cos(u) þ hR and yI ¼ A sin(u) þ hI, where yR and yI are the observed measurements for the real and imaginary parts, hR and hI are N(0, s2) error terms for the real and imaginary parts, and A and u are the noise-free (population) magnitude and phase. The joint probability distribution of a voxel’s bivariate real and imaginary observation (yR, yI) is " # " # 1 ðyR A cos uÞ2 1 ðyI A sin uÞ2 pðyR ; yI Þ ¼ pffiffiffiffiffiffiffiffiffiffiffi exp   pffiffiffiffiffiffiffiffiffiffiffi exp  2s2 2s2 2ps2 2ps2

ð31:1Þ

A change of variable can be performed from rectangular coordinates in equation (31.1) to polar coordinates, and the joint probability distribution of a voxel’s bivariate observed magnitude and phase (M, w) is    A 1  2 2 exp  2 M þ A 2AM cosðfuÞ pðM; fÞ ¼ 2ps2 2s

ð31:2Þ

The (marginal) distribution of the magnitude pM ðMÞ can be found by integrating equation (31.2) with respect to w to obtain the Rician distribution [4–6] pM ðMÞ ¼

  M ðM 2 þ A2 Þ=2s2 AM e I 0 s2 s2

ð31:3Þ

where I0 is the modified zeroth-order Bessel function of the first kind [1]. When A ¼ 0, which corresponds to areas where there is only noise and no signal, the Rician distribution in equation (31.3) collapses to the Rayleigh distribution [2, 3] pM ðMÞ ¼

M M 2 =2s2 e s2

ð31:4Þ

pffiffiffiffiffiffiffiffi The mean of the Rayleigh distribution in equation (31.4) is s p=2 and the variance is sð2p=2Þ. For a low signal to noise ratio (SNR), that is, SNR  1 where SNR ¼ A/s, the Rician distribution is far from being Gaussian. On the other hand, it starts to approximate a Gaussian distribution for SNR  3 pffiffiffiffiffiffiffiffiffiffiffi 2 2 1 2 2 pM ðMÞ ¼ pffiffiffiffiffiffiffiffiffiffiffi eðM A þ s Þ =2s 2 2ps

with a mean of

pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi A2 þ s2 and variance of variance s2.

ð31:5Þ

THE CTM METHOD

579

The phase (marginal) distribution p(w) can be found by integrating equation (31.2) with respect to M to obtain the phase marginal (pham) distribution [5, 10] pffiffiffiffiffiffi 

   2   2 1 A2 A 2p A cosðwuÞ A cosðwuÞ exp  2 1 þ cosðwuÞexp pðwÞ ¼ F 2p s 2s2 s 2s ð31:6Þ where K is the standard normal cumulative distribution function. This pham distribution in equation (31.6) was described in detail by Rowe in the context of fMRI [25]. When there is signal present, the phase noise distribution in the image can be considered as a Gaussian distribution with mean u ¼ 0 and standard deviation sphase. When SNR  1, the standard deviation is sphase ¼ s/A, and the distribution of the phase is ! 1 ðfuÞ2 ð31:7Þ pobject ðfÞ ¼ qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi exp 2ðs=AÞ2 2pðs=AÞ2 As is obvious in equation (31.7), the standard deviation of the phase is [13] sphase ¼

1 SNR

ð31:8Þ

where the units for sphase are in radians. In the phase image, when there is only noise, A ¼ 0, and the distribution of the phase is the uniform distribution 8 < 1 ; ifp < f < p ð31:9Þ pnoise ðfÞ ¼ 2p : 0; otherwise The mean of the phase in equation (31.9) is zero and the variance is p2/3. Our aim is to exploit the noise presence in both phase and magnitude images so as to provide a more powerful thresholding technique. The complex threshold method (CTM) and the magnitude and phase threshold (MAPHT) method for removing noise voxels in complex-valued images are described in detail in the following.

THE CTM METHOD The CTM consists of two steps. First, the magnitude image and the phase image are thresholded by ms0 and nsphase , where m and n are real and positive numbers, respectively. Then, through voxel connectivity, both false positive (the error of leaving noise voxels) and false negative (the error of eliminating signal voxels) rates are further minimized. A false negative error is called a Type I error and a false positive error is called a Type II error. More specifically, we define these errors as Probability of Type I error ¼

total number of signal pixels removed total number of signal pixels

ð31:10Þ

total number of noise pixels left total number of noise pixels

ð31:11Þ

Probability of Type II error ¼

The processing algorithm is outlined graphically in Figure 31.1 and in detail below.

580

COMPLEX THRESHOLDING METHODS FOR ELIMINATING VOXELS Phase MR image

Magnitude MR image M

Tm

T Phase threshold mask ′

Magnitude threshold Mask M ′

+ mIP Combined threshold mask V ′

magnitude connectivity Cm Magnitude connectivity restored mask V ′m

phase connectivity C Masked phase MR image

Phase connectivity restored mask V ′m

Phase MR image

Spike removal and hole restoration

Magnitude MR image

+

+

Final processed phase MR image ′′

Final processed magnitude MR image M ′′

FIGURE 31.1 Flowchart of the CTM. Thresholds are applied to magnitude and phase images, and a mIP noise-removing mask is generated. A connectivity algorithm is run on the magnitude image and the noise mask is then corrected by restoring recovered non-noise object voxels. Connectivity is run again, but this time on the phase image to create a final noise mask that is then used to filter noise voxels from both magnitude and phase images.

Magnitude Threshold Step Thresholding is applied to the magnitude image and a binary noise-removing mask image M 0 is created. This operation can be represented as Tm : M 0 ðx; yÞ ¼



0;

if Mðx; yÞ < ms0

1;

if Mðx; yÞ  ms0

ð31:12Þ

where M is the magnitude MR image, m is the magnitude threshold, s0 is the standard deviation of noise as estimated from the image, and Tm is the threshold operator.

CONNECTIVITY

581

Phase Threshold Step The useful information in the phase images is exploited by a phase threshold method. For the phase image f, a binary noise-removing mask f0 is created by retaining all phase values between ðnsphase Þ and ðnsphase Þ. Here, sphase is the sample standard deviation of noise in the phase image estimated from the SNR in the magnitude image (see equation (31.8)). Let fðx; yÞ be the phase image. Then the mask f0 is determined as ( 0

Tf : f ðx; yÞ ¼

0;

ifjfðx; yÞj > nsphase

1;

otherwise

ð31:13Þ

where Tw is the phase threshold operator. Combined Magnitude and Phase Thresholds By combining magnitude and phase thresholds, it is possible to eliminate more noise voxels than when either method is used independently. This is accomplished by taking the minimum intensity projection (mIP) n0 ðx; yÞ of the magnitude mask M 0 ðx; yÞ and phase mask f0 ðx; yÞ as follows: ( 0

n ðx; yÞ ¼

0;

if either M 0 ðx; yÞ ¼ 0 or f0 ðx; yÞ ¼ 0

1;

otherwise

ð31:14Þ

The effect of thresholding with the distributions of both the magnitude and the phase is shown in Figure 31.2. As seen in Figure 31.2, these thresholds still remove information from the object (Type I error) and fail to remove some noise voxels (Type II error). A short remark about Figure 31.2 is in order. When only the phase threshold is applied, Type I error can result for any value of the signal where the phase exceeds the threshold value. If both thresholds are applied, the dominant source of Type I error is from those true points to the left of the threshold being thrown out. Similarly, for Type II error, the phase-only threshold can still allow points to the left of the magnitude threshold to contribute to the noise being counted as part of the object. If both thresholds are applied, the dominant source of Type II error is from those noise points to the right of the magnitude threshold. CONNECTIVITY To reduce Type I error, we propose adding a local connectivity algorithm. Voxel connectivity describes a relation between the voxel under investigation and the surrounding neighborhood of voxels. Let p be a voxel with the coordinates (x, y), then its 8neighborhood N8(p) is defined as all those voxels that are immediate neighbors of p. The connectivity algorithm is applied only to those points that were discarded by the thresholding procedure. For the magnitude image, it is applied under the following conditional guideline: If the number of voxels connected to p in N8(p) of the magnitude image exceeding the magnitude threshold ms0 is greater than or equal to some integer number tM, then do not discard p. Similarly, for the phase image, if the number of voxels connected to p in N8(p) of the phase image exceeding the phase threshold nsphase is greater than or equal to

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COMPLEX THRESHOLDING METHODS FOR ELIMINATING VOXELS

# of voxels Type I error Noise

Signal

Type II error

Voxels removed by phase threshold Voxel intensity

Type I error by both magnitude and phase threshold

Type II error by both magnitude threshold

Potential Type I error by phase threshold

Type II error by threshold

FIGURE 31.2 CTM bimodal curve showing the Rayleigh distribution for the noise (left distribution) and Rician distribution for the signal (right distribution). The bold cutoff line shows the magnitude threshold, which removes all the noise to the left of the threshold. The region under the inner curve in the noise mode represents the voxels removed by the phase threshold. In the left insert, the region shown in dark gray represents Type I error introduced by the phase threshold, while the light gray region represents the conventional Type I error from the magnitude threshold. In the right insert, the light gray region represents Type II error from the magnitude threshold while the dark gray region represents Type II error from the phase threshold.

some integer number tP, then do not discard p. We refer to these two connectivity operators as Cm and Cw, respectively. Then the combined thresholded mask n0 ðx; yÞ is modified to n0 m ðx; yÞ ¼ Cm ðn0 ðx; yÞÞ and this in turn is modified according to n0 mf ðx; yÞ ¼ Cf ðn0 m ðx; yÞÞ.

583

CONNECTIVITY

Applying CTM Connectivity for Spike Removal and Hole Restoration As a final step, a simple spike removal and hole restoration algorithm is applied to reduce Type I and Type II errors. Since most of the noise has already been removed with the connectivity technique, the remaining points that constitute Type II error are predominantly single noisy points, whereas Type I error constitutes a few single voxels that are lost along the edges of the object. The spike removal and hole restoration algorithm works on these single voxels to remove or restore them. The algorithm works as follows: every voxel’s neighborhood in the noise-reduced image is examined for connected voxels. If the magnitude connectivity shows that there is no neighboring voxels that are connected to the one under consideration, then it most likely is noise and should be removed. If the surrounding voxels are all signal, the examined voxel should be regarded as signal as well. The MAPHT Method A local statistic based on the measured signal at the voxel of interest and its neighbors is defined. This statistic is a function of one or more random variables that does not depend on any unknown parameter and it has a distribution that approximates an F distribution [22]. Monte Carlo simulations are performed to determine critical values for this distribution, which is used to perform a statistical hypothesis test by thresholding [29, 30] to identify voxels containing predominantly noise. With a sample of n independently and identically distributed measurements (magnitude Mi and phase fi , i ¼ 1, . . ., n) from equation (31.1), the joint distribution of the measurements viewed as a function of the magnitude, phase, and error variance is the likelihood function: " # ( ) n n  Y   1 X 2 2 n 2 2 LðA; u; s Þ ¼ 2ps Mi exp  2 Mi þ A 2AMi cosðfi uÞ 2s i¼1 i¼1 ð31:15Þ To identify voxels that contain predominantly noise, MAPHT performs a hypothesis test to determine whether the magnitude and the phase are statistically different from zero. A formal statistic can be derived from equation (31.15) and a joint statistical hypothesis test can be performed on the population magnitude and phase parameters. A hypothesis test is performed to separate voxels that contain predominantly noise from those that contain predominantly signal. In hypothesis testing, there are four possible outcomes as depicted in Table 31.1. Note that the MAPHT Type 1 is similar to the CTM Type II (equation (31.10)) and that the MAPHT Type 2 is similar to the CTM Type I (equation (31.11)). Correct decisions are made in the top right and bottom left cells of Table 31.1. In the top left cell, a Type 1 error is made in which the null hypothesis is rejected when it is true. The probability of a Type 1 error is the false positive rate denoted by a. In the bottom right cell, a Type 2 error is made in which the null hypothesis is not rejected when it is false. The probability of a Type 2 error is TABLE 31.1 Four Outcomes from a Hypothesis Test

Reject H0 Do not reject H0

H0 True

H0 False

Type 1 error (a) Correct decision (1  a)

Correct decision (1  b) Type 2 error (b)

584

COMPLEX THRESHOLDING METHODS FOR ELIMINATING VOXELS

the false negative rate denoted by b. These two error rates will be examined in more detail later. Voxels will be thresholded by testing the null hypotheses H0: A ¼ 0, u ¼ 0 versus the alternative hypothesis H1: A > 0, u 6¼ 0. Maximum likelihood estimators (MLEs) of the magnitude, phase, and noise variance under the two hypotheses can be computed from the likelihood function [15] by simply setting the partial derivatives of the likelihood function with respect to the sought-after parameters to zero and solving the resulting equations. Under the constrained null hypothesis H0: A ¼ 0, u ¼ 0, the MLEs for the magnitude, phase, and noise variance are n  1 X ~ ¼ 0; ~ A u ¼ 0; s ~2 ¼ y2Ri þ y2Ii 2n i¼1

ð31:16Þ

while under the unconstrained alternative hypothesis H1: A > 0, u 6¼ 0, the MLEs are " # n n h i1=2 X X 2 2 ~ ¼ ðyR Þ þ ðyI Þ A ; ~ u ¼ tan1 yIi = yRi ; i¼1

s ~2 ¼

i¼1

n  i 1h 1 X y2Ri þ y2Ii  ðyR Þ2 þ ðyI Þ2 2n i¼1 2

ð31:17Þ

where yR is the mean of the real channel measurements and yI is the mean of the imaginary channel measurements. These estimates in equations (31.16) and (31.17) are then inserted back into the likelihood function in equation (31.15) and the ratio of null hypothesis likelihood over alternative hypothesis likelihood is taken to form a likelihood ratio statistic [27, 28] ~ ~ ^ ^u; s l ¼ LðA; u; s ~ 2 Þ=LðA; ^2Þ

ð31:18Þ

It is easily verifiable that the likelihood ratio statistic can be simplified to get l¼

 2 n s ^ s ~2

ð31:19Þ

Finally, a statistic is formed by letting

 F ¼ n 1l1=n

ð31:20Þ

According to equations (31.16) and (31.17), 0 < s ^2  s ~ 2 . Thus, l1=n ¼ s ^ 2 =~ s2 2 ½0; 1, 2 which implies that F 2 ½0; n. For voxels containing predominantly noise, s ^ approaches s ~2 and F approaches zero. On the other hand, for voxels containing predominantly signal, under the i.i.d. assumption of the measurements, it can be easily shown that s ^ 2 approaches zero and thus F approaches n. The hypothesis test on F statistic is then to determine a critical value (threshold) Fa for a given significance level a (Type 1 error rate). Obviously, given the same complex signal, as the error variance s2 increases, s ~ 2 increases and as a result F increases and vice versa. In other words, the critical value for the F statistic should be a monotone increasing function of the noise variance. This suggests bigger critical value for an F statistic when the noise variance is large, as we would expect. However, as described at

CONNECTIVITY

585

the beginning of this chapter, the noise variance is a constant throughout an MR image, which means that a single critical value can be applied to the whole image. Upon substitution of equations (31.16), (31.17), and (31.19) into (31.20), we get [22] i 0 h 1,  Pn 2  2 ! Pn 2 n ðyR Þ2 þ ðyI Þ2 =s2 i¼1 yRi þ i¼1 yIi =s @ A F¼ ð31:21Þ 2 2n n

h i n P 2 P yRi þ y2Ii =s2 are x2 distributed It can be shown that n ðyR Þ2 þ ðyI Þ2 =s2 and i¼1

i¼1

with degrees of freedom 2 and 2n, respectively. By dividing these two x2 distributed terms by their degrees of freedom and taking the ratio, the result is generally a statistic that under the null hypothesis has an F distribution with 2 and 2n degrees of freedom. However, this is not true in this case. These two x 2 statistics need be statistically independent in order for pffiffiffi this to be true. It can be shown that the correlation between these two statistics is 1= n. This correlation approaches zero for large n and the F statistic becomes F distributed with 2 numerator and 2n denominator degrees of freedom. In nonfunctional MR imaging applications, there may be a very small number of repeated images if any. For the case where only one single image is available, we take the voxel and its nearest neighbors as the sample set of independent measurements. Still, n is small, and this asymptotic result does not hold. Thus, critical values from the F distribution do not apply to this F statistic. However, critical values for small n can be achieved by way of Monte Carlo simulation. For a given level of significance (Type 1 error rate a), we reject H0 (do not threshold voxel) if the test statistic F is larger than the critical value Fa(2, 2n) and do not reject (threshold voxel) if F is smaller than the critical value Fa(2, 2n). When thresholding the statistic image, an adjustment for multiple comparisons such as with a Bonferroni corrected threshold can be performed [29, 30]. To examine the theoretical Type 1 error and Type 2 error relationship, 20 million independent simulated data values for n ¼ 9 were created under the null hypothesis A ¼ 0 and u ¼ 0 and under the alternative hypothesis with A ¼ (1, 3, 4, 5, 7.5, 10) and u ¼ 0. Normally distributed independent noise variates were generated for the real and imaginary parts with a mean of zero and a variance of s2 ¼ 1. Figure 31.3 shows a histogram for the million data sets when A ¼ 0 in light gray (unshaded) and A ¼ 1 in dark gray colors (shaded).

FIGURE 31.3 MAPHT histograms when H0 is true (A ¼ 0) and when H1 is true (A ¼ 1). (a) magnitude, (b) phase, and (c) F statistic. The vertical line in (c) is at F0.05(2, 18) ¼ 2.81, which is the critical value for a ¼ 0.05. Note that there is not a clear separation between the two populations in either the magnitude or phase, but there is better separation with the F statistics.

586

COMPLEX THRESHOLDING METHODS FOR ELIMINATING VOXELS

Figure 31.3a presents the distribution of magnitudes, (b) presents the distribution of phases, and (c) presents the distribution of F statistics. The black vertical line in Figure 31.3c is at F0.05 ¼ 2.81, which is the critical value when a ¼ 0.05. The false positive rate a is the intersection area that is to the right of Fa. The light gray and intersection areas less than Fa are the true positive rate 1  a. The dark gray and intersection areas to the right of Fa are the true negative rate 1  b. The false negative rate b is the intersection and the dark colored areas that are to the left of Fa. It can be seen in Figure 31.3 that as the null hypothesis false positive rate a decreases, the alternative hypothesis false negative rate b increases. Also, we note that the Monte Carlo results validated that the distribution of F values never exceeds n regardless of A. For each value Fa for the vertical line with corresponding false positive rate areas a to the right of it, we can determine the false negative rate b. A plot of a on the horizontal axis and 1  b on the vertical axis is called a receiver operating characteristic (ROC) curve [8]. This curve can be made for each combination of A. In Figure 31.4 are the ROC curves for A ¼ (3, 4, 5, 7.5, 10). Note that as A increases for a given false positive rate a, the true positive rate (1  b) increases. As A increases, the alternative hypothesis distribution (dark gray colored) in Figure 31.3c becomes more peaked and shifts to the right. As the alternative hypothesis distribution shifts to the right, the lower tail has less area below a given Type 1 error rate

(a)

(b) 1

1

A =3 0.7

0.997

A =0 0.3

0

(c)

0.99

0

0.3

0.7

0.90

1

(d)

1

0

0.003

0.007

0.01

1

A =4

A =7.5

0.9997

0.99997

1−

A =5 A =4 0.9993

0.9990

0.99993

A =3

0

0.3

0.7

1 × 10-3

0.99990

0

0.3

0.7

1 × 10-4

FIGURE 31.4 MAPHT ROC curves from Monte Carlo simulation for A ¼ (0, 3, 4, 5, 7.5, 10). Note that as A increases, for a given false positive rate a, the true positive rate 1  b increases.

CONNECTIVITY

0

1

2

3

4

5

6

7

8

587

9

F FIGURE 31.5 MAPHT histogram of F statistic for 5 107 data sets under null hypothesis for critical values. Note that larger F values are less likely. Adapted from Ref 22, with permission from Elsevier Science.

(false positive rate a), and thus the Type 2 error rate (false negative rate b) decreases and the true positive rate (1  b) increases. To determine Monte Carlo theoretical critical values for the F statistic when n ¼ 9, 5  107 data values were generated. For each data value, the F statistic was computed. A histogram of these F statistics for n ¼ 9 is presented in Figure 31.5. These F statistics were ordered and percentiles determined. Selected critical values are presented in Table 31.2 for n ¼ 9. Intermediate critical values can be reliably interpolated or extrapolated with Fmax ¼ n when a ¼ 0. In conclusion, when the MAPHT method is applied to a complex MR image, an F statistic is computed for all the voxels. A critical value is estimated for the whole image using the results of the Monte Carlo simulations and the voxels from the signal free area (noise measurements). The F statistic map is then thresholded by the critical value. A binary mask is produced in which the number 1 (unity) corresponds to an F statistic greater than the critical value and the number 0 (zero) corresponds to an F statistic less than the critical value. TABLE 31.2 MCMC F Statistic Significance Level and Critical Values for n ¼ 9 a 0.05 0.01 0.001 0.0001 0.00001 0.000001 0.05/256/256 0.05/352/512 0.05/384/512 0.05/512/512

Fa(2, 18) 2.8102 3.9377 5.1991 6.1512 6.8678 7.3911 7.5627 7.5869 7.7051 7.7575

588

COMPLEX THRESHOLDING METHODS FOR ELIMINATING VOXELS

This binary mask is used to threshold the original magnitude and phase images. The magnitude and phase of thresholded voxels are set to zero but for display the thresholded voxel phase values are set to –p.

SIMULATED DATA Simulated images were created to test the algorithm under controlled conditions for a circle with a radius of 128 voxels embedded in a field of view of 512 voxels. Using a Monte Carlo approach, the SNR in the circle was set to 3:1, 5:1, and 10:1 and the algorithm was tested in each case. A ROC [12] was produced for each SNR value in each of the steps defined in Figure 31.1. More specifically, the real and imaginary channels were created for a given A (of 3, 5, or 10) as A cos(u) þ hR and A sin(u) þ hI, where hR and hI are N(0, s2) with s ¼ 1 and u ¼ 0. Magnitude and phase data were then generated from this complex-valued data set.

HUMAN DATA To test the CTM under low SNR when phase is expected to have a zero mean, spin echo data were collected with a thin slice and high resolution at 1.5 Ton a Siemens Sonata. The imaging parameters were field of view (FOV) ¼ (192  256 mm2), matrix size ¼ 384  512, in-plane resolution ¼ 0.5  0.5 mm2, slice thickness ¼ 2mm, TR/TE ¼ 300 ms/15 ms, and flip angle (FA) ¼ 90 . To evaluate data with a bulk of the phase with zero mean but some structures within phase different from zero, such as the veins, SWI [23] data of brain and leg were collected. The SWI brain volume was acquired at 3 Ton a Siemens Verio. Imaging parameters were FOV ¼ 196  256 mm2, matrix size ¼ 384  512, in-plane resolution ¼ 0.5  0.5 mm2, slice thickness ¼ 2 mm, TR/TE ¼ 29 ms/20 ms, and FA ¼ 15 . The SWI leg data were collected at 1.5 T on a Siemens Sonata. The imaging parameters were FOV ¼ 150  200 mm2, matrix size ¼ 384  512, in-plane resolution ¼ 0.4  0.4 mm2, slice thickness ¼ 1 mm, TR/TE ¼ 21 ms/10.2 ms, and FA ¼ 15 . Simulated Data for CTM The ROC curves for magnitude and phase thresholds (both separately and combined) for the simulated circle are shown in Figure 31.6 without connectivity for an SNR of 3:1, and in Figure 31.7 with connectivity for SNRs of 3:1, 5:1, and 10:1. In Figure 31.7, we can see that both errors remain rather large for either the magnitude or the phase method with moderate improvement when both are combined. In order to keep Type II error less than 0.1, the best choice for m and n would be an m of 1.5 or 2 and an n of 2–2.5. Adding magnitude connectivity dramatically reduces the Type I error (figure not shown). Minimum error is achieved for a magnitude connectivity tM of 3. In order to keep Type II error less than 0.004, the best choice for m and n would now be an m of 3 or 4 and an n of roughly 2–4. In this case, all the Type I error will now be less than 0.003. Finally, adding phase connectivity reduces Type I error even further to less than 0.0001 for a phase connectivity tP of 2 or 3 and a magnitude connectivity tM of 2 or 3. In summary, the set of (tM, tP, m, n) that will work best for an SNR of 3:1 could range from the minimum of the above choices (2, 2, 3, 2) to the maximum of roughly (3, 3, 4, 4), with a Type I error of no more than 0.0001. Generally, the lower the n is, the lower the Type II error will be.

589

HUMAN DATA

0.7 (x,y) : x - magnitude threshold y - phase threshold

5.5 1.0

0.6

5.0 (0.5,5.5) 4.5 (0.5,5.0) 4.0 (0.5,4.5) 3.5 (0.5,4.0) (0.5,3.5) 3.0 1.5 (0.5,3.0) 2.5 2.0 (1.0,3.5) (1.0,3.0) (1.0,2.5)

0.5

Type II

0.4 0.3 0.2

1.5 2.0

(1.5,3.0)

(1.5,3.5)

0.1

mlP magnitude threshold phase threshold

(1.5,2.0) (2.0,2.0) (2.0,2.5)

(1.5,2.5)

0 0

0.025

0.05

0.1

0.075

0.125

0.15

0.175

0.2

Type I

FIGURE 31.6 The CTM ROC results combining both magnitude (circles) and phase (triangles) threshold operations (SNR 3:1). There is a clear reduction of Type I and Type II errors in the combined operation (diamonds).

0.01

(2,3,2.0,2.5) (x,y,x,w ) : x : Magnitude Connectivity Threshold y : Phase Connectivity Threshold z : Magnitude Threshold w : Phase Threshold

0.009 (2,2,1.0,2.5) (2,2,2.0,5.5)

0.008 0.007

(2,3,1.0,1.5)

Type II

0.006

SNR 3 to 1 SNR 10 to 1 SNR 5 to 1

(2,2,1.0,2.0)

0.005

(2,3,2.5,3.5) (3,2,3.5,1.5)

0.004

(3,3,4.0,2.0)

(3,3,1.5,3.5) (2,3,2.5,3.5) (3,3,4.5,2.5)

0.003

(3,3,4.0,1.5) (3,3,4.0,1.0)

0.002

(4,4,2.0,3.0) (4,3,2.0,3.5) (4,4,2.0,5.5) (4,2,4.0,3.0) (4,4,2.5,3.0) (4,4,2.5,3.0) (4,2,3.5,3.5) 0.001 (4,2,3.5,4.5)

0 0

0.00002

0.00004

0.00006

0.00008

0.0001

0.00012

0.00014

Type I

FIGURE 31.7 CTM Type I error versus Type II error for magnitude (tM ¼ 2–4) and phase (tP ¼ 2–4) connectivity along with magnitude threshold (m ¼ 0.5–4.5) and phase threshold (n ¼ 1.0–5.5) values for SNR of 3:1, 5:1, and 10:1. Choosing a Type II error less than 0.003 provides a broad range of possible (tM, tP, m, n) values with very small Type I error.

590

COMPLEX THRESHOLDING METHODS FOR ELIMINATING VOXELS

For higher SNR, tM and tP can range from 2 to 4, m from 1.5 to 4, and n from 2 to 4. Under these circumstances, Type I error will remain less than 0.0004 and Type II error will remain less than 0.006. For example, a (tM, tP, m, n) of (3, 3, 3, 3) fits in this domain for an SNR of 5:1 or higher. Running the spike removal and hole restoration once yields Type I and Type II errors of 1.944  105 and 0.0035, respectively, and running it twice yields errors of 0 and 0.005, respectively. For the higher SNR cases, a magnitude and phase connectivity of 4 performs the best. An example of the full processing as applied to the simulated circle for an SNR of 3:1 is shown in Figure 31.8. The final Type I error is 0.000486 (25 voxels thrown out) and the final Type II error is 0.002112 (445 voxels not thrown out), in good agreement with the above predictions. Finally, the time to fully process one complex-valued image is just under 3 s at a processing speed of 3.06 GHz.

FIGURE 31.8 CTM results for simulated data: (a) original magnitude image, (b) original phase image, (c) thresholded magnitude image with (tM, tP, m, n) ¼ (3, 3, 2, 2), and (d) thresholded phase image with (tM, tP, m, n) ¼ (3, 3, 2, 2), showing no noise remaining outside the image. In this case, Type I error is 0.000486 (25 points are removed, mostly around the edges) and Type II error is 0.002112 (445 noise voxels remain). The SNR in the magnitude image is 3:1.

HUMAN DATA

591

Human Data for CTM Estimation of background noise was done by selecting a region of interest outside the brain and using the voxel intensity values to obtain s0 as explained in the ‘‘Methods’’ section. We used the approach of taking the mean of the noise (signal) outside the object as being 1.25 standard deviations of that on the inside [12]. First, we tested a set of 1.5 T spin echo images with an SNR of 3:1 (Figure 31.9). The original magnitude image (Figure 31.9a) is very noisy and consequently shows little contrast. Figure 31.9b shows the usual magnitude-only threshold with m ¼ 2, and thus a great deal of noise still remains in the image. Figure 31.9c uses the full CTM processing with (tM, tP, m, n) ¼ (3, 3, 2, 4). Much of the noise is now suppressed. Figure 31.9d shows a heavily filtered and averaged image showing what the background contrast of this T1-weighted spin echo scan would look like if there were enough SNR. (This was accomplished by using a 4  4  3 average filter). Figure 31.9e is the original phase image and, as expected for a spin echo scan, the phase is flat (except in the vicinity of vessels that may not be fully flow compensated). The final masked phase image is shown in Figure 31.9f. It is now much easier to adjust window level settings and the image is beginning to look more like a conventional MR image.

FIGURE 31.9 CTM results for spin echo brain data. (a) Original magnitude image with a resolution of

0.5  0.5  2 mm3 and SNR of 3:1. (b) Magnitude result after CTM filter with (tM, tP, m, n) ¼ (0, 0, 2, 0), that is, magnitude threshold of m ¼ 2 and no connectivity. (c) Magnitude result after CTM filter with (tM, tP, m, n) ¼ (3, 3, 2, 4). (d) Magnitude image after 4  4  3 average filter on original magnitude, resolution decreased to 2  2  6 mm3. (e) The original phase image and (f) phase result after CTM filter with (tM, tP, m, n) ¼ (3, 3, 2, 4).

592

COMPLEX THRESHOLDING METHODS FOR ELIMINATING VOXELS

FIGURE 31.10 CTM results for SWI brain data with an SNR of roughly >30:1. (A1) Original magnitude image of midbrain, (B1) original phase image of midbrain, (C1) magnitude result after CTM filter with parameters (tM, tP, m, n) ¼ (3, 0, 5, 5), that is, thresholding with m ¼ n ¼ 5, in both magnitude and phase, p ¼ 5 in magnitude connectivity and no connectivity, of A1 and B1, (D1) phase result after CTM filter with parameters with (tM, tP, m, n) ¼ (3, 0, 5, 5). (A2) Original magnitude image of thalamostriate area; (B2) original phase image of thalamostriate area; (C2) magnitude result after CTM filter with parameters (tM, tP, m, n) ¼ (3, 0, 5, 5) of A2, B2; (D2) phase result after CTM filter with parameters (tM, tP, m, n) ¼ (3, 0, 5, 5) of A2, B2. (A3) Original magnitude image of motor cortex area; (B3) original phase image of motor cortex area; (C3) magnitude result after CTM filter with parameters (tM, tP, m, n) ¼ (3, 0, 5, 5) of A3, B3; (D3) phase result after CTM filter with parameters (tM, tP, m, n) ¼ (3, 0, 5, 5) of A3, B3.

HUMAN DATA

FIGURE 31.10

593

(Continued ).

Another example in the human brain is shown from an SWI data set at 3 T (Figure 31.10). Three slices are chosen, representing the midbrain (Figure 31.10A1 and B1), thalamostriate area (Figure 31.10A2 and B2), and motor cortex area (Figure 31.10A3 and B3). The SNR is very good, above 30:1, in the original magnitude image (Figure 31.10A1–A3). Thus, the CTM filtered magnitude result does not have much change with the original input (Figure 31.10C1–C3). The SWI filtered phase image, however, is fairly uniform except for the phase variations caused by air/tissue interfaces at the top (Figure 31.10B1 and B2). Phase aliasing or wrapping artifacts can be seen clearly (Figure 31.10B1). First, a threshold value of m ¼ n ¼ 5 on magnitude and phase is applied to keep most of the data inside the

594

COMPLEX THRESHOLDING METHODS FOR ELIMINATING VOXELS

FIGURE 31.10

(Continued).

brain. To delete most of the spike or islands of noise, a magnitude connectivity of tM ¼ 3 is used. No phase connectivity is run in this example since the spike removal part was run. In the resulting processed phase image, the noise outside brain has been discarded successfully without sacrificing signal loss from within the brain (Figure 31.10D3), The phase wrapping effects cause some signal lost at the air/tissue interface (Figure 31.10D1 and D2). The CTM parameters used here were (3, 0, 5, 5). Figure 31.11 shows the final example in the human leg SWI data, in which the method works in a 1.5 T dataset using (3, 3, 2, 2). The original unthresholded magnitude image is in

HUMAN DATA

FIGURE 31.11

595

CTM results for the SWI leg data. (a) Original magnitude image, (b) original phase image, (c) thresholded magnitude image (tM, tP, m, n) ¼ (3, 3, 2, 2), and (d) thresholded phase image (tM, tP, m, n) ¼ (3, 3, 2, 2). This thresholded phase image takes on more characteristics of the conventional magnitude image, except that it shows the veins clearly, whereas no veins are seen in the conventional image. The thresholded phase image is no longer hampered by the noise points, and so it is easier to adjust the window and the level and to avoid being distracted by the presence of phase noise cluttering the image. The SNR in the magnitude image is 5:1.

596

COMPLEX THRESHOLDING METHODS FOR ELIMINATING VOXELS

Figure 31.11a and original unthresholded phase image is in Figure 31.11b. A CTM threshold of (tM, tP, m, n) ¼ (3, 3, 2, 2) is applied and in Figure 31.11c is the resulting thresholded magnitude image and in Figure 31.11d is the resulting thresholded phase image. The phasethresholded image in Figure 31.11d not only shows a significant removal of most noise but also shows those areas where the veins have higher phase than the set threshold. This observation can be useful for processing the SWI data. Although Type I errors remain along the edges of the brain and the leg in the presented examples due to partial volume signal effects and result from the phase variations there, for display purposes, the overall feature of removing the noise from the phase image is quite robust. Simulated Data for MAPHT The ROC curves characterizing the theoretical Type 1 and Type 2 error rates for the MAPHT method were presented in Figure 31.4. To examine the empirical performance of the MAPHT method in comparison to the CTM, new simulated data was generated according to the same process as the simulated data that the CTM method was applied to. The simulated image has a matrix size of 512  512, and thus a Bonferroni corrected threshold of a ¼ 0.05/512/512 was applied with n ¼ 9. Figure 31.12a shows the original magnitude image with noise outside the object (simulated brain). Note that in Figure 31.12b there is high noise in the phase image outside the object and in some internal areas, while the magnitude noise in Figure 31.12a is relatively low. Figure 31.12c shows the computed F statistic map, and the anatomical structure of the object can be seen. In Figure 31.12d, the histograms of the image magnitudes (top), the image phases (middle), and the F statistic values (bottom) are shown. Note that in the histogram for F statistics, there appear to be two populations, but there is no such presence in histograms of either the magnitude or the phase. The population on the left for smaller F values

FIGURE 31.12 MAPHT results for simulated data. (a) Original magnitude image, (b) original phase image, (c) unthresholded F statistic map, (d) histograms, magnitude data (top), phase data (middle), and F statistics (bottom), (e) F ¼ 7.7575 Bonferroni thresholded magnitude image, (f ) F ¼ 7.7575 Bonferroni thresholded phase image, (g) F ¼ 5.75 thresholded magnitude image, and (h) F ¼ 5.75 thresholded phase image.

HUMAN DATA

597

(similar to the ones in Figures 31.3 and 31.5) corresponds to voxels that contain predominantly noise and the other on the right for larger F values (similar to the one in Figure 31.3) corresponds to voxels that contain tissue signal plus noise. The Bonferroni threshold F ¼ 7.7575 is depicted in Figure 31.12d (bottom) as a dashed vertical line. In Figure 31.12e and f are the thresholded simulated magnitude and phase images. Note that in Figure 31.12f there is not only an elimination of the voxels that contain predominantly noise but also an elimination of many voxels that contain signal plus noise. As seen in Figure 31.12d (bottom), many voxels that contain tissue signal plus noise appear to be below the Bonferroni threshold indicated by the dashed line and thus eliminated. This is due to low SNR of the object and the lack of a clear separation of two populations by magnitude in Figure 31.12d (top). The threshold can be lowered to a value such as F ¼ 5.5 denoted by a solid vertical line as in Figure 31.12d (bottom) at the expense of a very small number of false positives (voxels that predominantly contain noise not being thresholded). Figure 31.12g and h show the lower thresholded magnitude and phase images. More anatomical detail (true object) is present in the phase image of Figure 31.12h and less tissue plus noise voxels are eliminated. Human Data for MAPHT To examine the empirical performance of the MAPHT method compared to the CTM method, it was applied to the same human brain spin echo data. The human brain spin echo image has a matrix size of 384  512, and thus a Bonferroni corrected threshold of a ¼ 0.05/512/384 was applied with n ¼ 9. Figure 31.13b shows that there is high noise in the phase image outside the brain and in some internal areas while the magnitude noise in Figure 31.13a is relatively low. Some anatomical structure can be seen in the F statistic

FIGURE 31.13

MAPHT results for the spin echo brain data. (a) Original magnitude image, (b) original phase image, (c) unthresholded F statistic map, (d) histograms, magnitude data (top), phase data (middle), and F statistics (bottom), (e) F ¼ 7.7051 Bonferroni thresholded magnitude image, (f) F ¼ 7.7051 Bonferroni thresholded phase image, (g) F ¼ 4.5 thresholded magnitude image, and (h) F ¼ 4.5 thresholded phase image.

598

COMPLEX THRESHOLDING METHODS FOR ELIMINATING VOXELS

map (Figure 31.13c). Figure 31.13d shows the histograms for magnitudes, phases, and F statistics. Note again that there appear to be two populations in the histogram of F statistics, but there is no such presence in histograms of either the magnitude or the phase. The population on the left for smaller F values corresponds to voxels that contain predominantly noise and the other for larger F values corresponds to voxels that contain tissue signal plus noise. The Bonferroni threshold F ¼ 7.7051 is depicted in Figure 31.13d (bottom) as a dashed vertical line. Figure 31.13e and f show the thresholded SWI magnitude and phase images. Note in Figure 31.13f that there is not only an elimination of the voxels that contain predominantly noise but also an elimination of many voxels that contain signal plus noise, which renders the thresholded image of little value. As seen in Figure 31.13d (bottom), many voxels that contain tissue signal plus noise appear to be below the Bonferroni threshold indicated by the dashed line and thus eliminated. This is due to low SNR of the brain and the lack of a clear separation of two populations by magnitude in Figure 31.13d (top). The threshold can be lowered to a value such as F ¼ 4.5 denoted by a solid vertical line as in Figure 31.13d (bottom) at the expense of a small number of false positives (voxels that predominantly contain noise not being thresholded). Figure 31.13g and h shows the lower thresholded magnitude and phase images, respectively. More anatomical detail is present in the phase image of Figure 31.13h and less tissue plus noise voxels are eliminated. The MAPHT method is also applied to a human brain SWI data. The human brain SWI image has a matrix size of 352  512, and thus a Bonferroni corrected threshold of a ¼ 0.05/352/512 was applied with n ¼ 9. The results are shown in Figure 31.14. As seen in Figure 31.14d (bottom), the Bonferroni threshold identified by a vertical dashed line can be

FIGURE 31.14 MAPHT results for the SWI brain data. (a) Original magnitude image, (b) original phase image, (c) unthresholded F statistic map, (d) histograms, magnitude data (top), phase data (middle), and F statistics (bottom), (e) F ¼ 7.5869 Bonferroni thresholded magnitude image, (f) F ¼ 7.5869 Bonferroni thresholded phase image, (g) F ¼ 8 thresholded magnitude image, and (h) F ¼ 8 thresholded phase image.

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FIGURE 31.15 MAPHT processing on SWI leg image. (a) Original magnitude image, (b) original phase image, (c) unthresholded F statistic map, (d) histograms, magnitude data (top), phase data (middle), and F statistics (bottom), (e) F ¼ 7.7051 Bonferroni thresholded magnitude image, (f) F ¼ 7.7051 Bonferroni thresholded phase image, (g) F ¼ 5.5 thresholded magnitude image, and (h) F ¼ 5.5 thresholded phase image.

raised to the solid line in order to obtain better tissue contrast with little elimination of voxels that contain tissue signal plus noise. This is due to high SNR of the object. Figure 31.14g and h shows the higher thresholded magnitude and phase images. More anatomical detail (tissue contrast) is present in the phase image of Figure 31.14h. Finally, the MAPHT method is applied to the same human leg SWI data which was used for CTM method (Figure 31.11). The human leg SWI image has a matrix size of 384  512, and thus a Bonferroni corrected threshold of a ¼ 0.05/384/512 was applied with n ¼ 9. The results are shown in Figure 31.15. The Bonferroni threshold F ¼ 7.7051 is depicted in Figure 31.15d as a dashed vertical line. In Figure 31.15e is the thresholded SWI magnitude and in Figure 31.15f is the thresholded phase image. Note in Figure 31.15f that there is an elimination of the voxels that contain predominantly noise, but there is a possible elimination of a small number of voxels that contain signal plus noise. As seen in Figure 31.15d (bottom), a small number of voxels that contain tissue signal plus noise appear to be below the Bonferroni threshold indicated by dashed line and thus eliminated. This is due to some low SNR voxels in the object. The threshold can be lowered to a value such as F ¼ 5.5 denoted by a solid vertical line as in Figure 31.15d (bottom). The results of lower threshold value are depicted in Figure 31.15g and h.

CONCLUDING REMARKS Removing noise involves finding the delicate balance between removing unwanted signal components and components that are part of the object of interest. For low SNR, a simple

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COMPLEX THRESHOLDING METHODS FOR ELIMINATING VOXELS

magnitude threshold will remove a considerable amount of noise, but at the expense of removing signal as well. Complex Threshold Method The goal of using phase and connectivity is to increase the probability of retaining as much information about the object as possible (smallest Type I error) and removing as much noise as possible (smallest Type II error). The results of this study show that it is possible to reduce Type I and Type II errors to almost zero even for very noisy data with an SNR of 3:1. The remnant areas that are hard to remove represent first some voxels near the edges that are kept by applying the connectivity algorithm, and second, clusters of noise points that exceed the diameter of three neighboring points. The choice of connectivity ¼ 3 appears to be optimal and makes sense geometrically. If there are three connected points, then objects thrown out inside a rectangle-like object will be reinstated while circle-like objects may not. This keeps some noise points inside the object but will tend to enlarge the boundaries of the circle. A connectivity of 4 tends to throw out more of these noise points, but at the expense of throwing out signal points when the SNR is too low. However, if one extends this on a second pass to a connectivity of 4, then edges will remain essentially untouched. Other methods [15, 18] recognize the need for edge preservation as well. Although our focus has been on the low SNR cases (because these cases are perfect examples of where the simple magnitude threshold methods fail), the higher SNR data can be further optimized as well using CTM. From a practical point of view, ideally there exists a fixed set of values for connectivity and thresholds that would give a robust result. For an SNR of 3:1, the best choice of connectivity and threshold values (tM, tP, m, n) ranges from (3, 3, 2, 2) to (3, 3, 2, 4), as shown in Figures 31.8 and 31.9. For an SNR of 5:1 or higher, the best choice for (tM, tP, m, n) ranges from (2, 2, 3, 2) to (3, 3, 4, 4), as shown in Figure 31.11. Although many images in MRI have high SNR, with the recent push to higher resolution in MR angiography, susceptibility weighted imaging, and anatomical imaging (especially at high fields where the rf response is nonuniform), the SNR values will drop considerably (perhaps approaching 3:1), making the CTM filter more useful. For an SNR of 5:1 in the SWI leg data, (3, 3, 2, 2) suppresses the phase of veins more efficiently (Figure 31.11d), while (3, 3, 2, 4) keeps many more voxels within the veins and at the edge of air/tissue interfaces while still removing the background noise (image not shown). The choice of a phase threshold of 2 or 4 depends on whether one wants to simply remove phase noise higher than 4 standard deviations or to also remove signal from veins, for instance, as in SWI. In such a case, one may wish to push the phase threshold down to 2. In the SWI brain example (SNR > 30:1), (3, 3, 2, 4) works fine and one can afford to increase the magnitude threshold to 5 or even higher and use (3, 0, 5, 5). The choice of m ¼ 5 removes the outer boundary of the skull because of its lower signal but maintains the signal inside the brain. The higher connectivity of 4 tends not to restore many voxels because the connectivity is too stringent a constraint, especially for the very low SNR of 3:1. When the SNR is higher than 10:1, (tM, tP, m, n) has a large range to chose from. As demonstrated in Figure 31.10, the phase image can be well separated from the noise even if there are general baseline shifts. As a practical point, the condition for equation (31.7), in which the phase has a mean of zero, is valid only for a spin echo sequence with a perfectly centered echo. However, for an asymmetric placement of the p pulse relative to the echo time or for a gradient echo

CONCLUDING REMARKS

601

sequence (if the phase is high pass filtered), the mean phase will again tend to be zero [23]. There are other methods where the phase need not be zero for this approach to be useful. This could include removing major veins in SWI (as shown in Figures 31.11 and 31.14) and removing vessels in flow quantification techniques that use phase. Finally, this approach can also be used to set the voxels determined as noise to have a high signal rather than zero, such as a maximum value available to the system. Then, when a series of SWI data is evaluated using a mIP method, the noise in one slice no longer causes the removal of regions having signal in other slices. This is particularly valuable near the top of the brain where the head narrows and eventually disappears. In this example, even if an image is completely noisy, the algorithm will prevent the failure of the mIP operation. The use of phase information can be important not only for gradient echo methods such as SWI but also for spin echo methods if used as additional information for removing noise points. The CTM along with a connectivity criterion has been shown to give excellent results for an SNR as low as 3:1. The most prominent advantage of the CTM method is its easy implementation and reasonable computational time. The use of the phase information has proven successful in removing noise that would otherwise not be recognized if only noise in the magnitude image had been considered. Practically, using this approach makes it possible not only to improve the magnitude image but also to make phase images appear more like magnitude images. The noise in the phase images leads to wild swings in the phase values, causing a visually unappealing appearance in the phase images and difficulty in adjustments of window level settings. Using the complex threshold technique to suppress the noise, especially in the phase images used in susceptibility weighted imaging, makes phase data more easily viewable. The CTM method is robust with a limited set of connectivity parameters serving for a low SNR of 3:1 and another set for a broader range of SNRs of 5:1 and higher. Magnitude and Phase Thresholding Method The MAPHT method was successfully applied to both simulated and human MRI data. It was shown to perform well in separating voxels that contain tissue signal plus noise from voxels that contain predominantly noise. The MAPHT thresholding procedure is based on a likelihood ratio test and its theoretical statistical properties were shown through Monte Carlo simulation in terms of both false positives and false negatives. The MAPHT method for thresholding complex-valued magnetic resonance images was successfully applied to a simulated data set and three human data sets and shown to produce increased tissue contrast by eliminating false positives. It was seen that when the SNR is low, voxels cannot be reliably separated by only the magnitude data because the histogram of predominantly noise voxels overlaps with the histogram of tissue plus noise voxels. However, when the SNR was low, the MAPHT method produced an F statistic that could reliably separate the predominantly noise voxels from the tissue plus signal voxels. It was found that a Bonferroni threshold that is corrected for multiple comparisons may be too conservative. As an alternative to a Bonferroni threshold, an FDR threshold can be used as it is less conservative [29, 30]. The CTM approach to the elimination of voxels that contain predominantly noise utilized not only complex thresholding but also local connectivity to enhance suppression of noise or prevent the incorrect assignment of signal to noise in order to reduce Type I errors. The MAPHT method does not use connectivity but a local neighborhood of voxel values and looks at local variance on a voxel by voxel basis. The CTM approach may suffer when the

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COMPLEX THRESHOLDING METHODS FOR ELIMINATING VOXELS

phase itself deviates from zero or any set zero point. This can lead to the suppression of areas where the phase is offset from flow effects or susceptibility effects (the later being acceptable in some cases when the goal is to also suppress veins). However, the phase has a rapid variation near the air/tissue interfaces, and in these areas the CTM might fail and that part of the brain will be suppressed. It is not so with the MAPHT method that uses the local variance and keeps the local value as the phase offset (i.e., there is not a global offset of zero in phase). For this reason, this new approach is more robust to variations in phase caused by unwanted field inhomogeneity effects. This method can also easily be adapted for 3D images. In conclusion, two magnitude and phase thresholding procedures were described and successfully applied to both simulated and human images. Both the CTM and MAPHT methods were shown to produce increased tissue contrast by eliminating false positives. The joint use of magnitude and phase images improves the removal of noise voxels in magnetic resonance images. This can be useful in automated visualization of phase images without the highly distractive noise voxels or in susceptibility weighted imaging when taking the minimum intensity projections of variably sized regions.

REFERENCES 1. Rice SO. Mathematical analysis of random noise. Bell Syst. Tech. J. 1944;23:283. 2. Edelstein WA, Glover GH, Hardy CJ, Redington RW. The intrinsic signal-to-noise ratio in NMR imaging. Magn. Reson. Med. 1986;3:604–618. 3. Henkelman RM. Measurement of signal intensities in the presence of noise in MR images. Med. Phys. 1985;12:232–233. 4. Bernstein MA, Thomasson DM, Perman WH. Improved detectability in low signal-to-noise ratio magnetic resonance images by means of phase corrected real reconstruction. Med. Phys. 1989;16:813–817. 5. Gudbjartsson H, Patz S. The Rician distribution of noisy MRI data. Magn. Reson. Med. 1995;34:910–914. 6. Andersen AH. On the Rician distribution of noisy MRI data. Magn. Reson. Med. 1996;36:331–333. 7. Sijbers J, Den Dekker AJ, Van Audekerke J, Verhoye M, Van Dyck D. Estimation of noise in magnitude MR images. Magn. Reson. Imaging 1998;16:87–90. 8. Sijbers J, Poot D, den Dekker AJ, Pintjens W. Automatic estimation of the noise variance from the histogram of a magnetic resonance image. Phys. Med. Biol. 2007;52:1335–1348. 9. Chang LC, Rohde G, Pierpaoli C. An automatic method for estimating noise-induced signal variance in magnitude-reconstructed magnetic resonance images. SPIE Med. Imaging: Image Process. 2005;5747:1136–1142. 10. Rowe DB Logan BR. A complex way to compute fMRI activation. Neuroimage 2004;23:1078–1092. 11. Constable RT, Henkelman RM. Contrast, resolution and detectability in MR imaging. J. Comput. Assist. Tomogr. 1991;15:297–303. 12. Hendrick RE, Haacke EM. Basic physics of MR contrast agents and maximization of image contrast. J. Magn. Reson. Imaging 1993;3:137–148. 13. Haacke EM, Brown RW, Thompson MR, Venkatesan R. Magnetic Resonance Imaging: Physical Principles and Sequence Design, Wiley, New York, 1999.

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14. Madore B, Henkelman RM. A new way of averaging with applications to MRI. Med. Phys. 1996;23:109–113. 15. Macovski A. Noise in MRI. Magn. Reson. Imaging 1996;38:494–497. 16. Nowak R.D. Wavelet based Rician noise removal for magnetic resonance imaging. IEEE Trans. Image Process. 1999;8:1408–1419. 17. Sijbers J, den Dekker AJ, Van Der Linden A, Verhoye M, Van Dyck D. Adaptive anisotropic noise filtering for magnitude MRI data. Magn. Reson. Imaging 1999;17:1533–1539. 18. Lysaker M, Lundervold A, Tai XC. Noise removal using fourth-order partial differential equation with applications to medical magnetic resonance images in space and time. IEEE Trans. Image Process. 2003;12:1579–1589. 19. Chen B, Hsu EW. Noise removal in magnetic resonance diffusion tensor imaging. Magn. Reson. Med. 2005;54:393–407. 20. Cline HE, Dumoulin CL, Lorensen WE, Souza SP, Adams WJ. Volume rendering and connectivity algorithms for MR angiography. Magn. Reson. Med. 1991;18:384–394. 21. Lin W, Haacke EM, Maaryk TJ, Smith AS. Automated local maximum-intensity projection with three-dimensional vessel tracking. J. Magn. Reson. Imaging 1992;2:519–526. 22. Rowe DB, Haacke, EM. MAgnitude and PHase Thresholding (MAPHT) of noisy complex-valued magnetic resonance images. Magn. Reson. Imaging 2009;27(9):1271–1280. 23. Reichenbach JR, Venkatesan R, Schillinger DJ, Kido DK, Haacke EM. Small vessels in the human brain: MR venography with deoxyhemoglobin as an intrinsic contrast agent. Radiology 1997;204:272–277. 24. Haacke EM, Xu Y, Cheng YCN, Reichenbach J. Susceptibility weighted imaging (SWI). Magn. Reson. Med. 2004;52:612–618. 25. Rowe D.B., Meller C.P., Hoffmann R.G. Characterizing phase-only fMRI data with an angular regression model. J. Neurosci. Methods 2007;161:331–341. 26. Pandian D, Ciulla C, Haacke EM, Jiang J, Ayaz, M. A complex threshold method for identifying voxels that contain predominantly noise in magnetic resonance images. J. Magn. Reson. Imaging 2008;28:727–735. 27. Hogg RV, Craig AT. Introduction to Mathematical Statistics, 4th edn, Macmillan, New York, 1978. 28. Bain LM, Engelhardt M. Introduction to Probability and Mathematical Statistics, 2nd edn, PSWKent, Boston, MA, 1992. 29. Logan BR, Rowe DB. An evaluation of thresholding techniques in fMRI analysis. Neuroimage 2004;22:95–108. 30. Logan BR, Geliazcova MP, Rowe DB. An evaluation of spatial thresholding techniques in fMRI analysis. Hum. Brain Mapp. 2008;29:1379–1389.

32 Automatic Vein Segmentation and Lesion Detection: from SWI-MIPs to MR Venograms Samuel Barnes, Markus Barth and Peter Koopmans

INTRODUCTION 3D SWI venography data sets provide amazing detail about the vascular structure, but 2D visualization of the images limits the ability to fully describe the 3D structures. Tasks that are difficult when only looking at 2D images, such as understanding the shape of a network of vessels, become trivial when the data are visualized in 3D. Similar to maximum intensity projections (MIPs) that are used in angiography, minimum intensity projections (mIP) have traditionally been used as a pseudo-3D visualization method with SWI. Unlike maximum intensity projections that can be done through the entire data set at any orientation, minimum intensity projections are more limited as the brain is surrounded by a dark background that will mask any tissue if it is included in the projection. Due to this, minimum intensity projections are usually only done over 4–8 axial slices. The mIP is formed by combining multiple slices into one image by taking the minimum value at every position and displaying it on the mIP. This method relies on the simple assumption that a vein will have a lower value than any other point along the projection and so its value will be displayed. The limitation of the dark background masking the brain makes larger projections impractical as the slice where the brain is the smallest limits how much of the brain is visible on the mIP. To visualize the entire vasculature, a more advanced algorithm is required. Removing the background with a brain extraction algorithm before performing the mIP is a possibility (see Chapter 7), but this can leave remnant dark rings around the edge of the brain, and there is still the possibility of dark brain structures Susceptibility Weighted Imaging in MRI, By E. Mark Haacke and J€urgen R. Reichenbach Copyright Ó 2011 by Wiley-Blackwell

605

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AUTOMATIC VEIN SEGMENTATION AND LESION DETECTION: FROM SWI-MIPs TO MR VENOGRAMS

masking the veins resulting in a low-quality mIP. Segmenting out the veins allows them to be visualized directly using surface rendering techniques without the complication of them being obscured by larger veins or other dark structures. Many different techniques have been tried to solve the similar problem of segmenting out bright arteries from a dark background. For a review of these techniques please see Refs 1 and 2. Many of these methods can be adapted to segment veins from SWI data. To date, two main methods have been tried: a scale space analysis and a statistical thresholding model.

SCALE SPACE ANALYSIS Scale space analysis examines the local structure and shape at different scales to determine how to classify a voxel. For example, in 3D, a vein will look cylindrical. Since you wish to identify all veins, you must look for cylinders of different sizes (or at different scales) to identify both large and small veins. The local structure is commonly examined using the Hessian matrix that contains the partial second derivatives of Gaussian functions [3]. The eigensystem of the Hessian has direct geometrical interpretation that can be used to construct a vesselness measure, such as described by Refs 3–7. The standard deviation of the Gaussian used (how much smoothing is applied) determines the scale of the features that are being looked for. This vesselness measure can be used to segment the image by applying a threshold [3] or using an active contour [7]; it can also be visualized directly [4]. To improve segmentation results, the multiscale Gaussian smoothing used above can be replaced with a nonlinear diffusion filter that preserves vessel information. Images are preferentially smoothed in the direction of the vessel, which will enhance the vessels and still suppress the background and noise. Early work with nonlinear filters sought to preserve edges by only smoothing inside rather than across regions, as determined by gradient magnitude [8]. This work was later applied to angiograms using different vesselness measures to steer the diffusion [9–11]. A nonlinear smoothing to enhance vessels was also proposed by Du et al. [12]. However, this was only implemented for a single scale and lacked the flexibility that the more robust scale space approaches have. For a more detailed treatment of nonlinear diffusion filters, please see Ref. 13. Vein segmentation in highresolution SWI data sets can be performed based on the concepts described above where the combination of extraction of the local structure using the Hessian matrix and diffusion filtering proves particularly powerful. Here, we apply concepts that were originally developed for bright vessel segmentation by Frangi et al. [14] and further improved by using vessel enhancing diffusion (VED) [15] and then adapted for dark vessel segmentation [16]. In the following, we briefly describe these methods. A more detailed description can be found in Ref. 15. Vesselness Filter The vesselness filter is based on the second-order image information represented by the Hessian matrix. By analyzing the eigensystem of the Hessian, a likeliness function can be formulated to distinguish tubular structures (vessels) from nontubular structures (e.g., background noise). The Hessian is calculated at a particular spatial scale that will be varied to detect vessels of different diameters. The eigenvalues (lj) of the Hessian, sorted by

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increasing magnitude (|l1| < |l2| < |l3|), describe the local second-order structure in an image. For instance, if l3 has a high value and l1 and l2 are low, it means that there is an intensity change in a single direction only; in other words, we are dealing with a plate-like structure. The vesselness filter function is constructed to respond to dark tubular structures and to suppress all other structures by using these eigenvalues and three tuning parameters: one suppressing blob-like structures (a), one suppressing plate-like structures, (b) and one suppressing background noise (c). The last one is sensitive to the absolute intensity of the image. The total vessel-likeliness filter that selects vessels that are dark with respect to their surroundings is shown in equation (32.1). ( 0;

2 2 
 for l1 > 0 or l2 > 0 2 2 2 2 V¼ ð32:1Þ eRB =2b 1eS =2c otherwise 1eRA =2a with RA ¼

RB ¼

ðLargest cross-section areaÞ=p ðLargest axis semi-lengthÞ

2

Volume=ð4p=3Þ ðLargest cross-section area=pÞ sffiffiffiffiffiffiffiffiffiffiffiffi X ffi S ¼ kHkF ¼ l2j

3=2

jl2 j jl3 j

ð32:2Þ

jl1 j ¼ pffiffiffiffiffiffiffiffiffiffiffiffi jl2 l3 j

ð32:3Þ

¼

ð32:4Þ

jD

The values for a and b were both set to 0.5 as suggested in Ref. 17. Koopmans et al. investigated the influence of parameter c and found that too low a value will degrade the contrast of the vesselness filter output. Too high a value will not affect this contrast; however, it will lower the absolute value of the vessel likeliness that, in turn, degrades the performance of the VED filter (explained below) as it makes use of the vesselness filter output. A good value for c was empirically found by Koopmans et al. to be 10% of the median intensity value within the brain [17]. Vessel Enhancing Diffusion The VED filter method [15] is an iterative process making use of the vesselness filter. During each iteration, the data are processed in such a way that the vesselness filter output will be improved in the next iteration by applying a diffusion scheme of varying (an)isotropy to the data. The nature of this scheme is determined by the vessel-likeliness found by the vesselness filter. If the voxel in question has a low vessel-likeliness, isotropic diffusion occurs; if it has a high vessel-likeliness, anisotropic diffusion occurs in the direction of the vessel. The strength of the vessel-likeliness response is determined by separate parameters of the VED (the diffusion strength, anisotropy and diffusion time; for details see Ref. 15). After the data set has been ‘‘smoothed’’ in this fashion, the vesselness filter is applied again to determine the new vessel-likeliness and the process is repeated a number of times. Five iterations seem to be sufficient for a good performance of the method.

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AUTOMATIC VEIN SEGMENTATION AND LESION DETECTION: FROM SWI-MIPs TO MR VENOGRAMS

MR Venography Figure 32.1 shows MR venograms of the whole brain at 3 T (both vesselness filter results as well as VED results are shown). Note the detailed depiction of the connected venous structures by using the vesselness filter. The advantage of using a diffusion filter in addition

FIGURE 32.1

Whole brain MR venograms acquired at 3 T using the vesselness filter (first column) and five iterations of the vessel enhancing diffusion (VED) filter (second column). The first three rows show whole brain MIPs over sagittal, coronal, and transverse orientations. The last row shows a MIP limited to the midline to better visualize the major midline veins. Note the detailed depiction of the connected venous structures by using the vesselness filter (first column). The VED filter (second column) improves results by getting rid of false positives (typically noise) and restoring suppressed connections. Therefore, the images on the right tend to appear less cluttered and show the vessels more clearly.

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to a vesselness filter is that it gets rid of false positives (typically noise) and that it restores suppressed connections, where thresholding after application of the vesselness filter is too rigid [17]. A detailed analysis of noise suppression using the different filters compared to the gold standard of manual segmentation has been performed in Ref. 17 and clearly shows the superior performance when using VED filtering. Note that a brain mask is applied to all the final images. This is necessary because the skull, the sagittal sinus, and other surrounding structures/tissue would compromise the projection images. Another reason is that the vesselness filter seems to have problems to fully suppress the sharp boundary at the pial surface, an observation previously reported in Ref. 18 as well. It is shown in Ref. 16 that the results obtained from the VED method are comparable to manual segmentation results. This allows for segmentation of veins in a whole brain data set where laborious manual segmentation is highly undesirable. STATISTICAL MODELS Statistical methods have been used extensively in the similar problem of segmenting bright arteries from MRA images. They are easy to implement and efficient to run making them a widely used technique. Wilson and Noble first proposed a statistical model for segmenting blood vessels from time of flight (TOF) MRA data [19]. They proposed a statistical mixture model to describe the signals from background tissue and blood vessels, recursively calculating this for smaller volumes to get more accurate localized information. This does a good job on larger vessels but is insufficient in the small distal arteries. Hassouna et al. proposed segmenting TOF image using a stochastic model, modeling the background and vessels as a combination of one Rayleigh distribution and three Gaussian distributions. After the statistical thresholding, a Markov random field (MRF) is used to improve the quality of the segmentation [20]. This can restore areas of signal loss, but has a tendency to destroy small vessels. These methods seek to model the signal distributions as accurately as possible and then set a threshold for the volume or local subvolume, below which everything is classified as background and above which everything is classified as vessel. The advantage of this is that the algorithms are fast, intuitive, and easy to use; results can be automatically generated and then filtered to improve results. Similar methods can be used to segment SWI venography data by modeling the background signal and then looking for low statistical outliers rather than high outliers. This is complicated somewhat by the presence of a large number of dark structures (skull and background) that must first be removed before any relevant analysis can be done. Statistical methods thus have three steps: brain extraction to mask out the background and identify the region of interest, statistical thresholding to identify the vessels, and filtering to remove false positives and improve results. The following outlines how standard thresholding techniques can be successfully applied to segment both veins and lesions from SWI data, and how they can be separated using a support vector machine classifier. Figures 32.2– 32.6 demonstrate this technique on a 7 T SWI acquisition with TR ¼ 45 ms, TE ¼ 16 ms, FA ¼ 25 , and resolution ¼ 0.21  0.21  1 mm3. Brain Extraction Brain extraction can be accomplished by thresholding based on the magnitude and phase data. Regions of no signal can be identified by low intensities in the magnitude image and having uniform distribution over all values in the phase image. By using both the magnitude

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AUTOMATIC VEIN SEGMENTATION AND LESION DETECTION: FROM SWI-MIPs TO MR VENOGRAMS

FIGURE 32.2 A simple global threshold can often be used as a means to visualize the major veins. An example of the data produced by this process overlaid on the original mIP is shown here. This can be used as the first step in the more complicated segmentation using statistical local thresholding. Image acquired at 7 T with 0.21  0.21  1 mm3 resolution and mIP over 25 mm. Image quality and contrast may not be optimal due to conversion from color to grayscale display. Please see the color plates section for the original version of this figure.

and phase, the accuracy of the extraction is improved over using either of them independently [21]. A binary mask is created from both the magnitude and phase image and then combined to create a final binary mask. Isolated islands of points are removed and isolated holes in large regions are filled in to give more consistent results. For more details please see Ref. 21. Local Statistical Thresholding Local statistical thresholding looks at the mean and standard deviation of a local ROI; if the intensity of the voxel of interest is sufficiently below the mean, it is marked as a vein. This assumes that the background signal follows a Gaussian distribution and there are a small number of low-intensity vein values that do not significantly alter the mean or standard deviation of the region. To help ensure this assumption, an initial global thresholding is performed.

STATISTICAL MODELS

611

The global threshold intensity is set by the user to a safe value where only obvious vessels (usually the large ones) are marked (Figure 32.2). This step marks the large dark structures that could skew the mean and standard deviation values that are calculated in the local statistical thresholding. These voxels are marked as veins in the final results but are not used to calculate the local mean and standard deviation. Local thresholding is performed next (Figure 32.3). A small region of interest around a single voxel is considered. In this area, the mean and standard deviation are calculated excluding any points that have been previously marked as vessels. A local threshold is then calculated to be a certain number of standard deviations above the mean. If the voxel of interest is below this value it is marked as vessel. local voxelvessel < a  slocal þ x

ð32:5Þ

local voxelbackground  a  slocal þ x

ð32:6Þ

FIGURE 32.3 Statistical segmentation results before size and shape filtering to remove false positives. Notice many more small veins have been marked as veins by the statistical thresholding as compared with the global thresholding (Figure 32.2). Unfortunately, a significant amount of noise still remains marked as veins. Each color represents a cluster of connected voxels. Image quality and contrast may not be optimal due to conversion from color to grayscale display. Please see the color plates section for the original version of this figure.

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AUTOMATIC VEIN SEGMENTATION AND LESION DETECTION: FROM SWI-MIPs TO MR VENOGRAMS

where a is a user adjustable factor that can be set based on the data set, generally a ¼ 2.5 gives good results for most data sets. The area of interest is then moved and the process is repeated until the entire image has been processed. Practically, calculating a new threshold for every single voxel proved too computationally expensive, so a single threshold is applied to the center group of 5  5  3 voxels. This provided a decrease in computation time by a factor of 75 with little effect on the end results. In this calculation, it is assumed that the mean and standard deviation are dominated by background voxels that have roughly a normal distribution. Certain restrictions are placed on this calculation to help ensure this. First, the initial global threshold is performed to exclude large dark structures. Second, the local thresholding is iterated. Each time the local thresholding is preformed more points are marked as vessels that are then excluded from the mean and standard deviation calculation on the next iteration. Each successive mean and standard deviation calculation therefore includes fewer vessel voxels, so a more accurate threshold is obtained. This improves the identification of small vessels that lie near larger vessels and helps identify edge voxels. The size of the region used to calculate the mean and standard deviation can also be adjusted to help improve this assumption. A smaller region gives more localized results but runs the risk of having its mean dominated by a large vessel in the area. A larger region is less likely to have its mean skewed by a large vessel but is also less sensitive to local information. A balance must be struck between the two. The problem of large vessels is mostly alleviated by the global threshold, so a relatively small area of 40  40  5 pixels was chosen. Filtering Filtering the results from the previous step can significantly improve the segmentation as many false positives can easily be removed based on their size and shape. First, all marked voxels are sorted into connected clusters. Clusters below a certain size (set by the user) are removed. This is to remove isolated noise points that were included. Next, the connected clusters are evaluated based on shape. The shape of the vessels should be long and skinny, while noise is probably more spherical. Two shape factors are calculated to determine this, relative anisotropy (RA) and compactness. rffiffiffi 1 RA ¼  2

qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi ðabÞ2 þ ðbcÞ2 þ ðcaÞ2 aþbþc

ð32:7Þ

where a, b, and c are the eigenvalues of the covariance matrix of the cluster, a being the largest and c being the smallest. RA is a measure of how anisotropic a shape is, or how nonspherical it is; vessels should have a high RA value. Compactness is approximately a ratio of surface area to volume [22]; noise clusters being roughly spherical have a high compactness, while vessels have a very low compactness. These two measures can be effectively used by the user to filter out the majority of noise points leaving just segmented vessels (Figures 32.4–32.6). These shape factors are assumed to apply to small clusters of points. Large connected vessel structures are too complicated to be analyzed by these simple parameters. There are usually only a small number of separate large vessel structures so these can easily be manually marked as true vessels. The automated shape filtering needs only to be applied to the large number of small noise and vessel clusters.

AUTOMATIC MICROHEMORRHAGE AND LESION DETECTION

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FIGURE 32.4 Noise voxels that are removed by a specific choice of size and shape filter parameters. The level of the filter is manually adjusted and then specific objects can be added or removed as desired. These parameters are manually adjusted to achieve the desired level of noise reduction without significantly removing major vessels. In the future, this manual process could be replaced with a machine learning classifier as discussed in the next section.

VISUALIZATION Once the vessels have been accurately segmented they can be surface rendered. Surface rendering allows a complete 3D picture of the vessels with no loss of information if the segmentation was accurately performed. Surface rendering is a very fast technique with modern 3D graphics cards; this allows the user to easily change the orientation and interact with the data set. This interaction is very important to completely understand the 3D geometry of the vessels. There are many tools that can perform surface rendering. The surface rendered images (Figure 32.7, far right) were generated using the C þþ visualization tool kit (VTK) library. AUTOMATIC MICROHEMORRHAGE AND LESION DETECTION Segmentation algorithms designed to identify dark structures will inherently mark veins, hemorrhage, and some noise. To differentiate these structures, relevant features must be

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AUTOMATIC VEIN SEGMENTATION AND LESION DETECTION: FROM SWI-MIPs TO MR VENOGRAMS

FIGURE 32.5 Final segmentation results displayed on the mIP along with the original mIP for comparison. Notice the noise points have been largely removed, and nearly all of the veins (even very small veins) have been marked. This final result can be used for quantification of total venous blood volume, for histogram analysis or vessel size, or 3D volume rendering of the veins. Image quality and contrast may not be optimal due to conversion from color to grayscale display. Please see the color plates section for the original version of this figure.

FIGURE 32.6 Final segmentation results shown for a single slice. The small veins are well marked with only a few being missed. The large number of very small veins identified by this semiautomated process is far more practical than manual segmentation. Image quality and contrast may not be optimal due to conversion from color to grayscale display. Please see the color plates section for the original version of this figure.

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FIGURE 32.7 Original mIP (a), segmentation results overlaid on mIP (b), and surface rendered image of the segmented vessels (c). Surface rendering is very fast allowing the user to easily adjust the orientation of the image and fully understand the 3D geometry. Image quality and contrast may not be optimal due to conversion from color to grayscale display. Please see the color plates section for the original version of this figure.

identified that are unique to that class. The same tools described above that are used to examine the local structure and identify veins can be used to exclude the veins in an attempt to identify microhemorrhages. Relevant features depend on the type of data set. For microhemorrhages seen in aging patients, both compactness and RA of the covariance matrix work well as the hemorrhages are usually spherical. Mean and standard deviation of magnitude and phase signals also appear to help in the classification. These features allow a subset of possible microhemorrhages to be automatically generated that can then be sorted manually to identify the true microhemorrhages (Figures 32.8 and 32.9). Other types of lesions will probably be more challenging to identify, such as shearing hemorrhage caused by trauma, as the structure and shape of these lesions are less spherical and more structured and hence easily misinterpreted as veins. To separate microhemorrhages from veins and other noise based on a number of features, a supervised learning classifier can be used. In fact, this becomes almost necessary as the number of features is increased past two. For higher numbers of features, it becomes increasingly difficult to visualize the feature space and manually identify a way to divide the data. One such classifier that can be used is a support vector machine (SVM). A SVM classifier is a maximum margin classifier that constructs a separating hyperplane in a higher dimensional transformed space. While the hyperplane is a linear classifier in the transformed space when it is mapped back to the original feature space, it becomes nonlinear resulting in a nonlinear classifier. The SVM is trained on data that have been classified using another method that serves as a ground truth. Once it has been trained, it can rapidly classify novel data sets whose classification is unknown.

616

AUTOMATIC VEIN SEGMENTATION AND LESION DETECTION: FROM SWI-MIPs TO MR VENOGRAMS

FIGURE 32.8 A plot of features that can be used to identify microhemorrhage structures. The black triangles show all marked structures as generated by a statistical thresholding algorithm, the circles are the structures that correspond to actual microhemorrhages as determined by manual inspection of the data set. Using these features, it is possible to obtain a subset of a few hundred suspected microhemorrhages that can be quickly reviewed manually.

Good results have been obtained identifying microhemorrhages on aging subjects using 13 features: relative anisotropy of the covariance matrix, compactness, three eigenvalues from the covariance matrix, size, mean, standard deviation, and minimum and maximum of both the SW and phase data. Data sets that had been manually counted to obtain a ground

FIGURE 32.9 (a) MIP over 26 mm of SWI data. (b) Manually marked true microbleeds identified using magnitude, phase, SW, and mIP images. (c) Automatically marked suspected bleeds (80.9% sensitivity, 5–30% specificity). These would be treated as a candidate set of suspected microbleeds and manually reviewed to increase the specificity. The two that were missed here (bottom left, shown in blue in part (b)) were merged with the vein they lie adjacent to causing them to have more vein-like features. Image quality and contrast may not be optimal due to conversion from color to grayscale display. Please see the color plates section for the original version of this figure.

REFERENCES

617

truth were used to train the SVM classifier. Once the classifier had been trained, it was applied to novel data sets that had not been part of the training. As can be seen from Figure 32.9, most real hemorrhages were identified by the classifier along with some false positives. The two real hemorrhages that were missed in this image (bottom left, blue in part (b)) were merged with the vein that they are adjacent to in the thresholding step. This causes their features to be more vein-like and so they were misclassified. This is the dominant cause of false negatives. An added step to separate merged structures before classification could increase the sensitivity significantly. One proposed solution is to perform an erosion operation to split apart separate structures. They could then be expanded back to their original size by a dilation operation but not merged back together as a single object. The result from the classifier is a list of suspected microhemorrhages. This list is then reviewed manually to remove the false positives and keep the true microhemorrhages. From training and testing on six data sets, a sensitivity and specificity of 80.9% and 5–30% were achieved, respectively. But by allowing the manual removal of false positives, the specificity is increased to be equivalent to the gold standard for a sensitivity and specificity of 80.9% and 100%, respectively. The advantage this technique has over manually finding all microhemorrhages (which is taken here as the gold standard) or manually finding and adding missed microhemorrhages to increase the sensitivity is time savings. Removing false positives manually can be done very rapidly when presented with a finite list to make a yes or no decision. The entire list (an average of 118 false positives per scan) can be reviewed easily in less than 30 min. In addition to the time savings, a large advantage of automated methods in general is consistency. Manually counting can suffer from large inter- and intraobserver inconsistencies. The automated technique is completely reproducible and the manual removal of false positives is much more consistent as there is a small set of chosen microbleeds. So while the automated method currently shows an 80% sensitivity compared to manual counting, the consistency issues that plague manual counting could arguably make the automated method just as reliable an indicator of the true hemorrhage load. This is an active area of research that continues to develop rapidly as clinicians seek tools to quantify the number and volume of lesions and hemorrhage. While good results have been shown for microhemorrhages, work remains to be done to generalize this technique for other types of lesions, such as those caused by trauma.

REFERENCES 1. Suri JS, Liu K, Reden L, Laxminarayan S. A review on MR vascular image processing algorithms: acquisition and prefiltering: part I. IEEE Trans. Inf. Technol. Biomed. 2002;6(4):324–337. 2. Suri JS, Liu K, Reden L, Laxminarayan S. A review on MR vascular image processing: skeleton versus nonskeleton approaches: part II. IEEE Trans. Inf. Technol. Biomed. 2002;6 (4):338–350. 3. Sato Y, Nakajima S, Shiraga N, Atsumi H, Yoshida S, Koller T, Gerig G, Kikinis R. Threedimensional multi-scale line filter for segmentation and visualization of curvilinear structures in medical images. Med. Image Anal. 1998;2(2):143–168. 4. Frangi AF, Niessen WJ, Vincken KL, Viergever MA. Multiscale vessel enhancement filtering. Medical Image Computing and Computer-Assisted Intervention, MICCAI’98, Vol. 1496,1998, pp. 130–137.

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5. Koller T, Gerig G, Szekely G, Dettwiler D. Multiscale detection of curvilinear structures in 2-D and 3-D image data. In: Computer Vision, IEEE International Conference on Fifth International Conference on Computer Vision (ICCV’95), IEEE Computer Society, 1995, p. 864. 6. Krissian K, Malandain G, Ayache N, Vaillant R, Trousset Y. Model-based detection of tubular structures in 3D images. Comput. Vis. Image Understanding 2000;80(2):130–171. 7. Lorenz C, Carlsen I, Buzug T, Fassnacht C, Weese J. Multi-Scale Line Segmentation with Automatic Estimation of Width, Contrast and Tangential Direction in 2D and 3D Medical Images, CVRMed-MRCAS’97, 1997, pp. 233–242. 8. Perona P, Malik J. Scale-space and edge-detection using anisotropic diffusion. IEEE Trans. Pattern Anal. Mach. Intell. 1990;12(7):629–639. 9. Can˜ero C, Radeva P. Vesselness enhancement diffusion. Pattern Recognit. Lett. 2003;24 (16):3141–3151. 10. Krissian K. Flux-based anisotropic diffusion applied to enhancement of 3-D angiogram. IEEE Trans. Med. Imaging 2002;21(11):1440–1442. 11. Manniesing R, Viergever MA, Niessen WJ. Vessel enhancing diffusion: a scale space representation of vessel structures. Med. Image Anal. 2006;10(6):815–825. 12. Du YP, Parker DL, Davis WL. Vessel enhancement filtering in three-dimensional MR angiography. J. Magn. Reson. Imaging 1995;5(3):353–359. 13. Weickert J. A review of nonlinear diffusion filtering. In: ter Haar Romeny B, Florack L, Koenderink J, Viergever M, editors. Scale-Space Theory in Computer Vision, Lecture Notes in Computer Science, Vol. 1252, Springer, Berlin, 1997, pp. 3–28. 14. Frangi AF, Niessen WJ, Vincken KL, Viergever MA. Multiscale vessel enhancement filtering. In: Wells WM, III, Colchester ACF, Delp S, editors. Lecture Notes in Computer Science, Springer, 1998, pp. 130–137. 15. Manniesing R, Viergever MA, Niessen WJ. Vessel enhancing diffusion—a scale space representation of vessel structures. Med. Image Anal. 2006;10(6):815–825. 16. Koopmans PJ, Manniesing R, Niessen WJ, Viergever MA, Barth M. MR venography of the human brain using susceptibility weighted imaging at very high field strength. MAGMA 2008;21 (1–2):149–158. 17. Koopmans PJ, Manniesing R, Norris DG, Viergever M, Niessen WJ, Barth M. Vein Segmentation from 3D High Resolution MR Venograms by Using Vessel Enhancing Diffusion. European Society for Magnetic Resonance in Medicine and Biology, Warsaw, 2006, p. 361. 18. Deistung A, Kocinski M, Szczypinski P, Materka A, Reichenbach JR. Segmentation of venous vessels using multi-scale vessel enhancement filtering in susceptibility weighted imaging. Proceedings of the ISMRM, ISMRM, Seattle, 2006, p. 1948. 19. Wilson DL, Noble JA. An adaptive segmentation algorithm for time-of-flight MRA data. IEEE Trans. Med. Imaging 1999;18(10):938–945. 20. Hassouna MS, Farag AA, Hushek S, Moriarty T. Cerebrovascular segmentation from TOF using stochastic models. Med. Image Anal. 2006;10(1):2–18. 21. Pandian DS, Ciulla C, Haacke EM, Jiang J, Ayaz M. Complex threshold method for identifying pixels that contain predominantly noise in magnetic resonance images. J. Magn. Reson. Imaging 2008;28(3):727–735. 22. Bribiesca E. A measure of compactness for 3D shapes. Comput. Math. Appl. 2000; (40):1275–1284.

33 Rapid Acquisition Methods Song Lai, Yingbiao Xu and E. Mark Haacke

This chapter discusses the application of segmented echo planar imaging (SEPI) and parallel imaging techniques for improving the acquisition speed of SWI. We first describe the development of SEPI-based SWI, then the application of parallel imaging in SWI.

INTRODUCTION Multishot or interleaved segmented echo planar imaging offers higher resolution and better off-resonance behavior compared with single-shot EPI. Since the inception of EPI in 1977 [1] and that of SEPI in 1986 [2], the main challenges have been to remove offresonance effects from background field effects and to correct for nonideal sampling. Improved gradients and calibration techniques along with the echo time shifting (ETS) technique [3] effectively eliminate ghosting or blurring caused by the phase discontinuity between segments. However, the distortion caused by off-resonance phase errors in the phase encoding direction remains fairly large. There are even special applications in magnetic resonance angiography [4] and [5] and susceptibility weighted imaging (SWI) [6] when only even or odd echoes are sampled to maintain special flow properties, such as motion compensation. With increased interecho spacing, distortion also increases. Field mapping methods [7–9] can effectively reduce image distortion originating from offresonance effects such as B0 field inhomogeneity and chemical shift. The field map is usually derived from phase information obtained from either double-echo gradient echo images or offset spin echo images. However, the phase residual derived from different echo times has to be unwrapped to get the field inhomogeneity map [10]. Using multiple reference scans [11] and multi-echo gradient echo imaging [12] makes it possible to reduce B0 field inhomogeneity effects more accurately by eliminating eddy current effects. Chen and Wyrwicz [13] further developed a phase-shifted EPI pulse sequence that takes into

Susceptibility Weighted Imaging in MRI, By E. Mark Haacke and J€urgen R. Reichenbach Copyright
2011 by Wiley-Blackwell

619

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RAPID ACQUISITION METHODS

account all off-resonance effects, including gradient waveform imperfections, and their method does not require phase unwrapping. Finally, there are brute force approaches using the generalized inverse transform to perform off-resonance correction and attempts to speed these up by using fast conjugate phase reconstruction algorithms [14, 15]. In this study, we looked into one special case where only even or odd echoes are sampled and used a centerout k-space trajectory, instead of the conventional sequential bottom-up k-space trajectory, for SEPI. The technique is useful for SWI where a bright arterial signal is desired. The approach we take can account for phase variations between echoes caused by arbitrary moderate two-dimensional (2D) spatial field inhomogeneities. Although we focus on the use of phase from the central part of k-space, the method works even better when an accurate high-resolution phase image is available. Given the rapid scanning possible today, it is not excessive to imagine having the full phase information for use in future applications.

THEORY It is well known that the off-resonance artifact mainly manifests itself as distortion when cartesian k-space trajectories are used [14]. In this study, we ignored the phase error term related to the readout direction because the bandwidths used are usually very large [8, 12]. The segmented data collection scheme is shown in Figure 33.1. Only the even echoes are sampled. In our approach, the center of k-space is sampled first. Ignoring the relaxation effects, the sampled k-space data, s(mDkx, nDky, lDT), with the matrix size, Nx
Ny, can be

RF Gs Gs

Gr

0

1

2

3

4

Gp

ADC

FIGURE 33.1 Sketch of the proposed sequence diagram with a turbo speed factor of 4. Only the even echoes in the echo train are sampled (this represents what is often referred to as a flyback method). The top half of k-space is covered with the phase encoding table and phase encoding blips as shown (continuous lines), while the lower half of k-space is covered by inverting the polarity of the phase encoding table and phase encoding blips (dashed lines). Notice that data acquired at the 0th echo are for calibration purposes; hence, there is no phase encoding blip between echo 0 and echo 1. No ETS is applied to the acquisition.

THEORY

621

represented as (for a left-handed system)
 s mDkx ; nDky ; lDT ¼

ðð


 rðx; yÞ
expðimDkx xÞ
exp inDky y


expðifðx; y; lDT ÞÞ dxdy; Nx =2  m < Nx =2; Ny =2  n < Ny =2

ð33:1Þ

where r(x, y) is the spin density of the scanned object, DT is the interecho time interval (i.e., the time duration between two consecutive even echoes), and l is the echo index on the echo train (see Figure 33.1) (l is implicitly a function of n). In equation (33.1), l starts from 1 because the data sampled on the first echo (0th echo on the echo train) are not used to fill kspace (see Figure 33.2). In addition, l corresponds to the region number labeled in Figure 33.2 and w(x, y, lDT) is the phase error. This phase term originates from offresonance effects and is related to the phase evolution in the phase encoding direction as follows: wðx; y; lDTÞ ¼ iv0 ðx; yÞðlDT þ TEð0ÞÞ

(a)

ky

(b) ky

ð33:2Þ

32, 2, 1, 32, 2, 1, 32, 2, 1, 32, 2, 1, 1, 2,

kx

4 3 2 1 1′

32, 1, 2,

2′

32, 1, 2,

3′

32, 1, 2,

4′

kx

32,

FIGURE 33.2

(a) Sketch of the 2D k-space trajectory with a turbo speed factor of 4. The top half of kspace (continuous lines) is covered by 32-shot interleaved SEPI (assuming 256 k-space lines in total). Each k-space line is labeled as kj, with k as the shot number and j as the order on each interleave. Notice the center-out k-space trajectory. Thirty-two other shots are used to cover the lower half of k-space (dashed lines), with each line labeled as k0j . (b) Sketch of the 2D k-space coverage by region. Each shaded region represents that part of k-space acquired at the same echo time. The number in each shaded region corresponds to the echo number in the echo train (Figure 33.1). Each region contains 32 phase encoding lines.

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RAPID ACQUISITION METHODS

where v0(x, y) ¼ gDB(x, y) is representative of the local field inhomogeneity and TE(0) is the echo time of the first echo in the echo train. A formal means to compensate for the phase accrual due to local field inhomogeneities is to multiply each sampling point in k-space by the phase conjugate of the inhomogeneity accrued: r^ðx; yÞ ¼

XX
 S mDkx ; nDky ; lDT
expðimDkx xÞ m

ð33:3Þ

n



exp inDky y
expðifðx; y; lDT ÞÞ The difficulty in straightforward implementation of this method is that a Fourier transform of the corrected data must be applied for each (x, y) point. This is tantamount to having performed a generalized inverse transform in terms of the processing it would take to reconstruct the entire object. The main objective of this work was to show that this problem can be solved easily and quickly with a unique iterative Fourier transform approach between k-space and the imaging domain.

MATERIALS AND METHODS Sequence Design Figure 33.1 shows a sketch of the proposed 2D sequence diagram with a turbo speed factor of 4 (64-shot interleaved EPI to cover 256 k-space lines). Again, only the even echoes are sampled. The 0th echo is for calibration purposes only, and the first two echoes sample the same central k-space. The phase map derived from the first two echoes can be applied directly to later echoes without phase unwrapping. With high resolution (say, 256 or more k-space lines), the central k-space region (both regions 1 and 10 ) is practically large enough to give a good estimate of the phase map. The phase evolution w(x, y) between the first and second echoes is a linear function of v0(x, y) and echo spacing DT: wðx; yÞ ¼ v0 ðx; yÞDT

ð33:4Þ

This phase continues to evolve from echo to echo with the same functional form. Figure 33.2 shows a representative sketch of 2D k-space collected with a 64-shot interleaved SEPI sequence with a center-out trajectory. It takes the first 32 shots to cover the lower half of k-space and then another 32 shots to cover the upper half of k-space. The key observation here is that with the center-out k-space trajectory (and interleaving the data without an echo time shift), the k-space data can be separated into regions in which the data are acquired at the same echo time (Figure 33.2b) and, therefore, have the same phase evolution pattern. Regions in k-space are labeled with the corresponding echo number with which echo the data are acquired. Iterative Reconstruction Approach The main idea in this work was to take the data and merge them in a way that all data points have experienced effectively the same phase evolution—that is, they act as if they were all collected at the same echo time. We do this by starting with the central part of k-space and

MATERIALS AND METHODS

623

modifying its phase and then going through an iterative approach as described below to absorb all the different k-space regions collected. Let L be the largest region index; we then multiply both sides of equation (33.3) by exp(iv0(x, y)LDT): r^ðx; yÞexpðiv0 ðx; yÞLDT Þ ¼

XX
 S mDkx ; nDky ; lDT expðimDkx xÞ m n

exp inDky y
expðiv0 ðx; yÞðLl ÞDT Þ

ð33:5Þ

Equation (33.5) now serves as a guide in defining the iterative procedure. To correct from the center of k-space outward, first replace all data points in k-space in regions other than 1 and 10 with zero. Then, Fourier transform the zero-filled k-space to the image domain to get a complex image r(x, y). Next, multiply r(x, y) with exp(iw(x, y)) to get r0 (x, y). Then, Fourier transform r0 (x, y) back to k-space and replace the data points in regions 2 and 20 with the original data points. These new k-space data are in theory the same as those that would have been acquired if all the data in all regions (1, 10 , 2, and 20 ) had been collected at the third echo (i.e., the data points in regions 1 and 10 appear as if they had been collected at the same time as those in regions 2 and 20 ). Theoretically, there will be no phase discontinuity among regions 1, 10 and 2, 20 at this point. The next step is to let region 20 m represent the merged k-space of all regions (1, 10 , 2, and 20 ). The same procedure can now be applied to phase correct region 20 m to eliminate the effect of the phase evolution between echo three and echo four and create a new k-space that appears as if it was collected at the fourth echo. This method is continued one more time to correct for the phase evolution to the fifth echo. The final image will now appear to have been acquired (at least as far as phase effects are concerned) at effectively one echo time, the final echo time. The proposed iterative reconstruction approach is also illustrated in the flowchart in Figure 33.3. Simulation For the SEPI, the currently accepted technique for reducing ghosting is the ETS method [3]. ETS effectively reduces the k-space discontinuities between k-space lines. The ETS method helps reduce imaging artifacts such as ghosting, blurring, and Gibbs ringing, but image distortion still remains. Combining the center-out k-space trajectory and ETS not only doubles image distortion compared with the bottom-up k-space trajectory but also adds additional distortion in the opposite direction. Figure 33.4 shows the distortion artifacts related to the center-out k-space trajectory and ETS with both phantom simulation and an in vivo acquisition. Figure 33.4b and d shows simulated SEP images with ETS and the centerout k-space trajectory, respectively. The resolution phantom (Figure 33.4b) indicates that ETS is not a suitable method for center-out k-space trajectory approach since the doubledirection distortion makes a mess of smaller structures. Both the oil/water phantom (Figure 33.4d) and the in vivo image (Figure 33.4e) show a large fat shift in both directions. Obviously, the overlay of shifted fat signal on the brain parenchyma (pointed by white arrows) creates bad artifacts. How well does the proposed method fare under different conditions such as a smoothly varying field like the resolution phantom or sharp field changes like the water/oil phantom? We simulated images using k-space data sets acquired with a multi-echo gradient echo sequence. The multi-echo sequence has fixed echo spacing such that we could reassemble k-space from a set of k-space lines coming from different echo times as if the reassembled

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RAPID ACQUISITION METHODS

First compute φ (x, y) using central k-space data acquired at the second and the first echo. Initiate count l = 1, L = 4

Zero-filled k-space for all regions larger than l FT ρ (x, y) Phase correction ρ '(x, y) = ρ (x, y) exp (iφ (x, y)) IFT S'(k x, k y)

Set l = l + 1, and replace with original data for entire region l

No l = L? FT ρ (x, y)

FIGURE 33.3

Schematic flowchart of the iterative reconstruction method.

k-space had been acquired with the proposed SEPI sequence with a center-out k-space trajectory. We refer to this ability to create various k-space trajectories from a complete set of multi-echo data as our ‘‘k-space playground.’’ Figures 33.5 and 33.6 demonstrate that when the field is varying smoothly such that the phase map from the central k-space represents the phase reasonably well, the proposed geometric distortion-corrected (GDC) SEPI method works superbly. Measured profiles (Figure 33.5) indicate that the biggest residuals are actually still within the noise level. Figure 33.6 shows dramatically reduced coherent ringing as well. In the case of rapid field changes such as those shown in Figure 33.7, central k-space is not large enough to give a good estimation of the field at the boundary of the oil and water (Figure 33.7c). Poor estimation of the phase results in signal loss at the boundaries

MATERIALS AND METHODS

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FIGURE 33.4 (a) Gradient echo phantom image as a reference. (b) Simulated SEP image with ETS and center-out k-space trajectory. Note the duplication of the circles into two components. (c) Gradient echo oil/water phantom as a reference. (d) Simulated SEP image with ETS and center-out k-space trajectory. Note the duplication of the oil into two components. (e) In vivo brain image with ETS and centerout k-space trajectory. Note the splitting of the fat into two components each shifting in opposite directions (white arrows in part (e)).

FIGURE 33.5 (a) Gradient echo image as a reference. (b) Simulated image without proposed iterative phase correction. (c) Corrected GDC-SEP image. (d) Residual image between parts (a) and (c). (e) Measured profiles across the pixels along the gray line in part (c). Note that the gray line is across the visible coherent ringings between two resolution bars, which also happens to be close to the highest residual error. The measured profiles indicate that the biggest residual is still within the noise level.

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RAPID ACQUISITION METHODS

FIGURE 33.6

(a) Reference gradient echo image. (b) GDC-SEP image after phase correction. (c) Residual image between parts (a) and (b). (d) Image (b) before phase correction. Note the dramatically reduced coherent ringing after phase correction.

(Figure 33.7f). If we use the whole k-space to estimate the phase (Figure 33.7d), then the signal lost gets recovered (Figure 33.7e). However, both parts (e) and (f) have the same ringing artifacts (caused by the T2* difference between oil and water). Accounting for phase variations from echo to echo does not correct the artifacts related to discontinuities in kspace caused by T2* decay. Furthermore, Figure 33.7a shows a simulated SEP image showing a major fat shift along the phase encoding direction. Compared with Figure 33.7a, the fat signal in Figure 33.7d and that in Figure 33.7e do not shift relative to the reference image. This demonstrates that the proposed method is accomplishing its goal of removing geometric distortion. Image Acquisition Parameters Both phantom and in vivo data were acquired on a 1.5 T Siemens Sonata (Erlangen, Germany) system. The phantom data were acquired with the following parameters:

RESULTS

627

FIGURE 33.7 (a) SEP image. (b) Gradient echo image. (c) Phase image from central k-space. (d) Phase image from all of k-space. (e) GDC-SEP image using part (d) as a phase map. (f) GDC-SEP image using (c) as a phase map.

resolution, 0.5
1
2 mm3; 64 slices; number of echoes in the readout echo train, 5; echo spacing (DT) ¼ 8 ms; echo time of the first echo, 10 ms; and TR, 51 ms. The in vivo data were acquired with resolution ¼ 1
1
2 mm3, 64 slices, number of echoes in the readout echo train ¼ 5, echo spacing ¼ 7.5 ms, echo time of the first echo ¼ 22.5 ms, and TR ¼ 61 ms. The original raw data sets were downloaded to a PC for offline image reconstruction and the proposed phase correction. Improvement of SWI Acquisition Speed by Application of Parallel Imaging Parallel imaging was explored for speeding up data acquisition of SWI. Human brain data were acquired on a 3 T Philips scanner with an eight-channel head coil (Achieva, Philips Medical Systems, Best, The Netherlands). To compare and validate the use of various sequences using the sensitivity encoding (SENSE) technique [17] for SWI, multi-echo gradient echo images collected using a conventional 3D fast low angle shot (FLASH) sequence with flow compensation were used as reference images. In comparison were images acquired using the following pulse sequences: multi-echo 3D FLASH with SENSE and single-echo 3D SEPI with SENSE.

RESULTS Figure 33.8a is a phantom magnitude image reconstructed from the raw data acquired with the sequence shown in Figure 33.1 without any phase correction. The largest resolution

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FIGURE 33.8 (a) Magnitude image reconstructed without the proposed iterative phase correction. (b) Magnitude image reconstructed after the first iteration. (c) Magnitude image reconstructed after the second iteration. (d) Magnitude image reconstructed after the final (third) iteration of the phase correction. (e) Phase map estimated from the central k-space.

circle is reasonably well delineated with the central k-space region alone. The phase discontinuities between echoes cause severe artifacts, including distortion, ghosting, and blurring for the low-resolution circles. Figure 33.8b and c shows the intermediate results after the first and second iterations of the proposed phase correction, respectively. Figure 33.8d is the result after the final iteration of the phase correction. In Figure 33.8b–d, we see continued improvement of the image quality, although much of the improvement comes after the first iteration. Further effects refine the higher resolution components as expected, albeit only to the degree that the central phase correctly estimates the high-resolution phase behavior. After the full correction, geometric distortion, ghosting, and blurring are mostly gone, which indicates successful reduction of the effects of phase evolution between echoes. However, the correction is not perfect in the area of the smallest circles. There are residual ripples that are the result of missing high-frequency information in the phase map. There is also some remnant low spatial frequency Gibbs ringing present. Part of the motivation for this work was the need to obtain SW images that first could be acquired quickly at 1.5 T and second would appear to be flow compensated for arterial flow. To demonstrate that this is possible, we used the sequence shown in Figure 33.1 to acquire raw data in vivo for a neuroimaging example. For SWI, we need a longer echo time [4], so we began the sequence with the first echo time being 22.5 ms and echo spacing of 7.5 ms. With a turbo speed factor of 4 (64-shot EPI to cover 256 k-space lines), this sequence only took about 4 min to cover 64 slices (whole brain coverage) instead of the usual 16 min. Figure 33.9a shows a magnitude image reconstructed simply with the usual Fourier transform without any phase correction. Blurring is seen throughout the image especially where there is fat. Figure 33.9b shows a magnitude image reconstructed after the proposed phase correction. Figure 33.9b shows the improvement in the sharpness of the image. Two

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FIGURE 33.9

(a) Magnitude image of a human brain before the proposed phase correction. (b) Magnitude image reconstructed after the proposed phase correction. (c) Residual image between parts (a) and (b). (d) Same as part (c) showing only the signal change in the area of brain parenchyma. (e) Magnitude image acquired with a conventional SWI sequence. (f) Magnitude image acquired with a sequential sampled SEPI sequence. (g) Phase map estimated from the central k-space. Note the sharpened vessel and optic radiation (horizontal arrows in parts (a) and (b)). The vertical arrows point to the much improved magnitude image.

residual images (Figure 33.9c and d) between Figure 33.9a and b are displayed as well to show the improvement with the iterative phase correction technique. Figure 33.9c reveals that the dominant residual error is in the neighborhood of fat signal. Figure 33.9d shows only the area of brain parenchyma (the fat has been manually removed) in order to appreciate the improvement of fine structures in the brain. Figure 33.9e shows a magnitude image acquired with a conventional SWI sequence (with TE/TR ¼ 40/57 ms) (which took about 8 min to cover only 32 slices or half of the brain) and serves as a reference image here. For the conventional SW image, arterial and venous signals are naturally separated with the arterial signal being bright and the venous signal being dark. Figure 33.9f shows a magnitude image acquired with a Siemens SEPI sequence. Both arteries and veins appear dark in Figure 33.9f. This makes separating arteries and veins problematic. The center-out k-space acquisition used to acquire Figure 33.9b leads to bright arteries and dark veins as expected and produces contrast similar to that seen with conventional SWI. There does remain some vessel misregistration artifact caused by the fact that only the central part of k-space is flow compensated in the phase encoding direction. Figure 33.10 gives a comparison of SWI (in the form of minimum intensity projection or mIP images to highlight susceptibility effects, and all the images had 1 mm3 isotropic voxels) obtained with a conventional 3D FLASH sequence (TR ¼ 66 ms, TE ¼ 8, 14, 20, 26, 32, 38, and 44 ms, 75% partial-k, TA ¼ 60 5400 for 64 slices), a 3D FLASH with SENSE (with an acceleration factor of 3, TR ¼ 66 ms, TE ¼ 8, 14, 20, 26, 32, 38, and 44 ms, 75% partial-k, TA ¼ 60 2500 for 180 slices), and 3D SEPI with SENSE (with an acceleration factor of 3, TR ¼ 66 ms, 75% partial-k, TE/TA ¼ 8 ms/20 4700 , 14 ms/5400 , 20 ms/2300 , 26 ms/1500 ,

630

Comparison of minimum intensity projection (mIP) images by using different sequences on a normal human brain. The mIP images at each echo time was reconstructed from using 15 contiguous slices of 1 mm thickness. Upper panel: 3D FLASH (TR/a ¼ 66 ms/22 , TE ¼ 8, 14, 20, 26, 32, 38, and 44 ms, 75% partial-k, acquisition time ¼ 6 min 54 s, 64 slices); middle panel: 3D FLASH with SENSE (acceleration factor ¼ 3, TR/a ¼ 66 ms/22 , TE ¼ 8, 14, 20, 26, 32, 38, and 44 ms, 75% partial-k, acquisition time ¼ 6 min 24 s, 180 slices); lower panel: 3D SEPI (acceleration factor ¼ 3, TR/a ¼ 66 ms/22 (except for TE ¼ 32 ms), 180 slices). Acquisition time ¼ 2 min 47 s for TE ¼ 8 ms (EPI factor ¼ 3); acquisition time ¼ 54 s for TE ¼ 14 ms (EPI factor ¼ 9); acquisition time ¼ 23 s for TE ¼ 20 ms (EPI factor ¼ 17); acquisition time ¼ 15 s for TE ¼ 26 ms (EPI factor ¼ 23); acquisition time ¼ 16 s for TE ¼ 32 ms (EPI factor ¼ 29, TR/a ¼ 75 ms/30 ). The FLASH sequences (with or without SENSE) acquired seven echoes in each sequence, while the SEPI images (with SENSE) at different echo times were acquired for each echo time separately (the echo time quoted is that echo at the center of k-space). A gross mIP image, dubbed mega-mIP (rightmost column), of the mIP images at individual echo times was generated for each of the multi-echo FLASH sequences (with or without SENSE, i.e., upper and middle panels)

FIGURE 33.10

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FIGURE 33.10

(Continued)

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T*2

T*2 mapping using the multi-echo 3D FLASH with SENSE sequence. The evolution of the signals of two veins (arrowed) with echo time showed typical behavior. The images were on one slice of the same data set in Figure 33.10.

FIGURE 33.11

DISCUSSION

633

32 ms/1600 , corresponding EPI factor ¼ 3, 9, 17, 23, 29, respectively). The two FLASH sequences (with or without SENSE) collected seven echoes in each sequence, while the SEPI images (with SENSE) at different echo times were acquired using a single SEPI sequence (the echo time quoted is that echo at the center of k-space). The mIP images at each echo time were reconstructed from using 15 contiguous slices of 1 mm thickness. The conventional SWI that uses 3D FLASH sequence (upper panel) and 75% partial-k took nearly 7 min to cover 64 slices. Using SENSE with an acceleration factor of 3 (middle panel), similar acquisition time allowed for whole brain coverage (180 slices). Combination of SENSE with SEPI (lower panel) led to sub-minute data acquisition with whole brain coverage (180 slices). The two FLASH sequences (with or without SENSE) collected seven echoes in each sequence, while the SEPI images (with SENSE) at different echo times were acquired using a single SEPI sequence (one for each effective echo time). An advantage of multi-echo acquisition is that a gross mIP image, dubbed mega-mIP (rightmost column), of the mIP images at individual echo times could be generated, and this allows for more comprehensive depiction of the susceptibility effects, since the susceptibility contrast depends on the angle between the susceptibility interface with the B0 field, thus is a function of the echo time. Indeed, the mIPs at individual echoes highlighted different structures, and the mega-mIPs present the most comprehensive picture of susceptibility interfaces. Another advantage of multi-echo acquisition is the ability of mapping T2* . An example is given in Figure 33.11 where two veins examined showed typical T2* behavior. The images in Figure 33.11 were on one slice of the same data set as in Figure 33.10. The ability to use longer echo times with higher EPI factors makes this approach particularly useful for lower field strength scanners. Usually pffi speeding up data acquisition by a factor n leads to a reduced SNR by a factor of n. But that is not the case here for echo times up to roughly 60 ms at 1.5T since the signal loss depends on T2* decay not the bandwidth (at least when comparing sequences with the same bandwidth). In the examples presented here with the speed up factor of 4, we found that the SNR from the 4 minute SEPI SWI scan was about the same as that from the conventional 16 minute SWI scan with a single echo.

DISCUSSION The results shown here for the GDC corrected SEPI data represent an improvement in image quality and visualization of arteries compared with a sequential SEPI approach with ETS correction. The method is fast, requires no phase unwrapping and no extra reference scan, and should be easily implemented online. However, there is a trade-off between the turbo speed factor and the accuracy of the phase map. Practically, this approach becomes better and better as the matrix size increases and the number of shots remains the same. Along the same lines, if one could use an extra reference scan to get an accurate high-resolution phase map if time or motion between scans is not an issue, all shift effects would be ideally corrected. Furthermore, the use of higher resolution should improve the response for the smaller structures and fat signal, which was not possible with the current implementation of the central k-space approach (see Figure 33.9a and b). For example, for a 1024 acquisition, the central 256 points would be used to estimate phase and would be flow compensated as well, yielding even better recovered arterial signal. This is of particular value in methods such as SWI, where small veins and microbleeds are the major foci.

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For any high-resolution 3D imaging SWI method, a small voxel size requires a fairly low bandwidth to ensure enough signal to noise ratio. This implies that the turbo speed factor cannot be too high, for otherwise the duration of the echo train would be too long and T2* filtering will become a problem. Of course, as with any segmented approach, one assumes that the subject does not move between scans. However, using more modern techniques (e.g., propeller) may make segmented methods more viable in the future [16]. It is of interest to note that this method works very well on the sharp edges of the phantom, which is often very difficult for any reconstruction method to accomplish. Often, methods that do poorly on phantoms do reasonably well on human data. This gives us the confidence that it should be possible to fine-tune any remnant error in the human data from perhaps eddy current or other effects over time to make this approach clinically viable. Although we performed the iterative procedure from the central data outward, in principle, this process could also be done from the outermost k-space toward the center. In practice, we found that this approach was not as robust as the correction done from the center of k-space outward. The reason for this could be that the phase estimate from the center of k-space was not accurate enough to represent the high spatial frequency components well. The overall improvement of the clinically relevant images may not be as evident as that of the phantoms that have very sharp edges, but they are equally important. For example, Figure 33.9b has dramatically sharpened edges. This can be understood from the fact that the center of k-space already creates a reasonable (albeit blurred) lowresolution image itself. This GDC-SEPI method attempts to correct the local blurring (which is actually a form of ghosting or aliasing that manifests as only small shifts of several pixels and hence can equally be called blurring). This blurring is another form of geometric distortion in this case, where it is most evident both in the fat and at air–tissue interfaces, such as the edge of the brain. With the iterative correction, Figure 33.9b now has better definition of the internal structures, sharper edges and no remnant fat shift, and is much closer to the standard SW image compared with the sequential SEPI approach shown in Figure 33.9f.

CONCLUSIONS In summary, SEPI and parallel imaging can be applied to speed up data acquisition of SWI. For SEPI, we have introduced a new iterative phase correction method that makes it possible to collect and correct for full 2D phase evolution in interleaved SEPI. The method is capable of removing chemical shift and geometric distortion. If this proves to be robust in clinical situations, then the method would have major implications for high-resolution clinical applications of sequences such as SWI. We further demonstrated that parallel imaging can be utilized to speed up data acquisition of SWI. When parallel imaging is combined with SEPI, sub-minute SWI with full brain coverage can be achieved, which would greatly help to improve the clinical applicability of high resolution SWI.

REFERENCES 1. Mansfield P. Multi-planar image formation using NMR spin echoes, J. Phys. Chem. 1977;10: L5–L58.

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2. Haacke EM, Bearden FH, Clayton JR, Linga NR. Reduction of MR imaging time by the hybrid fast-scan technique., Radiology 1986;158:521–529. 3. Feinberg DA, Oshio K. Phase errors in multi-shot echo planar imaging, Magn. Reson. Med. 1994;32:535–539. 4. Luk Pat GT, Meyer CH, Pauly, JM, Nishimura DG. Reducing flow artifacts in echo-planar imaging, Magn. Reson. Med. 1997;37:436–447. 5. Beck G, Li, D, Haacke EM, Noll TG, Schad LR. Reducing oblique flow effects in interleaved EPI with a center reordering technique, Magn. Reson. Med. 2001;45:623–629. 6. Haacke EM, Xu Y, Cheng YN, Reichenbach JR. Susceptibility weighted imaging, Magn. Reson. Med. 2004;52:612–618. 7. Weisskoff RM, Davis TL. Correcting gross distortion on echo planar images. In: Proceeding of the SMRM 11th Annual Meeting Berlin, 1992, p. 4515. 8. Jezzard P, Bababan RS. Correction for geometric distortion in echo planar images from B0 field variations, Magn. Reson. Med. 1995;34:65–73. 9. Reber PJ, Wong EC, Buxton KB, Frank LR. Correction of off resonance-related distortion in echoplanar imaging using EPI-based field maps, Magn. Reson. Med. 1998;39:328–330. 10. Liang ZP. A model-based method for phase unwrapping, IEEE Trans. Med. Imaging 1996;15; 893–897. 11. Wan X, Gullberg GT, Parker DL, Zeng GL, Reduction of geometric and intensity distortions in echo-planar imaging using a multireference scan, Magn. Reson. Med. 1997;37:932–944. 12. Chen NK, Wyrwicz AM. Correction for EPI distortion using multi-echo gradient-echo imaging, Magn. Reson. Med. 1999;41:1206–1213. 13. Chen NK, Wyrwicz AM. Optimized distortion correction technique for echo planar imaging, Magn. Reson. Med. 2001;45:525–528. 14. Schomberg H. Off-resonance correction of MR images, IEEE Trans. Med. Imaging 1999;18:481–495. 15. Noll DC, Meyer CH, Pauly JM, Nishimura DG, Macovski A. A homogeneity correction method for magnetic resonance imaging with time-varying gradients, IEEE Trans. Med. Imaging 1991;10:629–637. 16. Pipe JG. Motion correction with PROPELLER MRI: application to head motion and freebreathing cardiac imaging, Magn. Reson. Med. 1999;42:963–969. 17. Pruessmann KP, Weiger M, Scheidegger MB, Boesiger P. SENSE: sensitivity encoding for fast MRI, Magn. Reson. Med. 1999;42:952–962.

34 High-Resolution Venographic BOLD MRI of Animal Brain at 9.4 T: Implications for BOLD fMRI Seong-Gi Kim and Sung-Hong Park

INTRODUCTION In vivo visualization of arterial and venous vascular structures is important for the assessment of vascular abnormalities as well as the determination of the vessel morphology during development and angiogenesis. Existing methods rely on time of flight, phase contrast, and dynamic contrast agent enhanced approaches; the first two noninvasive methods are sensitive to fast moving blood vessels, which are mostly large-sized vessels, while the last method is sensitive to arterial and venous vessels. Since arterial and venous vessels can be separated using dynamic properties of contrast agent passages through these vascular systems (i.e., the contrast agent travels from arterial to venous vessels), the contrast agent method is attractive. However, it is not easy to achieve high spatial resolution and high temporal resolution relative to a blood transit time (e.g., 2–3 s). Alternatively, venographic images can be obtained using the blood oxygenation level-dependent (BOLD) contrast [1, 2], where paramagnetic deoxyhemoglobin (dHb) serves as an intrinsic venous blood contrast agent. The first noninvasive visualization of venous blood vessels with the BOLD effect was performed on animal brains at high magnetic fields [1, 2]; hypointense signals were modulated by a change in oxygen concentration of inhaled gas, indicating that these pixels

Susceptibility Weighted Imaging in MRI, By E. Mark Haacke and J€urgen R. Reichenbach Copyright
2011 by Wiley-Blackwell

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were likely affected by the susceptibility effect of dHb. More recently, Haacke and his colleagues visualized detailed neurovasculature in humans using the BOLD contrast at the clinical field strength of 1.5 T [3]. The contrast between venous vessels and tissue can be significantly improved by using phase mask filtering, which relies on the phase difference between tissue and intravascular venous blood [3, 4]. However, the phase difference depends on various physiological and imaging parameters such as venous oxygenation level, angle between vessel orientation and main magnetic field, magnetic field strength, and echo time (TE). Thus, it is difficult to find a ‘‘single’’ optimal phase mask filtering scheme for all venous vessels. At field strengths
7 T, T2* of venous blood is much shorter than T2* of tissue. Thus, the contrast between tissue and venous blood can be improved at high field by setting TE sufficiently long relative to T2* of venous blood. In addition, longer TE values extend the blood susceptibility effect to greater distances in the surrounding tissue, resulting in the ‘‘apparent’’ larger vessel size [1, 2]; [5], which will increase their detectability. At this experimental condition, venous microvasculature may be detected in simple magnitude T2* -weighted images without phase mask filtering [6]. In this chapter, we obtained high-resolution T2* -weighted three-dimensional images from rat and cat brains at 9.4 T for visualization of pial and intracortical venous vasculatures. To obtain insights into detectability of venous vessels, we simulated signal intensity of a pixel containing one single vessel as a function of vessel diameter and oxygenation level. The efficacy of phase mask filtering was also evaluated. Signals of most commonly used BOLD fMRI originate from venous vessels and surrounding tissue; thus, its intrinsic spatial resolution is related to the distance between intracortical venous vessels. To examine the relationship between vascular architecture and BOLD fMRI foci, high-resolution BOLD fMRI was performed in rats during somatosensory stimulation and compared with BOLD venography.

THEORY AND COMPUTER SIMULATIONS T2* -weighted MRI signal in a given voxel at an echo time TE can be approximately described as a vector sum of signals from all subvoxels with index i, as follows X Sssi eTE=T2i eiv i TE ð34:1Þ S¼ i

where Sss is the steady-state signal intensity at TE ¼ 0, T2 is the transverse relaxation time, and v is the frequency shift relative to the tissue where the susceptibility effect does not contribute. Sss is described as Sss ¼ r 

1expðTR=T1 Þ  sinðaÞ 1cosðaÞ  expðTR=T1 Þ

ð34:2Þ

where r is the spin density, TR is the repetition time, T1 is the longitudinal relaxation time, and a is the flip angle. Since a blood vessel is relatively long compared to the diameter of the vessel, a cylinder model is applicable for determining frequency shifts induced by dHb [7–9]. The frequency shift inside (vin) and outside the blood vessel (vout) can be expressed by vin ¼ 2pDx0 ð1YÞv0 ðcos2 u1=3Þ

ð34:3Þ

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and vout ¼ 2pDx0 ð1YÞv0 ða=rÞ2 ðsin2 uÞðcos2 fÞ

ð34:4Þ

where Dx 0 is the maximum susceptibility difference between fully oxygenated and fully deoxygenated blood, Y is the fraction of oxygenation in venous blood, v0 is the frequency of applied magnetic field, u is the angle between the applied main magnetic field (B0) and vessel orientation, a is the radius of blood vessel, r is the distance from the point of interest to the center of the blood vessel, and f is the angle between r and the plane defined by B0 and the vessel axis. Assuming a hematocrit level of 0.4 and the susceptibility difference between 100% oxyhemoglobin and 100% dHb of 0.2 ppm [10], Dx 0 in whole blood is 0.08 ppm. To obtain insight into vessel detectability at 9.4 T as a function of local oxygen saturation level, computer simulations were performed based on the cylinder model of a single blood vessel perpendicular to both B0 and the imaging plane (u ¼ 90 ). To compute signal intensities using equation (34.1), a single pixel was divided equally to 10  10 subpixels (i ¼ 1–100). Since pixel intensity depends on the partial volume fraction of venous blood (which is related to the location and diameter of the venous vessel), two extreme conditions were chosen: the center of the vessel is located at the center of the pixel or at the corner of the pixel. Parameters for the simulation were T1 of tissue and venous blood ¼ 1.9 and 2.2 s, respectively [11]; tissue T2 ¼ 40 ms; venous T2 ¼ 4.0, 4.9, 6.4, 9.0, and 15.2 ms for oxygen saturation levels of 50, 60, 70, 80, and 90%, respectively [12]; spin density of tissue and venous blood ¼ 0.89 and 0.86, respectively [13]; TR ¼ 50 ms; and flip angle ¼ 13 . Two TE values of 10 and 20 ms were used for the two different vessel locations. Figure 34.1 shows

Center

1.0

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(a) (b)

(a)

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0.6 0.2

(b) (c)

TE = 10 ms

(e)

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0.7 0.1 0.3 Venous vessel diameter (pixel)

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FIGURE 34.1 MR signal intensities of a pixel containing a single venous vessel as a function of vessel diameter, vessel position, oxygen saturation, and TE. Simulations were performed at 9.4 T with the cylinder model with parameters obtained from literature (see text). Pixel intensity is lower at longer TE (bottom panel), at a lower oxygenation level (five different lines from 90% to 50% oxygenation level), and a larger vessel size. Also, the vessel position within a pixel can change signal intensity; the intensity is lowest when the vessel is located at the center of the pixel (left column), while the intensity is highest when the vessel is located at the corner of the pixel. Horizontal dotted lines show a potential intensity threshold for determining venous vessel candidates.

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the relative signal intensity of a pixel containing one single vessel as a function of vessel diameter at five different venous blood oxygenation levels. Longer echo time, larger vessel size, and lower oxygenation levels reduce the signal intensity further. When a venous vessel is concentric with a pixel, the signal intensity is the lowest due to the highest partial volume fraction of the vessel. When a pixel resolution is 100 mm and an intensity threshold of 0.8 is applied, detectability of venous pixels with an oxygenation level of 0.8 is 3652 mm diameter at TE ¼ 10 ms and 2541 mm at TE ¼ 20 ms. Similarly, when a venous oxygenation level is 0.6, vessel detectability is 24–40 mm diameter at TE ¼ 10 ms and 1830 mm at TE ¼ 20 ms. These simulation results indicate that small venules with diameters of 1525 mm are detectable when a pixel resolution is 78 mm. The intensity threshold of 0.8 was chosen based on the required minimal contrast to noise ratio (CNR) of 5 for discrimination of venous pixels [14], since the average signal to noise ratios (SNR) in cortical regions were >25 at TE ¼ 10 ms and 20 ms [15] (i.e., 25  0.2 ¼ 5). Magnitude Versus Phase Mask Filtered Venogram To examine whether magnitude T2* -weighted images have adequate contrast between venous vessels and surrounding tissue at 9.4 T, we performed venographic imaging studies of an isoflurane-anesthetized rat brain on a Varian 9.4 T/31 cm MRI system (Palo Alto, CA) with an actively shielded gradient coil with a 12 cm inner diameter, which operates at a maximum gradient strength of 400 mT/m and a rise time of 130 ms. A homebuilt quadrature radio frequency (RF) surface coil (inner diameter of each of two lobes ¼ 1.6 cm) was positioned on top of the animal’s head and provided RF excitation and reception. Detailed experimental design was described previously [15]. In short, BOLD venography was performed with a 3D RF-spoiled gradient echo (GE) pulse sequence similar to that presented by Reichenbach et al. [3]. The RF power level was adjusted to maximize subcortical signal intensities, expecting an Ernst flip angle at that region. Since the use of surface coil produced B1 inhomogeneity, the spatial intensity variation was reduced with a 2D nonuniformity correction algorithm [16]. To evaluate the effectiveness of phase mask filtering, venograms were obtained with imaging parameters: repetition time (TR) ¼ 50 ms, field of view (FOV) ¼ 3.0  1.5  1.5 cm3, matrix size ¼ 384  192  192, number of averages ¼ 2, and experimental time ¼ 34.5 min. Partial Fourier sampling (75%) was applied in both phase encode directions [17]. After zero-filling, an isotropic voxel resolution of 59 mm was achieved. In phase images of TE of 10 and 20 ms (Figure 34.2, left column), intracortical venous vessels are easily identified, especially at TE ¼ 20 ms. The phase difference between gray and white matter is also observed. Magnitude T2* -weighted images with TE
20 ms (Figure 34.2, middle column) show detailed venous vasculatures, including intracortical venules without phase mask filtering. The effect of phase mask filtering was examined for data sets with three different weighting schemes (negative, positive, and triangular schemes) and with the magnitude image multiplied by the phase mask filter two, four, and six times [4]. For all three weighting schemes, although contrast enhancement was observed in some vessels, there was little improvement in the overall detectability of vascular patterns with phase mask filtering, as shown in Figure 34.2 for the case of negative weighting filter multiplied four times to the magnitude data with TE ¼ 10 and 20 ms. Also, phase mask filtering introduced susceptibility artifacts at regions near air/tissue/bone interfaces (arrowheads in Figure 34.2), which were more severe at longer TE values (Figure 34.2, bottom row). This

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FIGURE 34.2 Effect of phase mask filtering and TE variation. Images are displayed after minimum intensity projection of 1 mm thick coronal slabs from two 3D data sets of one representative rat with 1.5% isoflurane anesthesia under a mixture of 30% oxygen and 70% nitrogen. TE values and image type (phase image, magnitude image, and magnitude image with phase mask filtering) are indicated. The gray bar indicates relative phase changes between 0.8 and 0.2 radians (corresponding to 6.4 and 1.6 Hz at TE ¼ 20 ms). Phase mask filtered images (right column) were generated from each complex data set by multiplying the magnitude image (middle column) four times by a filter constructed from the corresponding phase image (left column) where pixels with negative values were linearly scaled. Arrowheads indicate regions of susceptibility artifacts. CC, corpus callosum; IC, internal capsule.

indicates the magnitude T2* -weighted images with long TEs at high magnetic fields can be used for visualizing detailed venous vasculatures. At 9.4 T, the TE for the phase difference between tissues and veins at 180 is 8 ms according to Reichenbach et al. [3]. We found that the venous contrast for data with TE ¼ 8–10 ms was slightly improved by applying phase mask filter. However, the CNRs of the improved phase mask filtered images with TE of 8–10 ms were much worse than those of magnitude images with TE of 20–25 ms without any phase mask filtering. Therefore, for the BOLD venography at very high fields such as 9.4 T, it is better to optimize scan parameters for the magnitude contrast between tissues and veins, rather than for phase mask filters. Rat Venographic Atlas A rat venographic brain atlas may be useful for supplemental information in comparison of arteriograms and brain structures [18]. Thus, in vivo rat venographic images were obtained from a 3D data set of a isoflurane-anesthetized rat brain. Figure 34.3 shows venograms of one animal. To visualize venous vessels better, coronal 2D images were obtained from 3D magnitude images with a minimum intensity projection over 1 mm slabs. The positions of six contiguous 1 mm thick images approximately correspond to those of brain ‘‘Atlas’’ [18]; for example, interaural 8.2 mm position corresponds to 0.8 mm from the bregma and Plate 21. Detailed venous structure can be seen in cortical and subcortical areas, because of the enhanced susceptibility contrast and short T2* of venous blood at 9.4 T. Intracortical venules and even some of their branches are detectable in our venographic images. In addition to venous structures, white matter areas (between neocortex and hippocampus) can be distinguished from gray matter because of their shorter T2* values than gray matter T2* (but much longer than those of venous blood).

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FIGURE 34.3 Rat venographic brain atlas. A 3D image with a nominal isotropic voxel resolution of 59 mm was acquired with the similar imaging parameters shown in Figure 34.2 except TE ¼ 20 ms and TR ¼ 55 ms. Two-dimensional images with 1 mm thickness were constructed with a minimum intensity projection. Values in the left corner of images indicate approximated interaural coordinates in the Atlas stereotaxic frame [18]; interaural 8.2 mm, Plate 21; interaural 7.2 mm, Plate 25; interaural 6.2 mm, Plate 29; interaural 5.2 mm, Plate 33; interaural 4.2 mm, Plate 37; and interaural 3.2 mm, Plate 41. HL, hindlimb area; Par, parietal cortex; CPu, caudate putamen; GP, globus pallidus; FL, forelimb area; Th, thalamus; Hip, Hippocampus; Am, amygdala; Oc, occipital cortex; Te, temporal cortex.

Visualization of Intracortical Vessels in Cat Brains: Implication for BOLD fMRI To visualize venous vasculature in the cat brain, 3D images were obtained with TR ¼ 50 ms, TE ¼ 25 ms, FOV ¼ 4.0  2.0  2.0 cm3, and matrix ¼ 384  192  192. After zero-filling, an isotropic voxel resolution of 78 mm was achieved. Figure 34.4 shows 1.25 mm thick coronal and axial 2D images constructed from a 3D data set. When venous vessels (veins and venules) are oriented parallel to the plane, they appear as dark lines. This is clearly seen in a

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FIGURE 34.4 Venographic images of the cat brain, which were constructed from a 3D data set. The axial image was obtained from the 1.25 mm thick slab indicated by lines in the coronal image, and vice versa. Minimum intensity projection was performed to enhance the contrast of venous vessels. Since a surface coil was used, the ventral section in the coronal slice had poor signal to noise ratio, and thus vessels could not be detected in that region. The dotted box in the coronal image was expanded four times for the image shown in right. Black arrows in the right image indicate venous vessels draining from white matter, which are group 5 vessels. Arrows in coronal and axial planes indicate cerebrospinal fluid areas; P, posterior; A, anterior; R, right; L, left. Reprinted with permission from Springer.

coronal view where most intracortical vessels are perpendicular to the cortical surface. When venous vessels are oriented perpendicular to the plane, they appear as dark spots, as seen in an axial view. These intracortical venous vessels can be classified based on the cortical depth origin of the vessels. In the histology studies of the human brain, Duvernoy [19] classified intracortical emerging vessels into five groups; groups 1and 2 with an average diameter of 20–30 mm are originated from cortical layers II and III, group 3 with 45 mm diameter from layers IV and V (located at the middle of the cortex), group 4 with 65 mm diameter from layer VI, and group 5 with 80–125 mm diameter from white matter. Group 3–5 vessels are clearly detected in venographic images of a cat brain (Figure 34.4, right, for expanded view), while group 1 and 2 vessels are not easily observable. Generally, the ‘‘apparent’’ vessel size was larger, as its origin was deeper. The intracortical veins in the venogram appear larger than their actual size due to extending susceptibility effects of dHb beyond blood vessels. In group 4 and 5 vessels running the entire cortex (with 60–125 mm diameter in humans), a full-width at half-minimal signal intensity appears to be 100–200 mm. Thus, the observed vessel size in our venograms is much larger than actual sizes. Extraction of exact vessel size from the images is very complicated due to signal dependence on the oxygenation level of venous blood, physical angle between the vessel and main field, and partial volume effect. Instead, the ‘‘apparent’’ vessel size in the images can be compared with the actual diameter of intracortical vessels previously determined by histology. Assuming that the venous vessel size is similar in humans and cats, vessels with >45 mm diameter can be detected in our venographic images. In our previous rat studies [15], the detectability of venographic MR images was examined by comparing MRI data with diameter-dependent intracortical venous density in vivo obtained by two-photon

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excitation fluorescent microscopy. Density comparisons between the two modalities, along with computer simulations, show that venous vessels as small as 16–30 mm diameter are detectable at 9.4 T. Since conventional gradient echo BOLD signal is highly sensitive to large venous vessels, the density of venous vessels is a limiting factor of spatial resolution for fMRI. Therefore, cross-sectional views of vessels aligned perpendicular to the cortical surface were generated by performing cortical flattening along the lateral–medial dimension (minor anterior–posterior curvature was ignored). This procedure involved first manually defining a curve at a select cortical depth on a coronal view containing the visual area (see Figure 34.5a). Then, pixel intensities were calculated by linear interpolation of the four nearest pixels to construct a flat line. Cortical depth-dependent flattened images show that the density of intracortical veins decreases as the distance from the cortical surface increases (Figure 34.5c–e). The density of group 4 and 5 venous vessels (see Figure 34.5e) is 1–2/ mm2 [15]. If these large intracortical veins are uniformly distributed within the cortex, the average distance between these neighboring veins would be 0.7–1.0 mm. This implies that functional microarchitectures with spacing above 0.7 mm may be mapped using the GE BOLD fMRI technique.

FIGURE 34.5 Reconstructions from a 9.4 T BOLD 3D venographic data set of cat brain. (a) Coronal view reconstructed by averaging pixels across a 1.25 mm thick slab. Three black curves are 2.3 mm in length and indicate different cortical depths, within visual cortical area 18. (b) A single-pixel thick (78 mm) reconstruction at the location of the long white curve in (a). The square in (b) represents a 2.3  2.3 mm2 region within the visual cortex. (c–f) Expanded views of selected 2.3  2.3  0.078 mm3 regions at shallow, middle, and deep cortex, as indicated by three black curves in (a). Dark spots in expanded images indicate intracortical emerging venous vessels. Image quality and contrast may not be optimal due to conversion from color to grayscale display. Please see the color plates section for the original version of this figure.

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FIGURE 34.6

Comparison of high-resolution BOLD fMRI map (a) and BOLD venographic image in a rat brain (b). Activation foci in the somatosensory cortex (a) are correlated with intracortical veins (b), as indicated by arrows, and some activation foci outside the somatosensory cortex (arrowheads) are located around regions of large draining veins, including the superior sagittal sinus. The bar in (b) represents 3 mm. Image quality and contrast may not be optimal due to conversion from color to grayscale display. Please see the color plates section for the original version of this figure.

Relationship Between BOLD fMRI Foci and Vascular Architecture To examine the relationship between fMRI and intracortical vessels, three male Sprague Dawley rats weighing 300–450 g were used. Animal preparations were reported elsewhere [15]. An isoflurane level was maintained at 1.5% with O2:N2 gas of 3:7. For high-resolution fMRI studies, conventional 2D gradient echo sequence with first-order flow compensation along slice-select and readout directions was employed. Scan parameters were TR ¼ 20 ms, TE ¼ 10 ms, FOV ¼ 22  11 mm2, matrix size ¼ 256  128, nominal flip angle ¼ 8 , and thickness ¼ 1 mm. Each fMRI session was composed of 38.4 s resting, 15 s electrical stimulation, and 61.8 s resting states (total 115.2 s). Somatosensory stimulation was applied to a forepaw with repeated electric pulses with 3 ms duration, 1.5 mA, and 6 Hz frequency [20]. For each subject, 20–30 fMRI runs with at least 3 min interrun intervals were acquired. Functional MRI maps were calculated by a time-shifted cross-correlation analysis between MR time course and the stimulation paradigm. High-resolution fMRI maps were successfully obtained; localized activation was observed at the contralateral forelimb area. Interestingly, activation foci were located at intracortical veins (arrows in Figure 34.6) as well as large surface veins (arrowheads in Figure 34.6). Large signal changes in vessel regions can be induced by changes in inflow and BOLD effects. Signal changes in large pial veins (indicated by arrowheads) may contain inflow effects outside the imaging slice. However, it is unlikely that inflow effects are significant in the parenchyma due to a long travel time from arterial vessels outside the imaging slice to intracortical venous vessels (e.g., 1–2 s). Bar-like activation foci (arrows in Figure 34.6) follow large intracortical veins, which originate from deep cortical regions of depth around 1.2–1.7 mm. These results imply that even if fMRI data are acquired with high spatial resolution, venous vascular architectures will be a limiting factor of the intrinsic ability of GE BOLD fMRI to map functional sites. As discussed in the previous section, functional microarchitectures with spacing below 0.7 mm cannot be mapped using the GE BOLD fMRI technique. To improve spatial resolution, large vascular contribution to fMRI should be minimized by using improved data acquisition methods or processing approaches.

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CONCLUSIONS BOLD contrasts at high magnetic field (such as 9.4 T) can be utilized to visualize detailed venous vasculature, including cortical emerging venules along with highly resolved anatomical structures. The technique does not require any exogenous contrast agent or any phase mask filtering to enhance the contrast, thus it is reliable and robust. Based on the intracortical venous vessel density, the spatial limitation of GE BOLD fMRI in a specific region can be investigated.

REFERENCES 1. Ogawa S, Lee T-M, Kay AR, Tank DW. Brain magnetic resonance imaging with contrast dependent on blood oxygenation. Proc. Natl. Acad. Sci. USA 1990a;87:9868–9872. 2. Ogawa S, Lee T-M, Nayak AS, Glynn P. Oxygenation-sensitive contrast in magnetic resonance image of rodent brain at high magnetic fields. Magn. Reson. Med. 1990b;14:68–78. 3. Reichenbach JR, Venkatesan R, Schillinger DJ, Kido DK, Haacke EM. Small vessels in the human brain: MR venography with deoxyhemoglobin as an intrinsic contrast agent. Radiology 1997;204 (1):272–277. 4. Reichenbach JR, Haacke EM. High-resolution BOLD venographic imaging: a window into brain function. NMR Biomed. 2001;14:453–467. 5. Ogawa S, Lee TM. Magnetic resonance imaging of blood vessels at high fields: in vivo and in vitro measurements and image simulation. Magn. Reson. Med. 1990;16(1):9–18. 6. Christoforidis GA, Bourekas EC, Baujan M, Abduljalil AM, Kangarlu A, Spigos DG, Chakeres DW, Robitaille PM. High resolution MRI of the deep brain vascular anatomy at 8 Tesla: susceptibility-based enhancement of the venous structures. J. Comput. Assist. Tomogr. 1999;23(6):857–866. 7. Springer CS, Xu Y. Aspects of bulk magnetic susceptibility in in vivo MRI and MRS. New developments in contrast agent research. European Workshop on Magnetic Resonance in Medicine, Blonay, Switzerland, 1991, pp. 13–25. 8. Ogawa S, Menon RS, Tank DW, Kim SG, Merkle H, Ellermann JM, Ugurbil K. Functional brain mapping by blood oxygenation level-dependent contrast magnetic resonance imaging. A comparison of signal characteristics with a biophysical model. Biophys. J. 1993;64(3):803–812. 9. Springer CS. Physicochemical principles influencing magnetopharmaceuticals. In: Gillies R, editor. NMR in Physiology and Biomedicine, Academic Press, San Diego, 1994, pp. 75–99. 10. Weisskoff RM, Kiihne S. MRI susceptometry: image-based measurement of absolute susceptibility of MR contrast agents and human blood. Magn. Reson. Med. 1992;24:375–383. 11. Tsekos NV, Zhang F, Merkle H, Nagayama M, Iadecola C, Kim SG. Quantitative measurements of cerebral blood flow in rats using the FAIR technique: correlation with previous iodoantipyrine autoradiographic studies. Magn. Reson. Med. 1998;39(4):564–573. 12. Lee S-P, Silva AC, Ugurbil K, Kim S-G. Diffusion-weighted spin-echo fMRI at 9.4 T: microvascular/tissue contribution to BOLD signal change. Magn. Reson. Med. 1999;42: 919–928. 13. Silvennoinen MJ, Clingman CS, Golay X, Kauppinen RA, van Zijl PC. Comparison of the dependence of blood R2 and R2 on oxygen saturation at 1.5 and 4.7 Tesla. Magn. Reson. Med. 2003;49(1):47–60. 14. Rose A. The sensitivity performance of the human eye on an absolute scale, J. Opt. Soc. Am. 1948;38:196–208.

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15. Park SH, Masamoto K, Hendrich K, Kanno I, Kim SG. Imaging brain vasculature with BOLD microscopy: MR detection limits determined by in vivo two-photon microscopy. Magn. Reson. Med. 2008;59:855–865. 16. Cohen MS, DuBois RM, Zeineh MM. Rapid and effective correction of RF inhomogeneity for high field magnetic resonance imaging. Hum. Brain Mapp. 2000;10(4):204–211. 17. MacFall JR, Pelc NJ, Vavrek RM. Correction of spatially dependent phase shifts for partial Fourier imaging. Magn. Reson. Imaging 1988;6(2):143–155. 18. Paxinos G, Watson C. The Rat Brain in Stereotaxic Coordinates, Academic Press, San Diego, 1986. 19. Duvernoy HM, Delon S, Vannson JL. Cortical blood vessels of the human brain. Brain Res. Bull. 1981;7(5):519–579. 20. Kim T, Hendrich KS, Masamoto K, Kim SG. Arterial versus total blood volume changes during neural activity-induced cerebral blood flow change: implications for BOLD fMRI. J. Cereb. Blood Flow Metab. 2007;27:1235–1247.

35 Susceptibility Weighted Imaging in Rodents Yimin Shen, Zhifeng Kou, and E. Mark Haacke

INTRODUCTION Animal imaging plays an important role in the development of magnetic resonance imaging (MRI). Today’s experiments in animal models could be tomorrow’s practice in human subjects. One well-known example is Ogawa’s seminal work on functional MRI (fMRI), which was originally performed in an animal model in the laboratory [1] and then widely used in human subjects. Animal imaging has numerous advantages over human subjects due to its ease of control, histological validation, and so on. Meanwhile, animal imaging has its own unique difficulties and potential pitfalls since animals are generally unable to communicate with us directly and due to their size difference and the necessary difference in imaging platforms. Susceptibility weighted imaging (SWI) in an animal model is no exception. In this chapter, we attempt to give our readers a practical guide on how to do SWI experiments in animal models. We will use several exemplar projects as a vehicle to navigate through this topic. Generally, we used three-dimensional SWI images of either rat or mouse brains on a 4.7 T (AVANCE; Bruker, Karlsruhe, Germany) or a 7 T (ClinScan, Bruker, Karlsruhe, Germany) system. Technical aspects will be presented first and then SWI applications will be discussed. TECHNICAL ASPECTS Sequence Setup As discussed throughout this book, SWI is based on a fully flow-compensated, highresolution, 3D gradient echo method. It is a T2* -based sequence with long TE. Flow Susceptibility Weighted Imaging in MRI, By E. Mark Haacke and J€urgen R. Reichenbach Copyright
2011 by Wiley-Blackwell

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compensation ensures that there is no flow-induced phase in SWI filtered phase images. On the Bruker 4.7 T system using Paravision 3.0.2, there is an SWI-like sequence called gradient echo with flow compensation (GEFC). It is a gradient echo method with first-order flow compensation in three logical gradient directions. Echo asymmetry ranges from 20% to 50% with a symmetric echo (50%) being a good starting point. After data acquisition, the raw image data will be saved by default. The magnitude images will be reconstructed automatically. In order to get phase images, reconstruction parameters need to be set up properly. The type of image should be changed to ‘‘phase image.’’ The ‘‘in-line’’ phase correction mode should be selected as ‘‘first order’’ in three directions. The phase correction coefficients pc0 and pc1 should be set to 08 and 1808/point, respectively, in three directions for an in-plane isotropic acquisition. After data acquisition, users are encouraged to use signal processing in NMR (SPIN) software (Detroit, MI) to perform image postprocessing. In the Bruker 7 T ClinScan system, the console platform is a standard Siemens platform. This is the same as the Siemens clinical system and makes the magnet operation much easier. Indeed, the original purpose of choosing Siemens platform for this system is to allow researchers to develop techniques on animal magnet and then easily translate to human magnet. SWI has been standardized into a Siemens research package, which requires a license from the vendor. The Siemens version of SWI automatically generates four types of images: SWI magnitude, phase, minimum intensity projection (mIP), and a processed SWI image that combines both magnitude and phase images. The SWI mIP image is projected through four slices with a sliding window of one slice each step. However, to take full advantage of the latest developments in SWI, readers are still encouraged to use SPIN software to process the data. Animal Anesthetization Since SWI uses deoxyhemoglobin as an intrinsic contrast agent, which is the same as that used in the blood oxygenation level-dependent (BOLD) fMRI, the anesthetization method plays an important role in better visualizing the venous vasculature of the brain. To obtain a high-quality venous image of the rat or mouse brain, an intraperitoneal injection of a mixture of ketamine, xylazine, and atropine is a proper candidate for anesthetization. Using this approach, there is still a high level of deoxyhemoglobin remaining in the veins, so the corresponding SWI image is able to demonstrate high-quality venous structures (Figure 35.1). An alternative approach is to use isoflurane along with air or with a mixture of 20% oxygen and 80% nitrogen. In this case, the venous response on SWI strongly depends on the partial pressure of oxygen (pO2) in the supplied gas. Figure 35.2 shows a comparison between pure oxygen and air as the supplied gas. The rat brain venous vasculature almost disappeared in pure oxygen when isoflurane was used due to the fact that the venous system has higher level of oxyhemoglobin than usual. In a word, one should avoid using pure oxygen as the anesthesia gas in order to get good venous visualization with SWI. APPLICATIONS Measurement of Relative Changes in Cerebral Blood Flow (CBF) After Traumatic Brain Injury in Rats Using SWI Phase Filtered Images Magnetic resonance imaging offers a noninvasive means to study traumatic brain injury (TBI). In this work, we evaluated the use of SWI to study changes in the vasculature of the rat

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FIGURE 35.1 SWI phase images of a mouse brain at 4.7 T. The SWI parameters were TR ¼ 36 ms, TE ¼ 15 ms, FA ¼ 20 8, Nacq ¼ 4, FOV ¼ 20  20  16 mm3, data acquisition matrix ¼ 256  256  20, and 20 slices interpolated to 32 slices in image reconstruction. The image resolution ¼ 78 mm  78 mm  500 mm. The acquisition time was 26 min.

FIGURE 35.2 Isofluorane-anesthetized rat brain SWI phase (left) and magnitude (right) images under pure oxygen (top row) or air (mixture of 20% oxygen and 80 % nitrogen) (bottom row) as supplied gas. SWI parameters: TE ¼ 20 ms, TR ¼ 42 ms, FA ¼ 228, echo position 25%, FOV ¼ 32  32  32 mm3, antialiasing factor ¼ 1.333, with a matrix size of 512  256  32, interpolated to 512  512  48, and voxel size ¼ 62.5 mm  62.5 mm  0.667 mm after zero fill. Nacq ¼ 2 and total imaging time ¼ 16 min. The supply of pure oxygen renders the venous system almost invisible compared to breathing air that shows the normal levels of deoxyhemoglobin in the veins making them easily visualized with SWI.

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brain after TBI. Previous methods of evaluating brain trauma have included MR spectroscopy (MRS), diffusion weighted and diffusion tensor imaging (DWI/DTI), MR angiography (MRA), and perfusion weighted imaging (PWI). Each method offers its own advantages. On the other hand, SWI offers information about the intact structure of the venous system and about the oxygen saturation as well. These two added pieces of information can be used to improve the diagnosis of the state of the brain tissue after TBI. Prior to TBI, six male Sprague Dawley rats (350–400 g) were anesthetized. The rat skull was exposed and a steel helmet was placed at the bregma using dental cement. To induce brain injury, a 450 g weight was dropped from 2 m onto the helmet as proposed in the Marmarou model [3]. All the six rats were imaged under anesthesia using an intraperitoneal injection of ketamine, xylazine, and atropine. The MRI scans were repeated over 4 days at four time points: baseline scans and scans at 4 h, 24 h, and 48 h post-TBI. One rat died during experiment. All the MRI measurements were performed on a 4.7 T Bruker AVANCE spectrometer. Sequence protocol includes T1and T2-weighted imaging, arterial spin labeling as a means to measure flow, and susceptibility weighted imaging. For all sequences, FOV ¼ 40  40  24 mm3. The SWI parameters were as follows: TR ¼ 36 ms, TE ¼ 15 ms, FA ¼ 208, with a matrix size 512  512  24, and Nacq ¼ 2. The relative changes in flow are associated with the relative changes in oxygen saturation in veins that can be measured from the bulk susceptibility difference. Therefore, blood flow can be measured indirectly using the SWI phase filtered images. We define the relative changes in phase between the background and vessel (Dw) pre- and posttrauma as Rpc ¼ ðDw1 Dw0 Þ=Dw0

ð35:1Þ

and then the relative change in flow f is given by f ¼ Rpc =ð1Rpc Þ

ð35:2Þ

This fractional change in flow is independent of blood vessel orientation. The change in phase can be measured by drawing a profile in a straight line across the blood vessel in phase images (Figure 35.3). (Future applications of SWIM or SWI with susceptibility

FIGURE 35.3 Phase profiles across a vessel pretrauma (solid line) and posttrauma (broken line) on the left. Experimental profiles across all four studies on the right. Reprinted from Ref 2, with permission from Elsevier Science.

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FIGURE 35.4 Four time points in a single rat showing the change in phase from pretrauma (a), 4 hrs (b), 24 hrs (c) and 48 hrs (d) post trauma. It can be seen visually that the phase in the internal cerebral vein returns to normal at 48th hour. The profiles across all four studies are shown in Figure 35.3 (right). The smallest phase jump is shown in the pretrauma case, the largest at four hours posttrauma, while the other two time points show a return to normal phase values. Reprinted from Ref 2, with permission from Elsevier Science.

mapping, as described in Chapter 25, may make more direct measurements of oxygen saturation possible.) Demarcation of the internal cerebral veins pre- and posttrauma is shown in Figure 35.4. The profiles of these vessels are drawn from the black lines, and they are shown in Figure 35.3. The phase values associated with the changes from baseline to minimum were 888 (pre), 2118 (4 h), 1328 (24 h), and 1058 (48 h), respectively. Relative flow changes of the corresponding vessel were 58% (4 h), 33% (24 h), and 17% (48 h), respectively. We chose five large veins for analysis (Figure 35.5). Measures of flow changes of the five large venous vessels for a rat are shown in Figure 35.6. The same analysis was performed in each rat brain. The means of relative flow changes over five vessels after TBI for each rat are shown in Figure 35.7. The means and standard deviations over the five rats are depicted in Figure 35.8. The blood flow decreased by 62% for the dead rat and 10–30% in the remaining five rats. Note that although the equation for calculating flow change is valid

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FIGURE 35.5 The selection of five large venous vessels in a rat in the measurement of SWI phase values within the vessels. Reprinted from Ref 2, with permission from Elsevier Science.

only for small flow changes, the resulting value of 62% reduction in flow in the dead rat brain is not far from the ideal value of 100%. The overall mean and standard deviation of changes in phase values for all 25 vessels in the 5 rats at each time point were 588  308 (pre), 828  448 (4 h), 778  368 (24 h), and 778  368 (48 h), respectively; those of changes in flow were 26  18% (4 h), 23  18% (24 h), and 22  20% (48 h), respectively. All differences in blood flow between pre- and post-TBI were statistically significant (p < 0.02, n ¼ 5, t-test, paired two sample for means, alpha ¼ 0.05). We have shown here that it is possible to visualize changes in oxygen saturation in the veins of a rat posttrauma. This has been shown to correlate with expected reductions in flow from the perspective of predicted

FIGURE 35.6 Measures of flow changes of five large venous vessels for a rat. The internal cerebral veins show the biggest effect. Vessel labeling are shown in Figure 35.5. Reprinted from Ref 2, with permission from Elsevier Science.

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FIGURE 35.7 The means of relative flow changes over five vessels for each rat are plotted here to show the effective changes in flow over time posttrauma. Two of the rats, A2 and B2, had very high remnant flow decreases even 48 h posttrauma. The other three tended to recover. Reprinted from Ref 2, with permission from Elsevier Science.

FIGURE 35.8 Estimated relative blood flow changes in six rats posttrauma. One of the six rats died in the magnet (right-hand shaded region). The error bars represent the standard deviation of the measurements for the five surviving rats at the three time points: 4th, 24th, and 48th hour posttrauma. The difference in flow changes in brain between pre- and post-TBI was statistically significant (P < 0.02, n ¼ 5, t-test: paired two-sample for means). Reprinted from Ref 2, with permission from Elsevier Science.

changes, oxygen saturation results, and ASL changes. Readers are encouraged to read Ref. 2 for more details. Hemorrhage Detection in Rat Brain by SWI In the above TBI rat model, one rat exhibited brain damage in the fimbria of the hippocampus (septofimbrial nuclears). This was seen in only one hemisphere after 4 h and then spread to the other side a day later (Figure 35.9). Another example of rat brain hemorrhage detected by SWI is in a communicating hydrocephalus (CH) rat model [4]. CH is characterized by impaired cerebrospinal fluid (CSF) flow only in the subarachnoid spaces, allowing free passage of CSF within the cerebral ventricles and from the fourth ventricle through the foramina of Luschka and Magendie to the cisterna magna. This disorder occurs frequently, especially in older adults, and is often associated with persistent neurological deficits. CH has been difficult to model in rodents because the subarachnoid spaces are extremely small and difficult to

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FIGURE 35.9 The temporal evolution of a traumatic brain lesion as seen with SWI filtered phase images. (a) Pretrauma image showing intact vessel architecture. (b) An image recorded 4 hours posttrauma showing what may be hemorrhage on one side of the septofimbrial nucleus. (c) An image recorded 24 hours postimpact showing spreading of the trauma to the same part of the brain on the other side. (d) Image recorded 48 hours postimpact showing further darkening of the vessels, suggestive of a continued lowering of oxygen saturation in the brain. Reprinted from Ref 2, with permission from Elsevier Science.

access. Meanwhile, SWI was able to detect some hemorrhages in CH rat brain (Figure 35.10). Histological Validation and Temporal Transformation of Hemorrhagic Blood Products After Trauma Detected by SWI To date, little has been reported to confirm that the signal losses seen in SWI data are indeed blood products. In our preliminary data, we evaluated a number of rat brains posttrauma. Specifically, Prussian blue staining was performed to visualize ferric iron seen microscopically as bright blue products. Prussian blue staining is a sensitive histochemical test that demonstrates single granules of iron in blood cells [5–10]. We confirmed that these hemorrhagic locations are iron products, which evolved from hemorrhagic blood after injury. Figure 35.11 is a sample histological validation of SWI visualized blood products in one rat brain harvested 4 h after TBI. Hypointense signals in SWI were seen in the corpus callosum indicating possible hemorrhages. These hypointense signals matched the ferric iron pattern in the same location validated by Prussian blue staining. These ferric irons were

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FIGURE 35.10 Susceptibility weighted imaging (a, b, d, and e) and T2w (c and f) in a communicating hydrocephalus rat with Kaolin obstruction of the basal cisterns (BCs). SWI images show possible hemorrhage at the interface between the 4th ventricle and the medial/spinal vestibular nucleus (black arrows). SWI parameters: TE/TR ¼ 15/36 ms, NAverages ¼ 2, total acquisition time (TA) 19 m 40 s, flip angle ¼ 20 8, FOV ¼ 40  40  24, matrix size ¼ 512  512  24, space resolution ¼ 78 mm  78 mm  1 mm. MVePC medial vestibular nucleus, parvicellular part; SpVe spinal vestibular nucleus.

FIGURE 35.11 Histological validation of SWI of potential hemorrhage with that detected by Prussian blue staining in a rat induced brain injury with a Marmarou impact model. Image order: top left (preinjury SWI phase image); top right (4 hours after injury, SWI high-pass filtered phase image); lower (Prussian blue staining of corresponding corpus callosum area, blue (shown as dark color here) indicates the presence of iron product that is from blood). The iron pattern in histology matches the locations of the hemorrhagic blood seen on the SWI image.

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FIGURE 35.12 Temporal transformation of hemorrhagic blood product detected by SWI. The hemorrhagic blood originally detected by SWI at 4 hours postinjury almost disappeared at 24 hours postinjury, and then began to reappear at 48 hours postinjury. At 4 days after injury, it became almost identical to that initially seen 4 hours after injury. This shows the importance of imaging at the right time point as well as the potential predictive power of SWI in seeing early effects in tissue that later appears to become damaged. It is also possible that the 4 hours event represents an increase in deoxyhemoglobin that then temporarily recovers only to have bleeding later.

either in association with or away from blood vessels. In addition, disrupted blood vessel integrity was indicated by the appearance of a disrupted endothelial cell layer and accumulation of extravasated erythrocytes close to the external vessel wall in some regions of the corpus callosum. In our further follow-up scan of the rats in the same study, we also found a temporal pattern of hemorrhagic blood transformation detected by SWI. Figure 35.12 shows an animal being followed up to 4 days after injury. At 4 h after injury, SWI clearly identified the hemorrhagic blood in the corpus callosum, which is directly underneath the impact site. Then at 24 h after injury, the lesion is almost invisible. At 48 h after injury, the blood products became visible again but to a lesser degree. Finally, at 4 days after injury, the hemorrhagic blood pattern is almost the same as one that appeared 4 h after injury. After trauma, any bleeding from shearing will eventually lead to the production of hemosiderin that is highly paramagnetic. The MRI appearance of blood changes with time as the chemical structure of the hemoglobin changes. The different phases of blood during this transformation process can exhibit different contrast mechanisms. Within minutes to hours after hemorrhagic bleeding, the blood will become de-oxygenated and will appear hypointense on SWI images (see image at 4 h postinjury in Figure 35.12). After the red cells lyse (late subacute period), there is extracellular methemoglobin that appears bright on T1w and T2w but isointense on SWI due to dilutional effects by extracellular plasma mixing with methemoglobin, releasing extracellular methemoglobin (see image at 24 h postinjury) [11]. As the macrophages attack the debris in the damaged tissue, paramagnetic hemosiderin, the crystalline storage form of heme iron, begins to accumulate and appears dark on SWI images (see images at 48 h and 4 days postinjury) [7]. SWI is extremely sensitive to hemosiderin, because of its large magnetic moment, and provides superior capability over conventional MRI for detecting microbleeds in the brain after trauma [11]. Therefore, what

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FIGURE 35.13 The typical cavities and multifocal cerebral hemorrhages (arrows) of porencephaly in a brain of a mouse with mutations in Col4a1 are shown up on SWI magnitude images (top row). The normal vasculature in a control mouse brain is shown up on SWI magnitude images (bottom row) for comparison. SWI parameters are TE ¼ 15 ms, TR ¼ 36 ms, NA ¼ 4, TA ¼ 24 m 36 s, FOV ¼ 20  20  16, matrix size ¼ 256  256  20, interpolated to 256  256  32, resolution ¼ 78 mm  78 mm  0.5 mm, echo position 50%, SW ¼ 25 kHz, and 30 dummy scans.

we have seen in Figure 35.12 are the different phases of hemorrhagic blood transformation after trauma. SWI Monitoring Intracerebral Hemorrhages in Mice with Mutations in Col4a1 Mutations in a gene encoding type IV collagen a1 (Col4a1), a basement membrane protein, lead to weakened vasculature that predisposes to hemorrhage. Col4a1 causes perinatal cerebral hemorrhage and porencephaly [12]. Porencephaly is an extremely rare disorder of the central nervous system in which a cyst or cavity filled with CSF develops in the brain. Birth trauma in natural birth is a major factor contributing to perinatal hemorrhage in mice with mutations in Col4a1 [12]. In humans or in mice, this can lead to severe, fatal cerebral hemorrhage or subclinical microbleeds. SWI can be used to monitor these kinds of intracerebral hemorrhages. The typical cavities and multifocal cerebral hemorrhages of porencephaly in the brain of a mouse with mutations in Col4a1 show up on SWI magnitude images, while a control mouse brain shows normal vasculature (Figure 35.13). Improved Vascular Visualization in SWI by Contrast Agents in Rat Brain Contrast agents are chemical substances introduced to improve MRI contrast by altering the relaxation times. Gadolinium-based agents are T1 enhancing agents and in this case are referred to as positive contrast agents (appearing bright on MRI) and have a relatively short residence time in the vascular system. Another class of contrast agents are ultrasmall supermagnetic particles of iron oxide (USPIO) such as Guerbet’s P904 (Laboratoire, Guerbet, Aulnay, France). USPIO usually consists of a crystalline iron oxide core containing thousands of iron atoms and a shell of polymer, dextran, and polyethyleneglycol and produce very high T2 relaxivities. These agents exhibit strong T1 and T2 relaxation

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FIGURE 35.14 Brain SWI post-P904 2.5 h at a dose of 300 mmol Fe/kg. P904 improved microvascular visualization in SWI and potentially revealed the next order blood vessels. Resolution ¼ 63 mm  63 mm  1 mm. SWI parameters: TR ¼ 42 ms, TE ¼ 20 ms, FA ¼ 228, with a matrix size of Nx  Ny  Nz ¼ 512  256  32 interpolated to 512  512  48 image matrix size, and Nacq ¼ 2. TA ¼ 15 min.

properties, and therefore are referred to as negative contrast agents as the T2 relaxation effects reduce the signal. Manganese chloride (MnCl2) is also used to maximize the contrast of different tissues. Like MRA, SWI is also enhanced by contrast agents in either a positive or negative way. As examples, P904-enhanced SWI/MRA images are shown in Figures 35.14 and 35.15, Gd-DTPA-enhanced MRA in Figure 35.16, and manganese-enhanced SWI in rat brain in Figure 35.17.

FIGURE 35.15 Rat brain MRA pre (left)- and post-P904 2.5 h with dose of 300 mmol Fe/kg (right). For the given full dose, the straight sinus (white arrow) appeared and superior sagittal sinus (black arrow) enhanced and broaden in MRA. Resolution ¼ 63 mm  63 mm  250 mm. MRA parameters: TR ¼ 30 ms, TE ¼ 6.64 ms, FA ¼ 308, matrix size ¼ 512  512  24, and Nacq ¼ 2. TA ¼ 21 m 51 s.

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FIGURE 35.16

MRA magnitude images of a rat acquired at pre-Gd (left), post-Gd (middle), and day 1 (right). The large vessels with fast blood flow showed up at prescan. The straight sinus (white arrow) and a lot of blood vessels highlighted after Gd injection. The superior sagittal sinus became widening (black arrow). After 24 h, the image showed almost the same as prescan that indicated Gd drained out from blood system.

FIGURE 35.17 SWI magnitude (left) and phase (right) images comparison among postmanganese 7 h rat (top), control rat (middle), and a dead rat without manganese (bottom). Manganese SWI looks much like dead rat SWI. Paramagnetic manganese ion (Mn2 þ ) has large magnetic moment from its five unpaired 3d electrons and plays a role of deoxyhemoglobin in SWI.

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Monitoring Capture of P904 at Popliteal Lymph Node using SWI Phase Image The imaging of lymph modes is especially important in the early detection of nodal metastases in cancer patients. Iron-based agents such as Guerbet’s P904 have found its use clinically in MRA and as macrophage detectors. This has led to the several clinical applications, including vessel visualization, studying vascular effects in aging, stroke, and multiple sclerosis and assessing the vascular and lymphatic systems. Healthy lymph nodes are easily detected with USPIOs because of a large amount of USPIO capitation by the onsite macrophages (MF). The higher the concentration of P904, for example, the more the signal will be lost on a T2* -weighted GRE sequence. On the other hand, in metastatic lymph nodes, MFs are replaced by tumor cells that block USPIO accumulation. This is a reversed strategy compared to classical contrast agent models, where disease effects are sought, as now only healthy lymph nodes are targeted. Iron-based contrast agents have triple properties in MRI. First, at low concentrations, they act as T1 reducing agents. Second, at higher concentrations, they act as T2 reducing agents. And third, at any concentration, they can also create a local susceptibility effect and therefore create a bulk phase shift. The goals of this work are to address the sensitivity of SWI in assessing the ability of P904 to identify normal lymph nodes as a function of concentration and timing. Our hypotheses for this stage are (1) phase will provide a much more sensitive means to image uptake of P904 in the lymphatic system and (2) less contrast agent and/or shorter delay between imaging and injection will be required to do so. We evaluated the lymph nodes in a number of Wistar rats in this study. Because of the long T1 of the popliteal lymph node (PLN) (1.6 s at 4.7 T), we used low flip angle of 108. We also added fat saturation into the SWI sequence in order to highlight the PLN sitting in fat (Figure 35.18). The echo time was chosen to be a multiple 1.45 ms (4.35 ms) that made water and fat in phase at 4.7 T. Prior to image acquisition, anesthesia was induced by 2% isoflurane with oxygen (0.4 L/min). Prescans were done first and then P904 was injected

FIGURE 35.18 PLN sit in fat (lower right T2w image) and showed brighter in T1 map than its peripheral fat because of its long T1 (upper right). SWI magnitude/phase (left/middle) images with/without fat saturation (upper/lower) clearly differentiated PLN with surrounding fat.

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FIGURE 35.19 Temporal magnitude images of PLN after P904 administration (pre, 1 h–25 days). At prescan and just injection of P904, the PLN showed as a bean (arrow) with uniform brightness. After 1 h, the PLN became dark and disappeared at 2 h. A black hole replaced PLN at 8 h and intact at day 25. PLN SNR decreased as macrophages captured P904. The accumulated iron particles made the appearing size of PLN increase over time.

intravenously through an extension catheter into tail vein at a dose of 75 mmol Fe/kg. This was a quarter of the normal dose used in previous studies. The animal was kept in the same position in the magnet for pre, post, 1 h, and 2 h scans. The remaining MRI scan time points were 8 h, 24 h, 15 days, and 25 days. MRI data showed that the usually bright PLN in the SWI image became darker as P904 was taken up by macrophages and generated a growing black hole over time (Figure 35.19). The SNR of PLN reduced with time, while the size of the PLN (in pixel number) in the image increased with time. The signal loss remained

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FIGURE 35.20 Subtraction images between 1 and 2 h. The change in phase between 1 and 2 h reduced from 387  1278 to 752  1218, that is, 94% or 374  1298; the intensity of magnitude image reduced from 2158  1367 to 915  614, that is, 57% or 1242  1116.

TABLE 35.1 The Magnitude and Phase of PLN (49 Pixels) of the Quarter Dose Rat 9 Time

Magnitude

SD

Normalized

Phase (Degree)

SD

Normalized

Pre Post 1h 2h

5530 5456 2158 915

1703 1904 1367 614

1.00 0.99 0.39 0.17

141 156 378 752

29 27 127 121

1.00 1.11 2.68 5.33

intact even after 25 days in the quarter dose rat. The process of bright PLN getting darker can be monitored by both magnitude and phase images. Phase images appear to be more sensitive as no signal loss needs to take place for a change in phase to take place theoretically. The phases of PLN decreased by 11% after P904 injection, while the corresponding magnitudes decreased only by 1% (Table 35.1). Part of the phases of PLN changed over 2p at 1 and 2 h, thus showing a phase wrap inside the PLN. Magnitude and phase differences between 2 and 1 h clearly show P904 uptake by macrophages in the PLN (Figure 35.20). The temporal phase and magnitude images show that a large change in phase can occur with only a small change in magnitude. Generally, the SNR in the phase is about eight times that of the magnitude. This suggests that we may be able to cut the dose down at least a factor of 10 from the original dose (300 mmol Fe/kg) and according to the quarter dose animal perhaps even further. SWI Magnitude Image Showing Dramatic Blood Vessel Effect of P904 One full dose rat showed dramatic darkening in the post-P904 10 min images at overall blood vessels. A black hole appeared at a junction of major vessels. After 24 h, it seems P904

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FIGURE 35.21 Pre (top left), post (top right), 8 h (bottom left), and 24 h (bottom right) MRA of a rat with full dose P904 showed temporal blood vessel effect. The dramatic effect (arrow) took place at very beginning of P904 injection, the residual effect at 8 h, and no effect after 24 h. The joint of three large arteries (circle) showed a black hole after P904 injection.

was cleaned up from the vascular system (Figure 35.21). Generally, P904 made blood vessels darker in SWI, improved vascular visualization, and potentially revealed blood vessels of the next order level. Many vessels (primarily veins) that were hard to see prior to P904 now became clearly visible post-P904. High-Resolution Venography of Rat Brain at 7 T High field system offers better signal to noise ratio (SNR) and higher resolution. Therefore, the high-resolution SWI venography (41 mm  41 mm  1 mm) on 7 T Bruker ClinScan system is able to clearly demonstrate the small venules (Figure 35.22) that are invisible in 4.7 T. This offers new opportunity to detect microhemorrhages that are

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FIGURE 35.22 High-resolution SWI venography from a 7 T Bruker ClinScan system. Image resolution is 41 mm  41 mm  1 mm. Imaging parameters were TE ¼ 10 ms, TR ¼ 50 ms, FA ¼ 108, FOV ¼ 32  32  32 mm3, matrix size ¼ 768  768  32, BW ¼ 260 Hz/pt, and data acquisition time ¼ 40 min. Image order: Left is SWI phase image: Right is SWI magnitude image.

undetectable in lower fields and better reveal the relationship between microbleeds and vascular system.

REFERENCES 1. Ogawa S, Lee TM, Kay AR, Tank DW. Brain magnetic resonance imaging with contrast dependent on blood oxygenation. Proc. Natl. Acad. Sci. 1990;87:9868–9872. 2. Shen Y, Kou Z, Kreipke C, Petrov T, Hu J, Haacke EM. In vivo measurement of tissue damage, oxygen saturation changes and blood flow changes after experimental traumatic brain injury in rats using susceptibility weighted imaging (SWI). Magn. Reson. Imaging 2007;25(2): 219–227. 3. Marmarou A, Foda MA, van den Brink W, Campbell J, Kita H, Demetriadou K. A new model of diffuse brain injury in rats. Part I: pathophysiology and biomechanics. J. Neurosurg. 1994;80:291–300. 4. Li J, McAllister JP, 2nd, Shen Y, Wagshul ME, Miller JM, Egnor MR, Johnston MG, Haacke EM, Walker ML. Communicating hydrocephalus in adult rats with kaolin obstruction of the basal cisterns or the cortical subarachnoid space. Exp. Neurol. 2008;211(2):351–361. 5. Nakamura T, Keep RF. Deferoxamine-induced attenuation of brain edema and neurological deficits in a rat model of intracerebral hemorrhage. Neurosurg Focus 2003;15 (4):ECP4. 6. Atlas SW, Thulborn KR. MR detection of hyperacute parenchymal hemorrhage of the brain. AJNR Am. J. Neuroradiol. 1998;19(8):1471–1477. 7. Thulborn KR, Sorensen AG, Kowall NW, McKee A, Lai A, McKinstry RC, Moore J, Rosen BR, Brady TJ. The role of ferritin and hemosiderin in the MR appearance of cerebral hemorrhage: a histopathologic biochemical study in rats. AJNR Am. J. Neuroradiol. 1990;11:291–297. 8. Thulborn KR, Sorensen AG, Kowall NW, McKee A, Lai A, McKinstry RC, Moore J, Rosen BR, Brady TJ. The role of ferritin and hemosiderin in the MR appearance of cerebral hemorrhage: a histopathologic biochemical study in rats. AJNR Am. J. Neuroradiol. 1990 Mar–Apr;11 (2):291–297. 9. Atlas SW, Thulborn KR. MR detection of hyperacute parenchymal hemorrhage of the brain. AJNR Am. J. Neuroradiol. 1998;19(8):1471–1477.

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10. Nakamura T, Keep RF, Hua Y, Schallert T, Hoff JT, Xi G. Deferoxamine-induced attenuation of brain edema and neurological deficits in a rat model of intracerebral hemorrhage. Neurosurg. Focus 2003;15(4):ECP4. 11. Barkley JM, Morales D, Hayman LA, Diaz-Marchan PJ. Static neuroimaging in the evaluation of TBI. In: Zasler ND, Katz DI, Zafonte RD, editors. Brain Injury Medicine. Principles and Practice, Demos, New York, 2007. 12. Gould DB, Phalan FC, Breedveld GJ, van Mil SE, Smith RS, Schimenti JC, Aguglia U, van der Knaap MS, Heutink P, John SW. Mutations in Col4a1 cause perinatal cerebral hemorrhage and porencephaly. Science 2005;308(5725):1167–1171.

36 Ultrashort TE Imaging: Phase and Frequency Mapping of Susceptibility Effects in Short T2 Tissues of the Musculoskeletal System Jiang Du, Michael Carl, and Graeme M. Bydder

INTRODUCTION The human body contains many tissues with relatively long T2 relaxation components that can be visualized with conventional magnetic resonance imaging (MRI) techniques, as well as a smaller number of tissues with predominantly short T2 components such as menisci, ligaments, tendons, entheses, and cortical and trabecular bones. Usually, these tissues display little or no signal and cannot be visualized directly with conventional sequences [1]. MR signal from these tissues decays to low or very low levels before the receive mode of conventional clinical MR systems is enabled and data collection is completed, so that the signal cannot be spatially encoded usefully. One approach to detecting short NMR T2 signals is the use of ultrashort echo time (UTE) imaging sequences [1–4]. A typical two-dimensional (2D) UTE sequence employs a half-pulse radiofrequency (RF) excitation followed by radial ramp sampling of the free induction decay (FID). A complete slice profile is generated by collecting the data with the slice selection gradient in one polarity and adding this to the data collected with the

Susceptibility Weighted Imaging in MRI, By E. Mark Haacke and J€urgen R. Reichenbach Copyright
2011 by Wiley-Blackwell

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slice selection gradient polarity reversed. Using this approach, no refocusing gradient is required for 2D slice selective UTE imaging. As a result, the UTE sequence nominal TE can be reduced to less than 100 ms, making it possible to directly image short T2 tissues in the human body using clinical systems. The bulk susceptibility effect of water confined in the collagen extracellular matrix of tendons, ligaments, and menisci or the spaces of the haversian and lacuno-canalicular system in cortical bone can lead to local magnetic field variation, and thus off-resonance frequency shifts, voff [5–8]. The frequency shift is orientation dependent [9], and may result in different levels of phase accumulation in different tissues depending on their fiber orientation and water binding status. The phase evolution resulting from these frequency shifts may be used to create images of short T2 species in the form of UTE phase imaging. In addition, frequency differences can be mapped using UTE spectroscopic imaging (UTESI). Both techniques can produce high-contrast images of short T2 tissues resulting from susceptibility differences.

UTE PHASE IMAGING UTE imaging of short T2 tissues is usually achieved by acquiring the FID of the MR signal as soon as possible (e.g., beginning 8 ms after the end of the RF pulse). Despite the minuscule nominal TE, surprisingly high phase contrast can be achieved with this technique. The theoretical background and the experimental evaluation of UTE phase imaging are described below. With a standard gradient recalled echo (GRE) sequence TE is a well-defined quantity, starting at the center of the RF pulse and ending at the center of the data acquisition (DAQ) window where k ¼ 0 (Figure 36.1a). For typical phase imaging (as in the brain and in most other parts of body), TE is chosen to be from about 10 to 40 ms depending on the field strength, tissue T2, artifact level, and so on [10]. Phase evolution during the durations of the RF pulse (TRF) and data acquisition (TDAQ), which are each only of the order of a few milliseconds and are partly included in the usual definition of TE, generally can be ignored in this situation. Therefore, the phase evolution during a GRE sequence (FTE) of a spin with off-resonance frequency voff ¼ 2
foff is given by FTE ¼ 2
foff TE

ð36:1Þ

FIGURE 36.1 (a) GRE pulse sequence: TE is defined from the center of the RF pulse to the center of the data acquisition (k ¼ 0). (b) UTE pulse sequence: The nominal TE is defined as the time from the end of the RF pulse to the beginning of the data acquisition (k ¼ 0).

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671

With a typical 2D UTE sequence diagram shown in Figure 36.1b, the nominal TE is defined as the time from the end of the RF pulse to the beginning of the data acquisition (k ¼ 0). By using equation (36.1), with a nominal TE of 8 ms, for example, little or no phase evolution or phase contrast would be expected; however, with a UTE sequence the nominal TE does not include the phase evolution during excitation or readout, and the phase accrual during the RF pulse (FRF) and the data acquisition (FDAQ) needs to be included. The overall phase in the final MR image therefore contains contributions from all three periods, namely, that of the RF pulse, the TE, and the duration of the data acquisition so that F ¼ FRF þ FTE þ FDAQ ¼ FRF þ voff TE þ FDAQ

ð36:2Þ

Two of these phase evolutions occur outside of the nominal TE commonly used to describe UTE sequences. Phase Evolution During the RF Pulse The phase evolution during the RF pulse is readily determined using Bloch equation simulations; however, following two particular cases can be calculated analytically: 1. A nonselective hard RF pulse at an arbitrary flip angle. 2. A shaped RF pulse in the domain where the small tip angle approximation is valid. Nonselective Hard Pulse Case Using Bloch equations, one can derive an expression for the three spatial components of the magnetization vector, tipped into the transverse plane by a hard RF pulse of duration t and amplitude v1 ¼ gB1 (see Appendix 36.A): voff v1 ½cosðv2 tÞ1 v22 v1 My ðtÞ ¼ M0 sinðv2 tÞ v2  1
Mz ðtÞ ¼ M0 2 v21 cosðv2 tÞ þ v2off v2 Mx ðtÞ ¼ M0

ð36:3Þ

pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi where v2 ¼ v21 þ v2off . The in-plane phase of the transverse magnetization can be calculated as follows:     Mx voff ½cosðv2 tÞ1 FðtÞ ¼ atan ¼ atan ð36:4Þ v2 sinðv2 tÞ My Shaped Pulse Case The solution for an arbitrary shaped pulse is more complicated, but can readily be solved for the small tip angle approximation. The differential equation for the complex magnetization M ¼ Mx þ iMy during an arbitrary RF pulse B1(t) and slice selection gradient G(t) in the small tip angle approximation is given by [11] dM þ ivz M ¼ iv1 M0 dt

ð36:5Þ

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ULTRASHORT TE IMAGING

where vz ðt; zÞ ¼ gGðtÞzvoff . Equation (36.5) can be solved with an integration factor uðtÞ ¼ e

Ð

i vz ds

ð36:6Þ

resulting in the following solution: Mðt; zÞ ¼ iM0 e

i

Ðt

vz dt

ðt v1 ðtÞe

0

i

Ðt 0

vz ds

ð36:7Þ

dt

0

With 2D UTE sequences, slice-selective excitation is repeated twice (in separate TRs), with the slice selection gradient reversed (G ! G), and the complex data obtained after the excitations are added to generate the final slice profile: 0 Ðt Ðt ðt i ðgGðsÞz þ voff Þds M0 @ i 0 ðgGðtÞz þ voff Þdt e Mðt; zÞ ¼ i v1 ðtÞe 0 dt 2 0

Ð

t

þe

i

ðgGðtÞz þ voff Þdt

ðt v1 ðtÞe

0

i

Ðt 0

!

ðgGðsÞz þ voff Þds

dt

ð36:8Þ

0

The phase angle of the transverse magnetization at the center of the slice (z ¼ 0) reduces to 8t 9