Medical Imaging 9781119785392, 1119785391

Table of contents :
Cover
Title Page
Copyright Page
Contents
Preface
Acknowledgements
Chapter 1 Introduction to Medical Imaging
1.1 Medical Imaging – An Insight
1.2 Types of Diagnostic Imaging Modalities
1.2.1 Radiography
1.2.2 Tomography
1.2.3 Ultrasound
1.2.4 Nuclear Medicine
1.2.5 Magnetic Resonance Imaging
1.2.6 Functional Magnetic Resonance Imaging (fMRI)
1.2.7 Functional Near Infrared Imaging
1.2.8 Elastography
1.2.9 Photoacoustic Imaging
1.2.10 Magnetic Particle Imaging
1.3 3D Rendering
1.4 Diagnostic Images
1.5 Medical Imaging in Pharmaceutical Applications
Glossary-Appendix
Chapter 2 Fundamentals of X-Rays
2.1 Electromagnetic Radiations
2.2 Wave Nature
2.2.1 Particle Nature
2.2.2 Intensity of an X-Ray Beam
2.2.3 Roentgen (R)
2.2.4 Radiation Absorbed Dose (rad)
2.2.5 X-Ray Interactions
2.2.6 Interaction Between X-Ray and Matter
2.2.7 Coherent Scattering
2.2.8 Compton Effect
2.3 Photoelectric Effect
2.3.1 Pair Production
2.3.2 Photodisintegration
2.4 Interaction Between X-Ray and Tissues
2.5 Factors Affecting Attenuation Coefficients
2.6 Attenuation Due to Coherent Scattering (βcoh)
2.7 Attenuation Due to Compton Scattering (βcom) and Photoelectric Effect (βpho)
2.8 Generation and Detection of X-Rays
2.8.1 Generation of X-Rays
2.8.2 White Radiation
2.8.3 Characteristic Radiation
2.9 X-Ray Generators
2.9.1 Line Focus Principle
2.9.2 X-Ray Tube Ratings
2.9.3 Target Material
2.9.4 Tube Voltage
2.9.5 Tube Current
2.9.6 Filament Current
2.10 Filters
2.10.1 Beam Restrictors
2.10.2 Aperture Diaphragms
2.10.3 Cones and Cylinders
2.10.4 Collimators
2.10.5 Grids
2.11 X-Ray Visualization
2.11.1 Intensifying Screens
2.11.2 Image Intensifiers
2.12 Detection of X-Rays
2.12.1 X-Ray Film
2.12.2 Optical Density
2.12.3 Characteristic Curve
2.12.4 Film Gamma
2.12.5 Speed
2.12.6 Film Latitude
2.12.7 Double-Emulsion Film
2.13 Radiation Detectors
2.13.1 Scintillation Detector
2.13.2 Ionization Chamber
2.14 X-Ray Diagnostic Approaches
2.14.1 Conventional X-Ray Radiography
2.14.2 Penumbra
2.14.3 Field Size
2.14.4 Film Magnification
2.15 Fluoroscopy
2.16 Angiography
2.17 Mammography
2.18 Xeroradiography
2.19 Image Subtraction
2.19.1 Digital Subtraction Angiography (DSA)
2.19.2 Dual Energy Subtraction
2.19.3 K-Edge Subtraction
2.20 Conventional Tomography
2.20.1 X-Ray Image Attributes
2.20.2 Spatial Resolution
2.21 Point Spread Function (PSF)
2.21.1 Line Spread Function (LSF)
2.21.2 Edge Spread Function (ESF)
2.21.3 System Transfer Function (STF)
2.22 Image Noise
2.23 Image Contrast
2.24 Receiver Operating Curve (ROC)
2.25 Biological Effects of X-Ray Radiations
2.25.1 Determinants of Biological Effects
Glossary-Appendix
Chapter 3 X-Ray Computed Tomography
3.1 Introduction to X-Ray Computed Tomography
3.2 CT Number
3.3 X-Ray Detectors in CT Machines
3.3.1 Energy Integrating Detectors
3.3.2 Photon Counting Detectors
3.4 CT Imaging
3.4.1 Radon Transform
3.4.2 Sampling
3.4.3 2D Image Reconstruction
3.4.4 Direct Fourier Transform
3.4.5 Filtered Back Projection (FBP)/Convolution Back Projection (CBP)
3.4.6 Fan Beam Projections
3.5 Computer Tomography-Based Diagnostics
3.5.1 Single Slice Computed Tomography
3.5.2 Multislice Computed Tomography
3.5.3 Cardiac CT
3.5.4 Dual Energy Computer Tomography
3.6 Image Quality
3.6.1 Resolution
3.6.2 Noise
3.6.3 Contrast
3.6.4 Image Artifacts
3.7 CT Machine – The Hardware Aspects
3.8 Generations of CT Machines
3.9 Biological Effects and Safety-Based Aspects
Glossary-Appendix
Chapter 4 Ultrasound Imaging
4.0 Ultrasound
4.1 Basics of Acoustic Waves
4.2 Propagation of Waves in Homogeneous Media
4.3 Linear Wave Equation
4.4 Loudness and Intensity
4.5 Interference
4.6 Attenuation
4.7 Nonlinearity
4.8 Propagation of Waves in Non-Homogeneous Media
4.9 Reflection and Refraction
4.10 Scattering
4.11 Doppler Effect in the Propagation of the Acoustic Wave
4.12 Generation and Detection of Ultrasound
4.13 Ultrasonic Transducer
4.14 Mechanical Matching
4.15 Electrical Matching
4.16 Ultrasound Imaging
4.16.1 Gray Scale Imaging
4.16.1.1 Data Acquisition
4.16.1.2 Amplitude Mode (A-Mode)
4.16.1.3 Brightness Mode (B-Mode)
4.16.1.4 Motion Mode (M-Mode)
4.17 Image Reconstruction
4.18 Schlieren System
4.19 Doppler Imaging Approaches
4.19.1 Continuous Wave Doppler System
4.19.2 Pulse Wave Doppler System
4.19.3 Color Doppler Flow Imaging
4.20 Tissue Characterization
4.20.1 Velocity
4.20.2 Absorption
4.20.3 Scattering
4.21 Ultrasound Image Characteristics
4.21.1 Spatial Resolution
4.21.2 Image Contrast
4.21.3 Ultrasonic Texture
4.22 Biological Effects of Ultrasound
4.22.1 Acoustic Aspects at High Intensity Levels
4.22.2 Cavitation
4.22.3 Transient Cavitation
4.22.4 Stable Cavitation
4.22.5 Wave Distortion
4.22.6 Bioeffects (Thermal and Non-Thermal Effects)
Glossary-Appendix
Chapter 5 Radionuclide Imaging
5.1 Radionuclide Imaging – A Brief History
5.2 An Insight Into Radioactivity
5.2.1 Nuclear Particles
5.2.2 Radioactive Decay
5.2.3 Specific Activity
5.2.4 Interactions Between Nuclear Particles and Matter
5.2.4.1 Alpha Particles
5.2.4.2 Beta Particles
5.2.4.3 Gamma Particles
5.2.5 Properties of Radionuclides
5.2.5.1 Physical Properties
5.2.5.2 Biological Properties
5.3 Generation of Nuclear Emission
5.3.1 Nuclear Sources
5.3.2 99mTc Radionuclide Generator
5.3.3 Detection of Nuclear Emissions
5.3.3.1 Ion Collection Detectors
5.3.3.2 Scintillation Fetectors
5.3.3.3 Solid State Detectors
5.3.3.4 Collimator
5.4 Radionuclide Detection
5.4.1 Rectilinear Scanning Machines
5.4.2 Scintillation Camera (Gamma Camera)
5.4.2.1 Collimator
5.4.2.2 Scintillation Crystal
5.4.2.3 Photomultiplier Tube
5.4.3 Longitudinal Section Tomography (LST)
5.4.4 Single Photon Emission Computer Tomography (SPECT)
5.4.5 Positron Emission Tomography (PET)
5.5 Diagnostic Approaches Using Radiation Detector Probes
5.5.1 Thyroid Function Assessment
5.5.2 Renal Function Test
5.5.3 Blood Volume Assessment
5.6 Radionuclide Image Characteristics
5.6.1 Spatial Resolution
5.6.2 Image Contrast
5.6.3 Image Noise
5.7 Biological Effects of Radionuclides
Glossary-Appendix
Chapter 6 Magnetic Resonance Imaging
6.1 Basics of Nuclear Magnetic Resonance
6.2 Larmor Frequency
6.3 Relaxation
6.3.1 T1 (Longitudinal Relaxation)
6.3.2 T2 (Transverse Relaxation)
6.4 Image Contrast
6.5 Repetition Time (TR) and T1 Weighting
6.6 Echo Time (TE) and T2 Weighting
6.7 Saturation at Short Repetition Times
6.8 Flip Angle/Tip Angle
6.9 Presaturation
6.10 Magnetization Transfer
6.11 Slice Selection
6.12 Spatial Encoding
6.13 Phase Encoding
6.14 Frequency Encoding
6.15 K-Space
6.16 Image Noise
6.17 The MR Scanning Machine
6.17.1 The Magnet
6.17.2 Permanent Magnet
6.17.3 Resistive Magnets
6.17.4 Superconducting Magnets
6.17.5 Quenching
6.17.6 Shimming
6.17.7 Shielding
6.17.8 The Gradient System
6.17.9 The Radiofrequency System
6.17.10 The Computer System
6.18 Pulse Sequences
6.18.1 Spin Echo Sequence
6.18.1.1 Black Blood Effect
6.18.2 Inversion Recovery Sequence
6.18.3 Short TI Inversion Recovery (STIR) Sequences
6.18.4 Fluid Attenuated Recovery (FLAIR) Sequences
6.18.5 Gradient Echo Sequence
6.19 Parallel Imaging
6.20 MR Artifacts
6.21 Motion Artifacts
6.22 Flow Artifacts
6.23 Phase Wrapping
6.24 Chemical Shift
6.25 Magnetic Susceptibility
6.26 Truncation Artifact
6.27 Magic Angle
6.28 Eddy Currents
6.29 Partial Volume Artifact
6.30 Inhomogeneous Fat Suppression
6.31 Zipper Artifacts
6.32 Crisscross Artifact
6.33 Bioeffects and Safety
Glossary-Appendix
About the Authors
Index
EULA

Citation preview

Medical Imaging

Scrivener Publishing 100 Cummings Center, Suite 541J Beverly, MA 01915-6106 Publishers at Scrivener Martin Scrivener ([email protected]) Phillip Carmical ([email protected])

Medical Imaging

H. S. Sanjay and

M. Niranjanamurthy

This edition first published 2023 by John Wiley & Sons, Inc., 111 River Street, Hoboken, NJ 07030, USA and Scrivener Publishing LLC, 100 Cummings Center, Suite 541J, Beverly, MA 01915, USA © 2023 Scrivener Publishing LLC For more information about Scrivener publications please visit www.scrivenerpublishing.com. All rights reserved. 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, or otherwise, except as permitted by law. Advice on how to obtain permission to reuse material from this title is available at http://www.wiley.com/go/permissions. Wiley Global Headquarters 111 River Street, Hoboken, NJ 07030, USA For details of our global editorial offices, customer services, and more information about Wiley products visit us at www.wiley.com. Limit of Liability/Disclaimer of Warranty While the publisher and authors have used their best efforts in preparing this work, they make no rep­ resentations or warranties with respect to the accuracy or completeness of the contents of this work and specifically disclaim all warranties, including without limitation any implied warranties of merchant-­ ability or fitness for a particular purpose. No warranty may be created or extended by sales representa­ tives, written sales materials, or promotional statements for this work. The fact that an organization, website, or product is referred to in this work as a citation and/or potential source of further informa­ tion does not mean that the publisher and authors endorse the information or services the organiza­ tion, website, or product may provide or recommendations it may make. This work is sold with the understanding that the publisher is not engaged in rendering professional services. The advice and strategies contained herein may not be suitable for your situation. You should consult with a specialist where appropriate. Neither the publisher nor authors shall be liable for any loss of profit or any other commercial damages, including but not limited to special, incidental, consequential, or other damages. Further, readers should be aware that websites listed in this work may have changed or disappeared between when this work was written and when it is read. Library of Congress Cataloging-in-Publication Data ISBN 9781119785392 Front cover images supplied by Wikimedia Commons Cover design by Russell Richardson Set in size of 11pt and Minion Pro by Manila Typesetting Company, Makati, Philippines Printed in the USA 10 9 8 7 6 5 4 3 2 1

Contents Preface xiii Acknowledgements xv 1 Introduction to Medical Imaging 1.1 Medical Imaging – An Insight 1.2 Types of Diagnostic Imaging Modalities 1.2.1 Radiography 1.2.2 Tomography 1.2.3 Ultrasound 1.2.4 Nuclear Medicine 1.2.5 Magnetic Resonance Imaging 1.2.6 Functional Magnetic Resonance Imaging (fMRI) 1.2.7 Functional Near Infrared Imaging 1.2.8 Elastography 1.2.9 Photoacoustic Imaging 1.2.10 Magnetic Particle Imaging 1.3 3D Rendering 1.4 Diagnostic Images 1.5 Medical Imaging in Pharmaceutical Applications Glossary-Appendix

1 1 2 2 4 6 9 14 16 18 19 20 22 23 23 23 26

2 Fundamentals of X-Rays 2.1 Electromagnetic Radiations 2.2 Wave Nature 2.2.1 Particle Nature 2.2.2 Intensity of an X-Ray Beam 2.2.3 Roentgen (R) 2.2.4 Radiation Absorbed Dose (rad) 2.2.5 X-Ray Interactions 2.2.6 Interaction Between X-Ray and Matter 2.2.7 Coherent Scattering

27 27 28 30 30 31 31 31 31 32 v

vi  Contents 2.2.8 Compton Effect 32 2.3 Photoelectric Effect 34 2.3.1 Pair Production 35 2.3.2 Photodisintegration 36 2.4 Interaction Between X-Ray and Tissues 36 2.5 Factors Affecting Attenuation Coefficients 38 2.6 Attenuation Due to Coherent Scattering (βcoh) 39 2.7 Attenuation Due to Compton Scattering (βcom) and Photoelectric Effect (βpho) 39 2.8 Generation and Detection of X-Rays 41 2.8.1 Generation of X-Rays 41 2.8.2 White Radiation 41 2.8.3 Characteristic Radiation 42 2.9 X-Ray Generators 42 2.9.1 Line Focus Principle 43 2.9.2 X-Ray Tube Ratings 45 2.9.3 Target Material 46 2.9.4 Tube Voltage 46 2.9.5 Tube Current 46 2.9.6 Filament Current 46 2.10 Filters 47 2.10.1 Beam Restrictors 47 2.10.2 Aperture Diaphragms 48 2.10.3 Cones and Cylinders 49 2.10.4 Collimators 49 2.10.5 Grids 50 2.11 X-Ray Visualization 51 2.11.1 Intensifying Screens 51 2.11.2 Image Intensifiers 53 2.12 Detection of X-Rays 54 2.12.1 X-Ray Film 55 2.12.2 Optical Density 55 2.12.3 Characteristic Curve 56 2.12.4 Film Gamma 57 2.12.5 Speed 57 2.12.6 Film Latitude 59 2.12.7 Double-Emulsion Film 60 2.13 Radiation Detectors 60 2.13.1 Scintillation Detector 60 2.13.2 Ionization Chamber 61 2.14 X-Ray Diagnostic Approaches 62

Contents  vii 2.14.1 Conventional X-Ray Radiography 62 2.14.2 Penumbra 63 2.14.3 Field Size 64 2.14.4 Film Magnification 65 2.15 Fluoroscopy 66 2.16 Angiography 67 2.17 Mammography 68 2.18 Xeroradiography 68 2.19 Image Subtraction 69 2.19.1 Digital Subtraction Angiography (DSA) 70 2.19.2 Dual Energy Subtraction 71 2.19.3 K-Edge Subtraction 72 2.20 Conventional Tomography 73 2.20.1 X-Ray Image Attributes 74 2.20.2 Spatial Resolution 74 2.21 Point Spread Function (PSF) 75 2.21.1 Line Spread Function (LSF) 75 2.21.2 Edge Spread Function (ESF) 76 2.21.3 System Transfer Function (STF) 76 2.22 Image Noise 77 2.23 Image Contrast 78 2.24 Receiver Operating Curve (ROC) 79 2.25 Biological Effects of X-Ray Radiations  79 2.25.1 Determinants of Biological Effects 79 Glossary-Appendix 82 3 X-Ray Computed Tomography 3.1 Introduction to X-Ray Computed Tomography 3.2 CT Number 3.3 X-Ray Detectors in CT Machines 3.3.1 Energy Integrating Detectors 3.3.2 Photon Counting Detectors 3.4 CT Imaging 3.4.1 Radon Transform 3.4.2 Sampling 3.4.3 2D Image Reconstruction 3.4.4 Direct Fourier Transform 3.4.5 Filtered Back Projection (FBP)/Convolution Back Projection (CBP) 3.4.6 Fan Beam Projections 3.5 Computer Tomography-Based Diagnostics

85 85 87 88 88 88 89 89 92 94 97 98 101 104

viii  Contents 3.5.1 Single Slice Computed Tomography 3.5.2 Multislice Computed Tomography 3.5.3 Cardiac CT 3.5.4 Dual Energy Computer Tomography 3.6 Image Quality 3.6.1 Resolution 3.6.2 Noise 3.6.3 Contrast 3.6.4 Image Artifacts 3.7 CT Machine – The Hardware Aspects 3.8 Generations of CT Machines 3.9 Biological Effects and Safety-Based Aspects Glossary-Appendix 4 Ultrasound Imaging 4.0 Ultrasound 4.1 Basics of Acoustic Waves 4.2 Propagation of Waves in Homogeneous Media 4.3 Linear Wave Equation 4.4 Loudness and Intensity 4.5 Interference 4.6 Attenuation 4.7 Nonlinearity 4.8 Propagation of Waves in Non-Homogeneous Media 4.9 Reflection and Refraction 4.10 Scattering 4.11 Doppler Effect in the Propagation of the Acoustic Wave 4.12 Generation and Detection of Ultrasound 4.13 Ultrasonic Transducer 4.14 Mechanical Matching 4.15 Electrical Matching 4.16 Ultrasound Imaging 4.16.1 Gray Scale Imaging 4.16.1.1 Data Acquisition 4.16.1.2 Amplitude Mode (A-Mode) 4.16.1.3 Brightness Mode (B-Mode) 4.16.1.4 Motion Mode (M-Mode) 4.17 Image Reconstruction 4.18 Schlieren System 4.19 Doppler Imaging Approaches 4.19.1 Continuous Wave Doppler System

104 105 106 106 107 107 108 108 108 110 112 118 118 121 121 121 122 122 123 124 125 126 127 127 129 130 133 134 135 136 136 136 136 136 138 140 140 141 141 142

Contents  ix 4.19.2 Pulse Wave Doppler System 4.19.3 Color Doppler Flow Imaging 4.20 Tissue Characterization 4.20.1 Velocity 4.20.2 Absorption 4.20.3 Scattering 4.21 Ultrasound Image Characteristics 4.21.1 Spatial Resolution 4.21.2 Image Contrast 4.21.3 Ultrasonic Texture 4.22 Biological Effects of Ultrasound 4.22.1 Acoustic Aspects at High Intensity Levels 4.22.2 Cavitation 4.22.3 Transient Cavitation 4.22.4 Stable Cavitation 4.22.5 Wave Distortion 4.22.6 Bioeffects (Thermal and Non-Thermal Effects) Glossary-Appendix

142 143 144 145 145 145 146 146 146 146 147 147 147 147 147 147 147 148

5 Radionuclide Imaging 5.1 Radionuclide Imaging – A Brief History 5.2 An Insight Into Radioactivity 5.2.1 Nuclear Particles 5.2.2 Radioactive Decay 5.2.3 Specific Activity 5.2.4 Interactions Between Nuclear Particles and Matter 5.2.4.1 Alpha Particles 5.2.4.2 Beta Particles 5.2.4.3 Gamma Particles 5.2.5 Properties of Radionuclides 5.2.5.1 Physical Properties 5.2.5.2 Biological Properties 5.3 Generation of Nuclear Emission 5.3.1 Nuclear Sources 5.3.2 99mTc Radionuclide Generator 5.3.3 Detection of Nuclear Emissions 5.3.3.1 Ion Collection Detectors 5.3.3.2 Scintillation Fetectors 5.3.3.3 Solid State Detectors 5.3.3.4 Collimator 5.4 Radionuclide Detection

151 151 152 152 153 154 155 155 156 156 157 157 158 159 159 159 160 161 162 164 164 166

x  Contents 5.4.1 Rectilinear Scanning Machines 166 5.4.2 Scintillation Camera (Gamma Camera) 167 5.4.2.1 Collimator 167 5.4.2.2 Scintillation Crystal 168 5.4.2.3 Photomultiplier Tube 168 5.4.3 Longitudinal Section Tomography (LST) 170 5.4.4 Single Photon Emission Computer Tomography (SPECT) 171 5.4.5 Positron Emission Tomography (PET) 173 5.5 Diagnostic Approaches Using Radiation Detector Probes 174 5.5.1 Thyroid Function Assessment 175 5.5.2 Renal Function Test 175 5.5.3 Blood Volume Assessment 175 5.6 Radionuclide Image Characteristics 175 5.6.1 Spatial Resolution 175 5.6.2 Image Contrast 176 5.6.3 Image Noise 176 5.7 Biological Effects of Radionuclides 176 Glossary-Appendix 177 6 Magnetic Resonance Imaging 6.1 Basics of Nuclear Magnetic Resonance 6.2 Larmor Frequency 6.3 Relaxation 6.3.1 T1 (Longitudinal Relaxation) 6.3.2 T2 (Transverse Relaxation) 6.4 Image Contrast 6.5 Repetition Time (TR) and T1 Weighting 6.6 Echo Time (TE) and T2 Weighting 6.7 Saturation at Short Repetition Times 6.8 Flip Angle/Tip Angle 6.9 Presaturation 6.10 Magnetization Transfer 6.11 Slice Selection 6.12 Spatial Encoding 6.13 Phase Encoding 6.14 Frequency Encoding 6.15 K-Space 6.16 Image Noise 6.17 The MR Scanning Machine 6.17.1 The Magnet

179 179 182 185 185 186 188 188 189 191 192 192 192 193 196 196 197 198 199 201 202

Contents  xi 6.17.2 Permanent Magnet 6.17.3 Resistive Magnets 6.17.4 Superconducting Magnets 6.17.5 Quenching 6.17.6 Shimming 6.17.7 Shielding 6.17.8 The Gradient System 6.17.9 The Radiofrequency System 6.17.10 The Computer System 6.18 Pulse Sequences 6.18.1 Spin Echo Sequence 6.18.1.1 Black Blood Effect 6.18.2 Inversion Recovery Sequence 6.18.3 Short TI Inversion Recovery (STIR) Sequences 6.18.4 Fluid Attenuated Recovery (FLAIR) Sequences 6.18.5 Gradient Echo Sequence 6.19 Parallel Imaging 6.20 MR Artifacts 6.21 Motion Artifacts 6.22 Flow Artifacts 6.23 Phase Wrapping 6.24 Chemical Shift 6.25 Magnetic Susceptibility 6.26 Truncation Artifact 6.27 Magic Angle 6.28 Eddy Currents 6.29 Partial Volume Artifact 6.30 Inhomogeneous Fat Suppression 6.31 Zipper Artifacts 6.32 Crisscross Artifact 6.33 Bioeffects and Safety Glossary-Appendix About the Authors

202 202 202 202 203 203 203 204 204 204 205 206 206 207 207 207 209 210 211 211 211 212 213 213 213 214 214 214 214 215 215 215 219

Index 221

Preface I extend my warm greetings to all the readers of this book. I am mighty pleased to place before you the first edition of the textbook “Medical Imaging – Principles and applications,” written for graduate-level students in Biomedical Engineering and Instrumentation oriented domains. This book provides a comprehensive approach in terms of the functional aspects of diagnostic imaging systems. A strong emphasis is placed on the concept and the principle of working of various equipment along with practical applications and the recent advancements in the field of the medical image-based diagnosis process. The first chapter provides an introduction to various diagnostic imaging systems and modalities. The second chapter explains the basic principle and physics behind the generation of X-ray waves and also highlights the various imaging modalities based on X-rays and their salient aspects. This also emphasizes the shortfalls of X-ray imaging systems. The third chapter highlights the mathematics of computed tomography, based on radiographic X-ray images. This also describes the process of image reconstruction using various algorithms and approaches. This chapter concludes by elaborating on the advantages of computed tomography-based approaches, as compared to conventional X-ray imaging. The fourth chapter describes the principles of ultrasound waves and the physics behind the formation of ultrasound images. The various modes of ultrasound imaging and their salient features are highlighted as well. The fifth chapter explains the physics of radioactivity as well as the image formation in the case of radionuclide imaging systems. Various approaches for the detection of radioactivity are highlighted as well. Chapter six describes the basics of magnetic resonance and the formation of magnetic resonance images. This also explains the important aspects of MRI imaging modality and their advantages.

xiii

Acknowledgements Writing “Medical Imaging – Principles and applications” has indeed been a fantastic experience for me as an author. There are many individuals who deserve a mention in this section. I believe I have been able to write this book only because of the Almighty who is omnipresent and, in every form possible, has been there for me as my GURU. It is this great energy, in the form of my guide, teachers, well-wishers, friends, relatives and family, that has always helped me come out of every crisis in life and is the sole reason for the successful completion of my research work. I extend my acknowledgments to this GURU who has been by my side in the form of the amazing individuals mentioned below. I am thankful to the management of M S Ramaiah Institute of Technology, Sri B S Ramprasad (Hon Chief Executive, GEF), Dr. N V R Naidu (Principal), Dr. C K Narayanappa (HOD – Department of Medical Electronics Engineering) and Dr. N Sriraam (Head – R&D) for the constant encouragement. I am indebted to Dr. K R Phaneesh (Professor – Dept of Mechanical Engineering) and Dr. Kiran Kumar (Director – Physical education) for their advice and support. I wish to thank all my colleagues for having supported me through my professional journey at the college. I wish to express my respects to Dr. Bhargavi (Professor, Dept. of Electronics & Communication Engineering, SJC Institute of Technology, Chickballapura, India), my research supervisor during my doctoral course. I also thank Dr. Ramesh R Galigekere, my teacher during my post-­ graduation course who instigated the urge in me to learn the concepts of medical imaging and has always been the guiding light during the journey of my learning. I will fail in my duties if I do not mention the students of M S Ramaiah Institute of Technology who have always supported me in my writing of this book. Dattatreya M D, Nanakishor M D, Aishwarya M, Vishnu Prasad R, Rachana M and Pavitra have helped me with formatting and revisions. I extend my regards to Karthik M. P., Suraj K. K., Samyuktha Suresh Iyer

xv

xvi  Acknowledgements and Prakhya Vasudevan for having been my friends more than students in this fantastic profession of teaching and research. I wish to thank my friends, Suhas V Chebbi, Karthik Subramanian and Dr Subramanya Bhaskar for having believed in me and for always encouraging me to write down all that I used to understand while reading. It is these pieces of notes that have finally culminated in a book today. Finally, I take this opportunity to dedicate this work to the most important people in my life, my father Sri Sudheendra Murthy H. V., mother Smt. Sheela Bai L., brother Sri Sujay H. S. and my wife Smt. Prithvi B. S. It is they who are the reason behind my every achievement. There are no words to thank them and no gesture grand enough to help me express my gratitude to them. These four human beings have always shielded me from any issues and problems in life and have ensured that I concentrated solely on my research work during any given circumstances. All I can say is that without these people, nothing would have been possible with respect to anything in life, let alone this book. Dr. Niranjanamurthy M - I am thankful to the Management, Principal and Department of MCA of M S Ramaiah Institute of Technology, Bangalore, for their continuous support and encouragement.

1 Introduction to Medical Imaging 1.1 Medical Imaging – An Insight As per the World Health Organization, medical imaging is related to the various imaging modalities and connected processes to obtain images from inside the human body, which is extremely useful for diagnostic as well as therapeutic applications. Medical imaging is preferred during a clinical examination for various disorders. It also refers to the process and the protocols involved with the development of visual representation of the anatomical as well as the physiological aspects of the body often useful for diagnostic and therapeutic applications. Different compositions and structures of the muscles and bones are visualized so as to identify any plausible anomalies in the body. The most common aspect of medical imaging is the radiology and hence, medical imaging with respect to clinical applications is termed as radiographic imaging, and the related science of study is called radiology. X-rays, computed tomography, Catheter laboratories, Ultrasound, Positron emission tomography, single photon emission computed tomography, Magnetic resonance imaging, and Functional magnetic resonance imaging are a few examples of radiological imaging principles used for medical diagnosis in the field of medicine. Although there exist numerous approaches to diagnose different pathological aspects in the human body, this book shall be confined to radiological imaging modalities alone. The medical imaging equipment are conventionally equipped with a source which would emanate the signals and a detector to detect the strength of these rays passing through the body or being reflected by the body. Based on predefined information about the nature of the different parts of the body, in terms of the ability to absorb or reflect these rays, an image of the corresponding body is developed. However, with the advent of technology, medical imaging systems have slowly evolved from being mere hardware setup, to a stage driven more by electronics and software-based

H. S. Sanjay and M. Niranjanamurthy. Medical Imaging, (1–26) © 2023 Scrivener Publishing LLC

1

2  Medical Imaging technologies. Modern medicine hence prefers such approaches for better clinical diagnosis as well as treatment. The main advantage of medical imaging is the ability of the equipment to provide a pictorial representation of the internal organs of the body without even accessing the organ, in a noninvasive approach. This makes the medical imaging techniques one of the most preferred approaches for the diagnostics of different anatomical as well as physiological disorders in the human body. Almost every clinician depends on these approaches for diagnostic applications. A large aspect of this is attributed to the mathematical approaches incorporated in the processing of the signals acquired. The observed signal is subjected to different reconstruction algorithms so as to arrive at a meaningful image of the region of interest. Such images provide a plethora of information to the clinician to help plan the line of treatment for different disorders. This makes medical imaging the most important aspect of diagnostic equipment and it is of great demand in the healthcare industry. From a clinical perspective, Visible light-based photographic approaches are useful in the field of dermatology as well as wound care. However, certain equipment use the light from a spectrum which is not visible to the human eye and are often related to radiology, and the images obtained are interpreted by a radiologist, with a medical background. This is called as diagnostic radiology and is often known to be the field of medicine which uses noninvasive imaging approaches for the diagnosis of the health condition of an individual.

1.2 Types of Diagnostic Imaging Modalities While numerous modalities are being used at different levels in the field of diagnostic radiology, this book shall be confined to a few important modalities which are very commonly used in every clinical facility for diagnostic applications. Figure 1.1 below provides a pictorial representation of the different types of medical imaging modalities.

1.2.1 Radiography Radiography is an imaging technique using the properties of X-rays, gamma rays and similar ionizing/non-ionizing radiations so as to obtain a visual description of a given organ. Conventional radiography includes the generation of X-rays by a suitable X-ray source and projected towards the body. This was the first-ever approach in modern science to image the

Introduction to Medical Imaging  3 Medical Imaging Modalities Structural MRI T1weighted T2weighted Proton Density

Functional CT Structural CT

MRI

CT

US

CE-MRI

CE-CT

4D MRI

Dynamic CE-CT

PET

SPECT

Diffusion MRI

MRA fMRI Perfusion MRI Tagged MRI MRS

Figure 1.1  Types of medical imaging modalities (Categories of medical image modalities based on the type of information that they provide about the organ being imaged Source: https://www.researchgate.net/publication/260124237_Developing_Advanced_ Mathematical_Models_for_Detecting_Abnormalities_in_2D3D_Medical_Structures/ figures?lo=1

body part using noninvasive approaches. Some quantity of these X-rays are absorbed by the body, based on the structure and density of the body. The rest of the X-rays pass through the body and are detected by a detector placed behind the body. Detectors can either be photographic or digital in operation. In the case of photographic detectors, commonly called as films, these X-rays would create an image called the X-ray image highlighting the structural aspects of the region of interest. In the case of digital detectors, the X-rays detected are transformed into signals and processed for further applications. There are two approaches in radiography, projection radiography and fluoroscopy. While projection-based approaches are used for conventional diagnostic imaging, fluoroscopy is more of a catheter guidance-based system. Of late, 3D volumetric reconstruction techniques have been successful in the provision of a better insight into the region of interest. However, 2D scans are still common due to cost effectiveness and resolution.

4  Medical Imaging Conventional projection radiography, known as X-ray imaging, is used to visualize the hard structures of the human body, specifically, bone fractures. With the usage of contrast agents such as those of barium, X-ray imaging is also useful in applications such as the diagnosis of ulcer and certain types of cancers. Shown in Figure 1.2 below are the pictorial representations of the same. Fluoroscopy is useful in the production of real-time images of the internal organs of the body, at a lower intensity of X-rays. Usage of contrast agents make it possible to obtain a visual cue of the organ being probed into. Hence this is extremely useful in image guides procedures which need a constant visual feedback while a medical process such as an angioblast is being performed.

1.2.2 Tomography Tomography refers to the process of obtaining an image of an organ based on the cross sectioning of the same. This involves methods such as those of

Figure 1.2  Mobile X-ray machine (Skanray technologies, SKANMOBILE). Source: https://www.skanray.com/?q=content/skanmobile

Introduction to Medical Imaging  5

Figure 1.3  X-ray image The Antero Posterior X-Ray showing the magnification of heart and widening of the mediastinum. Source: https://iem-student.org/ how-to-read-chest-x-rays/

Figure 1.4  Fluoroscopy system (Discovery IGS 730, GE healthcare). Source: https://www. medicalexpo.com/prod/ge-healthcare/product-70717-647375.html

6  Medical Imaging

Figure 1.5  Fluoroscopy procedure (X-ray Barium enema showing normal colon mucosa. Image Credit: Richman Photo/Shutterstock). Source: https://www.news-medical.net/ health/Fluoroscopy-Procedure.aspx

X-ray computed tomography (CT), Computed Axial Tomography (CAT) and Positron Emission Tomography (PET). CT involves an X-ray source which is used to obtain the X-ray images of the ROI at different angles of projection thereby arriving at multiple X-ray images of the ROI from different angles of view. These images are processed using different tomographic algorithms so as to arrive at a reconstructed imager, which provides a cross sectional view of the ROI. The entire process is software oriented and includes multiple mathematical approaches as well. Figure 1.6 below shows a CT machine and a CT image as well.

1.2.3 Ultrasound Ultrasound imaging in clinical applications incorporates the usage of high-frequency broadband acoustic waves (in the range of Mega Hertz) which are incident on the ROI and are reflected/transmitted and are utilized for the imaging of the corresponding ROI. While the other medical imaging modalities discussed in this chapter are a part of the electromagnetic spectrum of light (light waves) such as X_rays, Gamma rays, etc., ultrasound is the only modality which is sound based and not light

Introduction to Medical Imaging  7

Figure 1.6  CT machine (GE Optima CT 660) (128 slice full body tomography CT scanner). Source: https://www.medicalexpo.com/prod/ge-healthcare/product-70717-428667.html

Figure 1.7  CT Image (Normal chest CT – lung window). Source: https://radiopaedia.org/ cases/normal-chest-ct-lung-window-1?lang=us

8  Medical Imaging oriented. Real-time imaging functionality of ultrasound makes it more preferable for the imaging of the fetus, heart, arteries and veins. This does not involve any ionizing radiation and is hence considered to be the safest of all modalities. This makes it a preferable imaging for pregnant women as well. A predefined set of high-frequency sound waves are generated using an ultrasound generator, mostly a piezoelectric crystal and is incident on the ROI. This signal is attenuated as it passes through the ROI and returned at different intervals. The transmission and reflection coefficients of this sound wave are obtained and are used to arrive at an image of the ROI. Ultrasound is safe, quick and easy to perform. However, while all the other modalities are machine dependent (i.e., the more the detector, the better the image), ultrasound is user dependent (i.e., the quality of the image depends on how best the transducer is placed by the user who is obtaining the image from the patient). Doppler-based approaches have made it possible to obtain the blood flow patterns in the blood vessels as well.

Figure 1.8  Ultrasound scanner (GE healthcare LOGIQ S8 ultrasound scanner).

Introduction to Medical Imaging  9

Figure 1.9  Ultrasound scan (Ultrasound image (sonogram) of a fetus in the womb, viewed at 12 weeks of pregnancy (bidimensional scan)). Source: https://en.wikipedia.org/ wiki/Ultrasound

1.2.4 Nuclear Medicine Nuclear medicine, also called as molecular medicine, utilizes the properties of radio isotopes and the particles emitted from radio active materials to diagnose as well as to treat certain pathological conditions by the assessment of physiological variations at the ROI. This is suitable for various oncological diagnosis. Gamma cameras are used to detect the regions of biological activity associated with the pathology. Scintigraphy (gamma scan) involves an oral consumption of the radioisotope and then the capture of the radiations emitted using a gamma camera. SPECT (Single photon emission computed tomography) is a 3D tomographic approach which uses the images obtained from gamma camera, from different projections and then reconstructs an image of the ROI. A dual detector head gamma camera combined with a CT scanner, called the SPECT-CT camera, provides localization of the functional SPECT data. The patient is injected with radio isotope and the radio active gamma rays emitted from these isotopes are captured by the detectors placed around

10  Medical Imaging

Figure 1.10  Scintigraphy machine. (Source: https://en.wikipedia.org/wiki/Scintigraphy)

Rt

Lt

Rt

Lt

Lt

Rt

Lt

Figure 1.11  Bone scintigraphy (diagnosis of bone metastasis). Source: https://www. medscape.com/viewarticle/878516

Rt

Introduction to Medical Imaging  11 the body. Thallium 201TI, Technetium 99mTC, Iodine 123I and Gallium 67Ga are the most commonly used radioisotopes in SPECT. This information of emission is used in combination with CT, which is then called as SPECT-CT. In case of SPECT-CT, the nuclear medicine images are superimposed with CT images to obtain a better view of the ROI, based on the concept of image fusion. Thus the features of the ROI obtained from SPECT as well as CT can be made available to the clinician.

Figure 1.12  SPECT-CT scanner (GE healthcare Optima NM/CT640 SPECT-CT scanner machine). Source: https://www.medgadget.com/2012/06/ges-new-optima-nmct640-spectctsystem.html

(a)

(b)

coronal

sagittal (right lung)

transaxial

(c)

(d)

Figure 1.13  SPECT-CT image (Lung SPECT-CT). Source: https://radiologykey.com/ lung-spectct/

12  Medical Imaging Positron emission tomography (PET) also functions, as similar to CT. But the major difference between a CT and a PET is that PET works on the principle of positron emission. CT is absorption based (absorption of X-rays) while PET is emission based (emission of positron from the body) tomography. PET is often used to assess the degree of tumors in the body. PET is a type of nuclear medicine imaging which uses minor quantity of radioactive materials (radio tracers) to diagnose or evaluate diseases such as cancers, neurological disorders and other abnormalities. This can detect the disease at a very early stage due to the ability of nuclear medicine to ascertain the molecular activity in the body. This is also useful to assess the patient response to a treatment process. Radiotracers are molecules labelled with a minor quantity of radioactive materials which are identifiable on the PET scan. These radiotracers accumulate at the region of tumors and also can bind to specific proteins in the body. The most commonly used radiotracer is the F-18 (Fluoro-de-oxy-glucose or FDG), which is absorbed by the body as similar to that of glucose. Due to the fact that cancerous cells absorb more glucose due to a higher rate of metabolic activity, the F-18 accumulates in a similar fashion, which is detected in the PET scans. The radiotracers are injected, swallowed or inhaled as a gas, as required. Once the radiotracer accumulates at the ROI, a special set of cameras and imaging devices are used to detect the radioactivity (the positrons being emitted) from these radiotracers and in turn, the molecular level information could be obtained. This information of emission is used in combination with CT, which is then called as PET-CT. In the case of

Figure 1.14  PET-CT equipment (GE healthcare – Discovery). Source: https://www. gehealthcare.com/products/molecular-imaging/pet-ct

Introduction to Medical Imaging  13 PET-CT, the nuclear medicine images are superimposed with CT images to obtain a better view of the ROI, based on the concept of image fusion. Thus the features of the ROI obtained from PET as well as CT can be made available to the clinician. The radiotracer (F-18) is manufactured using a separate equipment called the cyclotron which is essential for every PET scan. Cyclotrons are used to prepare radioactive isotopes with short life used for molecular imaging in case of PET scans. Cyclotron accelerates the particles such as those of hydrogen atoms at very high speeds and focuses them on a target substance where the reaction takes place, thereby producing a radioactive element. With regard to the F-18, water enriched with oxygen 18 is used. Oxygen 18 nuclei are targeted with protons accelerated by cyclotron due to which a nuclear reaction is seen which converts oxygen to fluorine 18. The radioactive fluorine 18 is isolated after about three hours of irradiation and then attached to a radiopharmaceutical glucose molecule. Nuclear reactors are used to produce radio-isotopes in large quantities in a cost-effective approach. The neutrons trigger the fission reaction in a target containing uranium 235. The radio isotopes are chosen such that their half life is long enough for the radiotracer to be transported from the manufacturing unit

CT scan

PET scan

Combined CT-PET scan

© MAYO FOUNDATION FOR MEDICAL EDUCATION AND RESEARCH. ALL RIGHTS RESERVED.

Figure 1.15  PET-CT scan (Whole body PET-CT scan) developed based on PET scan and CT scan. Source: https://www.mayoclinic.org/tests-procedures/pet-scan/about/ pac-20385078

14  Medical Imaging

Figure 1.16  Cyclotron machine (PET trace 800, GE healthcare). Source: https://www. gehealthcare.in/products/molecular-imaging/cyclotrons.

to the hospital where the PET scans happen and also to administer the same to the individuals.

1.2.5 Magnetic Resonance Imaging Magnetic Resonance Imaging (MRI), often called as Nuclear Magnetic Resonance (NMR) imaging uses magnetic properties of the body to obtain an image of the ROI. This is based on the fact that more than 80% of the human body is composed of water, which in turn contains hydrogen atoms. The MRI machine contains powerful magnets which polarize and excite the hydrogen nuclei present inside the water molecule. The Radiofrequency (RF) signal is generated with an RF coil which is sent into the ROI. This RF energy is absorbed by the protons which are then excited and align themselves parallel to the magnetic field they are subject to. Turning off the RF

Introduction to Medical Imaging  15

Figure 1.17  MRI machine (GE healthcare signa 1.5T machine). Source: https://www. 24x7mag.com/medical-equipment/imaging-equipment/mri/upgrade-ge-healthcare-mri/

pulse makes the protons relax and get back to their original phase by releasing the energy which was absorbed by the RF pulse. This energy is detected by an RF antenna and the image is constructed based on this information. As similar to ultrasound, MRI does not involve any ionizing radiations and is hence deemed to be safe without any health hazards. While CT provides the information about hard tissues, the MRI provides the soft tissue contrasts and hence provides excellent image quality. However, this is costlier than CT and ultrasound modalities. MRI is used for numerous applications such as those of liver studies, breast tumors and in the assessment of vascular disruptions. Different aspects of MRI such as those of T1 and T2 weighted images make it possible for the MRI to produce excellent images of the anatomical

16  Medical Imaging

Figure 1.18  MRI scan image (Whole body scan). Source: https://affordablescan.com/ blog/full-body-mri/

aspects of the ROI. Also, with regard to the instrumentation, Shimming and monitoring of the magnets are useful in the maintenance of the machine.

1.2.6 Functional Magnetic Resonance Imaging (fMRI) fMRI is an extension of MRI technique and measures the neurological activity in the brain with the aid of the variations in the blood flow and is hence confined to the neurological mapping alone. This is based on the fact that when a particular part of the brain is active, then it requires more energy to be so and hence more metabolism at that location. This requires more oxygen and hence an increased blood flow is seen to such parts of the brain. Hence fMRI uses the Blood Oxygen Dependent (BOLD) contrast to map the neuronal activity based on the imaging of the change in blood flow, called as hemodynamic response. Due to the fact that the signal measured is buried in noise, numerous statistical approaches are used to extract the signal corresponding to the activation area of the brain which is color coded. fMRI is also used in cognitive as well as memory-based task monitoring as well.

Introduction to Medical Imaging  17

Figure 1.19  MRI machine with fMRI extension (Optima MR 450W 1.5T GE healthcare). Source: https://www.medicalexpo.com/prod/ge-healthcare/product-70717-428727.html

Figure 1.20  fMRI scan (activation map of the brain during a predefined activity) Source: https://www.open.edu/openlearn/body-mind/health/health-sciences/ how-fmri-works

18  Medical Imaging In terms of the equipment, fMRI is a result of BOLD signals and MRI scan, fused together to obtain a functional color coding on the anatomical brain structure. So, most of the MRI equipment provide an enhanced software module so as to conduct fMRI scans.

1.2.7 Functional Near Infrared Imaging Functional Near Infrared Imaging (FNIR) is a recent noninvasive medical imaging technology used for functional neuroimaging applications. This is specifically employed for the imaging of the brain and its functions. This is based on near infrared spectroscopy approach which works similar to fMRI technique tracking the blood oxygenation as well as the volume of blood flowing into the parts of the brain during different functional. However, this is capable of monitoring the oxygenated as well as deoxygenated blood flowing into and out of the brain. This involves the quantification of chromophore concentration resolved by the measurement of near infrared light attenuation or phasic changes as well. This works on the fact that the near infrared light is transmitted through skin, tissues and bone, at about 700-900 nm spectrum whereas oxygenated as well as deoxygenated blood is known to be a strong absorber of this light. The light source and the detector are generally placed on the same side of the skull of the individual. The inrfrared light is known to interact in different ways, with the blood inside the skull. Different aspects such as transmission, diffusion,

Tablet running COBI Studio

(Data Acquisition, Analysis & Display)

Sensor cable fNIR Sensor Pad (under headband)

Wireless fNIR Box (integrated battery)

Figure 1.21  FNIR system (Biopac FNIR 100 system). Source: https://www.biopac.com/ application/fnir-functional-near-infrared-optical-brain-imaging/advanced-feature/ nirs-near-infrared-spectroscopy-fnir/

Introduction to Medical Imaging  19

log(Sensitivity)

0 –0.5 –1 –1.5 –2 HbO HbR HbT

0.6 µMol 50 s

Figure 1.22  FNIR image. Source: https://journals.ke-i.org/index.php/mra/article/ view/1240

reflection, scattering and absorption of light are seen. FNIR concentrates on the absorbed light and hence, the attenuated light is considered as a reference to assess the relative concentration of blood inside the brain. This allows the visualization of the activation patterns in the brain and hence a neurological functional map is obtained.

1.2.8 Elastography Elastography is yet another technology developed since the last two decades in the field of medical imaging based on the mapping of the elastic properties of soft tissues. This is based on the fact that healthy tissues are more elastic than their unhealthy counterparts. For instance, malignant tumors are less elastic/harder than the surrounding normal tissues. Similarly, diseased livers are stiffer than healthy ones. A distortion is induced in the tissues and their response to this distortion is obtained as an image. Such a distortion is generally induced by pushing or vibrating the surface of the body with a probe or by the usage of acoustic radiation force impulse imaging using ultrasound to remotely induce a mechanical distortion inside the tissue or even by observing the distortions created by normal physiological functions such as that of a pulse or heartbeat. The response of the ROI for such distortions are observed using ultrasound, MRI and tactile imaging approaches (using tactile sensors) and are transformed into images with a quantified value of stiffness at the ROI.

20  Medical Imaging

Figure 1.23  Elastography machine (ultrasound machine with elastography module – Hitachi ARIETTA 850). Source: http://www.hitachi-medical-systems.eu/products/ ultrasound/platforms/arietta-850.html

1.2.9 Photoacoustic Imaging Photoacoustic imaging is a hybrid imaging modality based on the photoacoustic effect. This encompasses the advantages of optical absorption contrast with ultrasonic spatial resolution for deep imaging in diffusive regime. This can be used in vivo for tumor angiogenesis monitoring, blood oxygenation mapping, functional mapping of the brain, etc. In this approach, nonionizing laser pulses are incident into the biological tissues wherein some of their energy would be absorbed and converted into heat

Introduction to Medical Imaging  21

Figure 1.24  Elastography (investigation of liver fibrosis). https://www.qldxray.com.au/ liver-elastography-investigating-liver-fibrosis/

Ultrasound imaging system

Urinary bladder

Optical fiber Laser Needle

Handheld imaging probe

SLN

Figure 1.25  Handheld ultrasound photoacoustic imaging system. Source: https://www. biophotonics.world/magazine/article/657/handheld-ultrasound-photoacoustic-imagingsystem-for-clinics

22  Medical Imaging leading into transient thermoelastic expansion, and hence a wideband ultrasonic emission is seen. These generated ultrasonic waves are detected by appropriate transducers which are then assessed to arrive at corresponding images. Optical absorption depends on the physiological aspects such as blood concentration and oxygen saturation. So, the ultrasonic emission is proportional to the local energy deposition which is used to form images accordingly. Photoacoustic imaging is of two types, namely photoacoustic computed tomography (PAT) and Photoacoustic microscopy (PAM). PAT uses ultrasound detector to acquire acoustic signals and the image is reconstructed using different tomography-based approaches. PAM uses spherically focused ultrasound detectors with 2D point-by-point scanning and does not need any reconstruction algorithms for the formation of images.

1.2.10 Magnetic Particle Imaging Magnetic particle Imaging (MPI) is an imaging technique used to track the super paramagnetic iron oxide nanoparticles. This provides a high sensitivity and specificity and tissue depth as well. This is used to ascertain the functional aspects of the heart, in case of neuroperfusions as well as for cell tracking applications.

Figure 1.26  Magnetic particle tracking system (momentum system). Source: https:// www.trendbio.com.au/all-products/momentum-magnetic-particle-imaging-system

Introduction to Medical Imaging  23

1.3 3D Rendering Software-based approaches have been developed for conventional CT, Ultrasound and MRI-based imaging systems so as to enable volume rendering approaches. Conventional CT and MRI scans provide 2D images. But introduction of volume rendering provides a 3D view of the ROI and hence provides a better diagnosis of the same. 3D scans help to visualize the structure with better detailing. For instance, 3D ultrasound is extremely useful in the assessment of pregnancy scans, ovaries, bile ducts, etc. There are numerous mathematical approaches for 3D volume rendering imaging that are used for different clinical applications.

1.4 Diagnostic Images Most of the images obtained by different diagnostic imaging modalities are digital. In this regard Picture Archiving & Communication Systems (PACS) is essentially used in ultrasound imaging to capture the image for archiving and telemedicine-based applications. A frame grabber is used to capture the video feed from the machine and is stored in computers for further processing. Of late PACS is placed in the cloud to utilize the technical advancements of cloud computing and big data analytics as well. Similarly, Digital Imaging and Communication in Medicine (DICOM) Standard is used globally to store, exchange, and transmit medical images. The DICOM Standard incorporates protocols for imaging techniques such as radiography, computed tomography (CT), magnetic resonance imaging (MRI), ultrasound, and radiation therapy.

1.5 Medical Imaging in Pharmaceutical Applications Medical imaging is an integral part of clinical trials due to its ability of swift diagnosis with a quantified visual assessment. Clinical trails which take years and years of research culminate in the determination of the safety and effectiveness of a given therapeutic approach. The cost involved as well as the sample size required is a matter of concern in such conventional clinical trials. However, usage of Imaging biomarkers have facilitated the development of surrogate endpoints instead of conventional trial-based

24  Medical Imaging clinical end points and hence reduce the time taken for the assessment of clinical benefits of the drugs under experiment. Such imaging biomarkers are measured by imaging techniques for better assessment of the therapeutic progression and can be ascertained by reducing the direct contact to the patient. PET and MRI-based approaches are extremely useful in the assessment of oncological and neurological therapeutic effects. For instance, reduction of tumor does not need a repetitive biopsy, but instead can be assessed using PET scans. MRI scans of the entire brain can provide an accurate assessment of the rate of hippocampal atrophy. Image-based trial are often composed of three major aspects, namely, a realistic imaging protocol, imaging centre and clinical sites. A realistic imaging protocol is an outline that provides a standard approach for the acquisition of images using different modalities. The imaging centre collects the images, performs the quality control and provides facilities for data storage and analysis. Clinical sites recruit patients for the data generation.

Introduction to Medical Imaging  25

26  Medical Imaging

Glossary-Appendix 1. Medical Imaging - Techniques and processes used to create images of various parts of the human body for diagnostic and treatment purposes within digital health 2. Diagnostic radiology - Procedures to obtain images of the inside of the body 3. Radiography - Using radiation to provide images of the tissues, organs, bones 4. X-ray imaging - X-rays have higher energy and can pass through most objects 5. Fluoroscopy - Type of medical imaging that shows a continuous X-ray image on a monitor 6. Tomography - Radiologic technique for obtaining clear X-ray images of deep internal structures 7. Ultrasound - Uses high-frequency sound waves to create an image of the inside of the body 8. PET - Positron emission tomography 9. Nuclear Medicine - Area of radiology that uses very small amounts of radioactive materials, or radiopharmaceuticals, to examine organ function and structure. Nuclear medicine imaging is a combination of many different disciplines. 10. Scintigraphy machine - Diagnostic test in nuclear medicine 11. SPECT - Single Photon Emission Computed Tomography 12. CT - Computed tomography 13. MRI - Magnetic resonance imaging 14. fMRI - Functional magnetic resonance imaging 15. Radiotracers - Chemical compound in which one or more atoms have been replaced by a radioisotope 16. Functional Near Infrared Imaging - Optical brain monitoring technique which uses near-infrared spectroscopy 17. Elastography - Imaging test that checks the liver for fibrosis 18. Photoacoustic imaging - Biomedical imaging modality 19. Magnetic Particle imaging - Imaging modality that directly detects iron oxide nanoparticle tracers 20. Neuro perfusions - Brain test that shows the amount of blood taken up in certain areas of your brain

2 Fundamentals of X-Rays X-ray, an acronym of X-radiation, was discovered by a German physicist, Wilhelm Roentgen, in 1895. X-ray ranges from 10-12 to 10-9 wavelength and a frequency range of 30×1015Hz to 30×1018 Hz in the band of electromagnetic radiation and has an ambit of 1.24 × 102 eV – 1.24 × 105 eV. X-ray was termed so by Roentgen so as to signify an unknown type of radiations. Since then, X-rays have been most commonly used in the field of diagnostic imaging medicine.

2.1 Electromagnetic Radiations The electromagnetic spectrum is categorized into various bands with respect to the wavelength encompassing various types of waves such as Visible light Radio Waves

102

Micro waves

10

1

Infrared light

Ultraviolet light

X-rays

γ-rays

10–1 10–2 10–3 10–4 10–5 10–6 10–7 10–8 10–9 10–10 10–11 10–12 10–13 400nm

Wavelength (m)

700nm

MRI

endoscopy

radiography CT

nuclear imaging

Proton energy (eV)

10–8 10–7

10–6 10–5

10–4

10–3 10–2

10–1

1

10

102

103

104

105

106

107

Figure 2.1  Electromagnetic spectrum. H. S. Sanjay and M. Niranjanamurthy. Medical Imaging, (27–84) © 2023 Scrivener Publishing LLC

27

28  Medical Imaging those of radio waves, micro waves, infrared light, visible light, ultraviolet light, X-rays and Gamma (γ) rays. This is depicted in Figure 2.1. For a better understanding, it is essential to assess both the wave nature as well as the particle nature of x-ray waves, as shown in the succeeding sections.

2.2 Wave Nature X-rays form a part of the electromagnetic radiation spectrum and are considered to travel as waves. In this regard, X-ray is characterized by numerous wave parameters such as those of Electric field, Magnetic field and various aspects of the medium in which it travels. In terms of a monochromatic radiation, we can represent the electric as well as the magnetic fields in time and space as shown in Equation 2.1

φ(x, t) = φo cos(ωt – kx)



(2.1)

Where φ = Electric field x = distance travelled by the wave t = time taken k = wave number = 2π/λ where λ = wavelength Figure 2.2 depicts the X-rays for a definite distance x, in terms of time t whereas Figure 2.3 represents the same as a function of distance x over a finite time t.

φ (x, t)

Fixed, x T

Time, t

Figure 2.2  Sinusoidal electromagnetic wave represented as a function of time at a fixed distance x.

Fundamentals of X-Rays  29

φ (x, t)

Fixed, t λ

Distance, x

Figure 2.3  Sinusoidal electromagnetic wave represented as a function of distance at a fixed time t.

Wavelength is regarded to be the distance between the successive crests of an electromagnetic wave. In this regard, one could infer equation 2.2 in this regard

Tc = λ

(2.2)

Where c = speed of the electromagnetic wave propagation f = 1/T Consider the generic wave equation as shown in equation 2.3

E 2ϕ 1 E 2ϕ = Ex 2 c 2 Et 2

Where −

1

(2.3)

 1  2 -6 c =  and μ = permeability of the medium = 1.257 × 10 henry/m µε   in free space Ε = permittivity of the medium = 8.854 × 10-12 Farad/m in free space  x Equation 2.3 has a general solution of the form f  t ±  in which the  c - sign denotes that the wave is travelling in a positive direction and the + sign denotes the wave to be travelling in a negative direction in terms of x. In this regard, equation 2.1 is considered to be a specific solution of the equation of the wave denoted in equation 2.3. This analysis is extremely

30  Medical Imaging useful while considering the wave nature of light which aids in the analysis of various x-ray characteristics such as those of reflection, refraction, scattering and diffraction.

2.2.1 Particle Nature Considering X-ray to be portraying a particle nature, travelling at the same speed as that of the light, with an energy E, the energy of an x-ray photon can be mathematically represented as shown in equation 2.4, generally in the order of keV wherein the particles are called photons or quanta.



= E hf= h

c λ

(2.4)

Where E = energy of an x-ray photon f = frequency of the x-ray photon λ = wavelength of the x-ray photon h = planks constant = 4.13 × 10-18 keV where 1eV = 1.6 × 10-19 Joules c = speed of light = 3×108 m/s A photon with an energy of a few eV can knock off a given electron from its orbit (ionize the atoms and molecules) and can be hence aptly termed as ionizing radiation. Example problem: Find the energy of an X-ray photon of a 1nm wavelength. −15 8 c  (4.13x10 x 3 x 10  3 Solution: = E hf= h =   = 1.2 x 10 eV λ  10−9  From the above solution, it is evident that x-ray definitely possesses ionizing properties.

2.2.2 Intensity of an X-Ray Beam Intensity of a generic beam is regarded to be dependent on both quantity as well as the quality of the beam for a given specific area onto which it is exposed. In other words, this can be considered as the power per unit area of the beam. With respect to X-rays, the intensity is relative to the quantity of photons crossing the cross-sectional area for a unit interval of time as well as the energy of the photons. So, the quantity as well as the energy of the photons produce the intensity of the X-ray beam. It is hence obvious to

Fundamentals of X-Rays  31 infer that this intensity could be changed by changing either of these factors. The energy value is often quantified using two units, namely Roentgen (R) and Radiation Absorbed Dose (RAD).

2.2.3 Roentgen (R) Roentgen (R) is defined as the overall ion pairs produced by the X-ray radiations in 1 cubic centimetre of air under standard pressure and temperature conditions. It also denotes the radiations which are adequate for the generation of an electric charge separation of 2.58 × 10-4 coulomb per kilogram of air.

2.2.4 Radiation Absorbed Dose (rad) Radiation Absorbed Dose (rad) denotes the radiation that is absorbed by a given medium, i.e., 0.01J of energy which is absorbed by 1 kilogram of the material considered. As a matter of fact, various materials absorb different quantity of energy for a given standard quantity of radiation. Hence rad is of a high importance as a measure of X-rays. 100 rad are often termed as 1 gray (Gy).

2.2.5 X-Ray Interactions To simplify the understanding of the interaction of X-rays, two important aspects are considered here due to the fact that X-rays interact with the matter on which it is incident. Also, more specifically, with regard to medical imaging, X-ray is often incident on the body while scanning. Hence the interaction of X-rays with the tissues are also discussed in this section.

2.2.6 Interaction Between X-Ray and Matter X-rays are known to portray a definite and a varying nature of interaction with the atom, with regard to the central nuclei as well as its orbital electrons. It is this interaction with the orbital electrons which falls in the range of X-rays used in diagnostic imaging. It is also to be noted that such diagnostic X-rays are not strong enough to interact with the nuclei of the atoms. Such interactions often depend upon the energy value of the X-ray photon itself as well as the atomic number of the atom with which it is interacting, so as to conclude upon the type of interaction. The most common types of interactions between X-ray and matter are explained in the sections below.

32  Medical Imaging

2.2.7 Coherent Scattering Often, when an X-ray photon is incident on a particle, it gets deflected and changes its path of motion by parting away with some of its energy content and hence, results in a very small variation in terms of its wavelength. This interaction between the X-ray photon and the particle (matter) is termed as Coherent Scattering and is depicted in Figure 2.4. This type of interaction is often observed in the case of X-rays with lower energy values which are not substantial enough to knock out the electrons in the orbit and hence cannot ionize the atom. This is the only kind of interaction between X-ray and matter which does not yield an effect of ionization.

2.2.8 Compton Effect The Compton effect is solely responsible for the radiations seen to be scattered in X-ray scans. In this type of interaction between the X-ray photons and the matter, some of the energy of the X-ray photon is seen to be transferred onto the electron knocking off the electron itself. Also, due to the fact that the X-ray photon gets scattered, there is a shift in its direction of motion and a substantial reduction of the original energy which it possessed as well. This phenomenon if depicted in Figure 2.5. Due to the fact that the outer shell electron is knocked off, out of its orbit by the incident X-ray photon, most of its energy is absorbed by this electron. However, a part of the energy is retained by the X-ray photon itself, which normally is dependent on the angle at which the X-ray photon gets scattered (θ of Figure 2.6) as well as the initial energy which the X-ray photon possessed before being incident on the electron. This is denoted Incident X-ray photon

Scattered X-ray photon

Atom

Figure 2.4  Coherent scattering with x-ray photons.

Fundamentals of X-Rays  33 Incident X-ray photon

Scattered X-ray photon

θ

Electron Atom

Figure 2.5  Compton scattering.

by given by equation 2.5. It is, however, to be noted that the electron is assumed to be stationary as well as free prior to this collision of X-ray photon onto the electron under consideration.

E′ =

E  E  1+  (1 − cosθ ) 2   mec 

(2.5)

Where E = energy of the incident photon E′ = energy of the scattered photon me = rest mass of the electron = 511 keV When the X-ray photon possesses a lower energy value, then the energy of the same X-ray photon after it gets deflected will not be related to the angle at which it gets scattered (θ). Such a case is observed in isotropic scattering in which the wavelength is large, in comparison to the size of the scatterer. When this energy value increases, the photons are seen to be scattered at small angles in forward direction of motion, as similar to that seen in the case of wave scattering phenomenon. In X-ray diagnostic imaging, this scattering poses the following challenges due to the fact that these scattered X-ray photons possess large energy values and can result in a negative effect to the subject involved: • Background noise in the X-ray film • Safety hazard for the users

34  Medical Imaging

2.3 Photoelectric Effect An atom can often be regarded as a well of energy and the nucleus of the atom is normally seen at the bottom and filled with electrons. In this setup, the electrons towards the top of the well can escape from this well easily, with a lesser effort as compared to the electrons present towards the bottom of the well, which require a higher effort to come out of this well. The atomic number of such an atom denotes the depth of this well. For instance, in case of iodine which has an atomic number of 53, for a K-shell electron to escape from this well, an energy of 33.2 keV is needed. This is due to the fact that the K shell has a binding energy of -33.2 keV in this case and a minimum of 33.2 keV would be required by the K-shell electron to escape the nucleus and become a free electron. This is denoted in Figure 2.6. With regard to the interaction of the X-ray photon with the matter, in photoelectric effect, this photon possesses an energy more than the binding energy of the electron of the K-shell onto which this photon collides. This electron then gets ejected from its orbit. The X-ray photon gets absorbed and loses its entire original energy. Most of this energy is required to mitigate the binding energy of the K-shell. The rest of the energy is transformed into the kinetic energy of the electron which is dislodged. Due to this release of electron, there is a vacancy created in the orbit. This void is filled up by another electron from the outer shell. Photoelectron

Characteristics radiation Atom

X-ray photon

Figure 2.6  Photoelectric effect with x-ray photon.

Fundamentals of X-Rays  35 This process continues and the atom becomes positively charged because of losing a stable electron from its orbit. The freed electron is called as the photoelectron. The X-ray photon which is absorbed is released, and this now will possess an energy which is the difference of the energy of the K-shell electron and the outer shell electron. The photon being released will be in the form of a characteristic radiation. Alternately, the auger effect is observed wherein the outer shell electron compensates for the vacancy created in the inner shells by releasing an energy onto another orbital electron. If at all, this orbital electron possesses substantial energy to get freed, then such an electron is called as Auger Electron. In this scenario, two vacancies are observed in the orbit which are compensated by two outer shell electrons. This in turn results in the formation of further auger electrons or characteristic radiations. The occurrence of such characteristic radiations depends on fluorescent yield (fluorescent yield is dependent on the atomic number). Lighter atoms result in more auger electrons whereas heavier atoms emit more characteristic radiations. Hence, photoelectric effect results in three components by the end of the process, namely • Auger electron/characteristic radiation • Photoelectron • Positive ion In case of iodine, if a K-shell electron is ejected from its orbit, then the characteristic radiation may be seen at 33.2 keV / 32.6 keV / 28.3 keV when an N-shell / M-shell / L-shell electron falls into the void. For photoelectric effect to be seen, the energy of the X-ray photon being considered needs to have an energy which is of a higher value than that of the binding energy of the orbital electron which is intended to be ejected out. This is, however, the best type of interaction between the X-ray and matter that can happen due to the fact that the X-ray photon under consideration is entirely absorbed without causing any kind of scattered radiations. Hence we obtain a good image quality in such kind of interaction and the user safety is achieved as well.

2.3.1 Pair Production In case of pair production, the X-ray photon needs to have a higher energy value. This photon would be absorbed by the nucleus due to its high energy nature and is converted into an electron as well as a positron.

36  Medical Imaging

2.3.2 Photodisintegration In the case of Photodisintegration, the X-ray photon results in the ejection of neutrons/protons from the nucleus itself. Both pair production and photodisintegration are of least importance in the case of X-ray radiography as there is no interaction with the electrons. However, these are more relevant with regard to nuclear imaging.

2.4 Interaction Between X-Ray and Tissues When X-ray beam incidences on a material, its intensity reduces due to the different types of interactions seen between the X-ray photon and the material, as described in the preceding section. Consider one such X-ray beam of intensity I and a cross sectional area A. Also let us assume that the atomic nature of the material upon which the X-ray beam is incident, are similar in nature with a cross sectional area σ. If the per unit volume of the material contains say n atoms, then, the total number of atoms upon which the X-ray beam interacts, is An and the area consumed by the atoms in the beam considered is Anσ. In such a scenario, the probability of the interaction between the X-ray photon and the atoms present is the material of interest is Anσ / A = nσ. In this regard, the X-ray energy reduced when it passes through a material of thickness dx is given in equation 2.6.

dI = −nσI dx

(2.6)

On rearranging equation 2.6, we get equation 2.7



dI = −nσ I dx

(2.7)

It is a known fact that β denotes the strength of X-ray discarded per unit thickness of the material upon which it is being incident, per unit intensity (equation 2.8)



β = nσ

(2.8)

Substituting equation 2.8 in equation 2.7 and integrating, we get equation 2.9

Fundamentals of X-Rays  37

I = Ioe−βx

(2.9)

Where I = X-ray intensity at x Io = Intensity of the incident X-ray β = Linear attenuation coefficient (np/cm or cm-1) x = length of propagation So, the length of propagation of a material required to reduce the original beam intensity to half its original value is termed as Half Value Layer (HVL) and given by equation 2.10. Both the HVL and the β depend on the photon energy

HVL =



0.693 β

(2.10)

This is depicted pictorially in Figure 2.7. The mass attenuation coefficient is the ratio of linear attenuation coefβ ficient to density and is depicted mathematically as where η denotes η Area = A

Area = σ

x

X-ray Beam

Figure 2.7  X-ray beam of a cross sectional area A interacting with a medium of thickness x.

38  Medical Imaging

Mass-Attenuation coefficient, cm 2/g

100

Iodine

10

Lead Bone 1 Muscle Fat 0.1 0

50

100

150

X-ray Photon Energy, keV

Figure 2.8  Mass attenuation coefficients of various materials as a function of X-ray energy.

the mass density of the material, with an unit of cm2/gm. In general, this indicates the attenuation property of the matter. For instance, the linear attenuation coefficient at 50keV, for water is 0.214 cm-1, for ice, it is 0.196 cm-1 and for water vapour, the linear attenuation coefficient is 0.00013 cm-1. However, their mass attenuation coefficient is the same value ie 0.214 cm2/gm. Figure 2.8 depicts the mass attenuation coefficients of various materials, as a function of energy.

2.5 Factors Affecting Attenuation Coefficients As seen in the previous sections, the X-ray photons interact with the nucleus as well as the orbital electrons of the atoms of the materials considered. However, in diagnostic X-ray imaging, the Compton effect as well as the photoelectric effect–based interactions between the X-ray and matter are of utmost importance. Coherent scattering is very minimal. In this regard, during the interaction between the X-ray photons and the materials, these photons may be scattered or absorbed, either of which results in attenuations. This is shown in equation 2.11.

Fundamentals of X-Rays  39



β = βs + βa

(2.11)

Where β = overall attenuation of the x-ray beam βs = attenuation due to scattering βa = attenuation due to absorption On similar lines, the mass absorption coefficient is defined as

βa η

2.6 Attenuation Due to Coherent Scattering (βcoh) Attenuation due to coherent scattering (βcoh) occurs when the binding energy of the orbital electron is higher than the energy of the X-ray photon and is as shown in equation 2.12



βcoh ≅ ηZ2E−1

(2.12)

Where Z = Atomic number of the atom n = Density of the atom E = Energy of the X-ray photon In case of coherent scattering we observe that most of the energy is retained by the X-ray photons as they scatter and very less energy is absorbed by the atom. These scattered photons result in attenuation. Also, due to the fact that the energy of the X-ray photon in the diagnostic range is much higher than that of the average atomic numbers of the biological tissues, when they are considered as the matters upon which these X-ray photons are incident, this type of attenuation, seen because of coherent scattering is of negligible nature.

2.7 Attenuation Due to Compton Scattering (βcom) and Photoelectric Effect (βpho) The attenuations due to Compton scattering (βcom) and that of photoelectric effect (βpho) depend upon the energy of the X-ray photon as well as the density of the material and are related to each other as shown in these equations

40  Medical Imaging



βpho ≅ ηZ3E−3 βcom ≅ ηρcE−1

(2.12)

Where ρc = the electron density (number of electrons present per gram of material) In case of the attenuation phenomenon seen due to photoelectric effect is mostly due to the X-ray photons being absorbed into the material. But in the case of the Compton effect, the attenuation is due to both scattering as well as the absorption. The overall attenuation is however a combined effect of all these types of attenuations seen due to various interactions of X-ray photon with matter, as shown in equation 2.13. Also, the X-ray attenuation depends upon the density of the material as well as the atomic number.



β = βcoh + βpho + βcom

(2.13)

In other words, one could summarise that a rise in the energy value of the X-ray photon results in a decrease in the attenuation of the X-ray beam. To understand this phenomenon in a better manner, consider the X-ray photons as particles of size of their wavelengths. The wavelength reduces as their energy rises resulting in the particles becoming smaller than before. As they get smaller and smaller, it becomes easier for them to travel across the electrons as well as to reach until the nuclei. However, these are a few exceptions in this nature of the particle. This is due to that fact that the X-ray beam gets attenuated majorly due to coherent scattering, Compton effect and photoelectric effect with the best one being that of the photoelectric effect which has a higher probability of occurrence when the energy of the X-ray photon is almost similar to the binding energy of the orbital electron. During such a scenario, we observe a sudden rise in attenuation which again reduces with a further increase in the energy of the X-ray photon. As discussed before, equation 2.9 denotes the X-ray intensity. However, this is valid only for a homogeneous beam of X-rays (monochromatic beam). But seldom is this seen. Instead, X-rays are often observed to be polychromatic in nature. They seem to be distributed across various energy levels. Due to this, the X-ray photons of various energy levels get attenuated in a different manner as they propagate across the medium. So, assessment of the transmitted X-ray intensity in such cases cannot be done using

Fundamentals of X-Rays  41 equation 2.9. The effective energy of the polychromatic X-ray beam can be considered to be similar to that of the monochromatic beam with the same HVL. One such example is that of aluminium. Overall, such polychromatic beam would retain less photons in lower energy values which results in a rise of the effective energy value of the X-ray beam. This is called beam hardening.

2.8 Generation and Detection of X-Rays 2.8.1 Generation of X-Rays X-ray radiations are obtained when a high energy electron beam hits a target material such as that of tungsten or molybdenum. Once such beam hits the target, it produces general radiation (also called as white radiation or Bremsstrahlung) when the beam interacts with the nuclei of the target material. If the beam interacts at all with the orbital electron, then characteristic radiations are produced.

2.8.2 White Radiation When a negatively charged electron gets closer to the nucleus which is positively charged, under such circumstances, this electron would get attracted further towards the nucleus thereby getting deflected from its initial path in which it was traversing. Under such a scenario, if at all this electron retains its energy as it gets deflected, then such a process is termed as elastic scattering during which no X-ray photons are generated. However, the

E1 > E2 X-ray Photon

e– (E1)

N+

e– (E2)

Figure 2.9  Production of white radiation due to the deflection of high energy electron by nucleus.

42  Medical Imaging X-ray intensity in the tube

Intensity

α1 α2

Characteristic Radiation

β1 β2

White Radiation 0

50

100

150

200

Photon Energy in keV

Figure 2.10  Radiations produced by the tungsten material.

radiations produced in this process are called white radiation, as shown in Figure 2.9. Under the same circumstance, as the atomic number of the atom rises, the probability of the electron to lose its energy rises as well. In such cases, X-ray photons are generated and the general radiations produced span over a wide range of values, as shown in Figure 2.10.

2.8.3 Characteristic Radiation Characteristic radiations are seen when the electrons interact with the orbital electrons (of the target) of the inner shell. This process is almost similar to the interaction seen in the case of photoelectric effect. Figure 2.9 depicts the X-ray spectrum seem with tungsten as the target material. The solid lines denote the general radiations seen outside the X-ray tube. α1, α2, β1 and β2 denote the characteristic radiations arising from the electrons of the L shell falling into the K shell as well as the M shell and the N shell electrons shifting into the K shells.

2.9 X-Ray Generators The main component of an X-ray generator is the X-ray tube. The essential aspects of an X-ray tube are as shown in Figure 2.11. Conventionally, an X-ray tube houses the electrodes which are found to be sealed under a vacuum environment. This setup is essential to facilitate the quantity as well as the movement of the accelerated electrons which are supposed to

Fundamentals of X-Rays  43 hit the tungsten anode. A vacuum environment ensures that there are no undesired variations in the number of electrons. Also due to the presence of a vacuum setup, the speed of the electrons is constant while hitting the tungsten anode. The cathode is made up of a filament as well as a focusing metallic cup. The filament is composed of a tungsten wire helically coiled, with a diameter of about 0.2 mm and 1 cm in length, and the metallic cup helps to focus the electrons after being emitted by the tungsten filament. This wire gets heated when the current is supplied and this heat is absorbed by the electrons present in the wire. When the temperature increases beyond a particular value, then the electrons absorb this extra energy and acquire the strength to escape by foregoing the surface barrier current. Such electrons which escape the metal hover around the tungsten filament and is called the space charge. This further alerts the electrons to move away from the filament. The space charge, once formed, ensures that more electrons are not emitted from the filament. This is called as the space charge effect. Also, because of the escaping of the electron, the filament becomes positively charged. Hence these electrons which have escaped remain around the filament itself and do not move away from the wire because of the tungsten filament being positive and the electrons being negative. However, by providing a high voltage, these escaped electrons can be made to accelerate towards the anode. Often, tungsten is used in these applications due to its property of a high melting point (3370°C) and its higher strength and less vaporizing traits.

2.9.1 Line Focus Principle Every electron which hits the tungsten target possesses some amount of energy. As these electrons hit the tungsten target, almost 99% of the energy is simply converted into heat. Such a huge accumulation of heat mandates a larger focal spot. On the contrary, a smaller focal spot results in a higher quality of X-ray images. This issue is resolved based on the line focus principle. This is depicted in Figure 2.11. The angle between the target and the electron beam is called the anode angle. This is normally around 10o. The actual as well as the effective focal size is related as shown in equation 2.14.



f = F sin θ

(2.14)

44  Medical Imaging Focal Spot

Electrons

Filament

e– e–

Anode

Cathode

X-ray Photons Apparent Focal Spot Size

Figure 2.11  Basic components of an X-ray tube.

where θ = anode angle f = Effective focal size F = Actual focal size As a matter of fact, a larger anode angle results in a wider area for the bombardment of the electrons. But this also results in a larger focal spot. In essence, the anode angle is controlled by the heel effect, as shown in Figure 2.12. As seen before, the X-ray intensity is smaller towards the anode and larger towards the cathode. This is due to the fact that the X-ray photons towards the anode need to traverse a higher distance, as compared to those which are away. Also because of the repeated bombardment of electrons, the anode gets heated and the fidelity of the anode reduces. This Target

Anode

X-ray Photons

Figure 2.12  Heel effect in X-ray tube.

Fundamentals of X-Rays  45

Figure 2.13  Typical X-ray tube.

is mitigated by using a rotating anode. This increases the target location drastically and results in the improvement of the fidelity of the production of X-ray photons as well. A generic X-ray tube is as shown in Figure 2.13.

2.9.2 X-Ray Tube Ratings Various aspects such as those of filament temperature (which is based on the filament current if ), the tube voltage (Vt), the electrons hitting the anode target as well as the target material result in the variation of the X-ray beam being produced as well as their intensity. A circuit-based representation of a generic X-ray generator is shown in Figure 2.14. Vf

Vt mA

If

mA

X-ray Tube Filament mA

If

Figure 2.14  X-ray generator – An electrical perspective.

Target

46  Medical Imaging In Figure 2.14, if = Filament current – This is directly proportional to the filament temperature Vt = Tube voltage – This is a simple potential difference value between the anode and the cathode which provides the filament current.

2.9.3 Target Material The efficiency of the production of X-ray radiations is directly proportional to the atomic number of the anode material. For instance, tungsten with atomic number of 74 results in a lesser number of radiations than platinum which has an atomic number of 78, for the same set of tube voltage and current values.

2.9.4 Tube Voltage Tube voltage (V) can be direct current or alternating current based. Either a half wave- or full wave-based approach is acceptable in this regard. In case of AC based X-ray generators, the X-ray intensity produced is measured as kilovolts peak (kVp). In general, the tube voltage is around 150 kVp.

2.9.5 Tube Current The X-ray intensity is also seen to be linearly varying as per the tube current. This is due to the fact that the tube current in turn affects the strength of the electrons hitting the tungsten target material at anode. The tube current normally is around 500 mA.

2.9.6 Filament Current When the tube voltage begins to increase, for a fixed filament current, the tube current too rises, up to a particular level and slowly reaches saturation. Beyond this saturation point, the tube current does not rise with increase in tube voltage. The voltage at this point is called as the saturation voltage wherein the filament temperature limits the current value. The above-mentioned criteria is mathematically expressed in equation 2.15, with a fixed value of if.

I ≅ Z(mA)(kVp)2F

(2.15)

Fundamentals of X-Rays  47 Where I = the X-ray intensity, generated by the tube Z = Atomic number of the anode material used as the target F = Rectification factor for Vt, (F = 1 for DC current) It is interesting to observe that the maximal energy which can be carried by the X-ray photon (Emax) changes as the kVp varies. However, the same scenario is not seen as mA varies. On the contrary, Emax does not vary at all in the second case.

2.10 Filters The X-rays are polychromatic in nature. In this regard, not every radiation is useful and intended to be used for diagnostic imaging. Based on the body part being imaged, certain aspects of these X-ray spectrum are essential while the rest of it needs to be discarded as these may result in noise in the images as well as harm to the subject while imaging. This can be achieved by using appropriate filters which also will end up decreasing the radiation dose to the subject. While the ultimate destination of an X-ray beam after being generated from an X-ray source which is the tube, would be the X-ray detector such as that of a simple X-ray film, it normally travels through the various electronic and mechanical components such as those of filters to process these beams and then reach the subject. Often, thin sheets of metals such as those of aluminium and copper act as filters and are placed between the source and the subject. Copper can filter high-energy X-ray beams whereas aluminium can absorb low-energy X-ray beams. A practical compound filter is a combination of both aluminium and copper. For instance, copper can result in a characteristic radiation of about 8keV which is substantial enough to increase the skin dose to the subject. On the contrary, about 90% of the X-ray beam, say at 20keV can be attenuated by using aluminium of about 3 mm thickness. So, copper is always placed above aluminium sheet as a compound filter. Also due to the fact that the X-ray beams produced by the conventional X-ray generators are not uniform in nature, wedge filters are used which are normally thinner towards the anode. Such a setup is successful in mitigating the non-uniform nature of X-ray beams in practice.

2.10.1 Beam Restrictors Beam restrictors are used to alter and regulate the shape as well as the size of the X-ray beam being incident on the subject. Such an arrangement can

48  Medical Imaging be extremely useful to reduce the scattered X-ray radiations as well as to reduce the exposure of X-rays to the subjects. Following are the types of beam restrictors used in X-ray equipment in general: • Aperture diaphragms • Cones and cylinders • Collimators

2.10.2 Aperture Diaphragms An aperture diaphragm is a lead-based sheet metal with a punctured hole at the centre. The size and share of the X-ray beam being provided to the subject depends upon the size as well as the shape of this hole. The penumbra (P) is dependent upon the diameter of the X-ray source by equation 2.16

P=



D I L

(2.16)

Where D = width of the source I = distance between the X-ray source and the object (subject) L = distance between the X-ray detector and the object (subject) D Focal Spot L Beam Restrictor

I

P

Figure 2.15  Aperture diaphragm.

Fundamentals of X-Rays  49 Penumbra is an undesired aspect and needs to be mitigated in which regard; beam restrictors would be a good option. For instance, if one needs to reduce penumbra, then the aperture diaphragm needs to be stationed as far away as possible from the source; however, the source in that condition needs to be as small as possible. An illustration of this is provided in Figure 2.15.

2.10.3 Cones and Cylinders At times, cones and cylinders are used to restrict the X-ray beams as well. However, as a matter of fact, the variations in the size of the X-ray beam achieved using them is limited. This causes a huge drawback for the usage of not only cones and cylinders, but in case of beam restrictors as well.

2.10.4 Collimators Collimators are preferred over beam restrictors as well as cones and cylinders due to the fact that there are no limitations with the resultant X-ray beam size, while using collimators. Also, a light beam is often used to specify the precise size of the X-ray field with collimation process. A generic collimator setup is shown in Figure 2.16. A mobile aperture diaphragm is used to adjust the beam size of X-rays. A bulb is used to provide a light beam which is helpful to mark the X-ray X-ray Source X-ray Beam

Light Beam Light Bulb

Filter Mirror

Movable Diaphragm

Figure 2.16  Collimator.

X-ray or Light Beam

50  Medical Imaging field. This bulb is often placed inside the collimator for the ease of usage. However, such a setup is still not completely successful in the reduction of noise due to scattered X-ray beams. This can be handled by grids.

2.10.5 Grids Radiographic grids find their use in diagnostic imaging to improve the image quality and reduce the exposure to the subject by removing the scattered X-ray radiations. These grids are made up of lead strips and are separated by transparent spacers made up of aluminium. These grids allow the primary X-ray radiations to pass through them and block the scattered radiations. Radiographic grids are quantified by grid ratio (gr), defined as the ratio between the height of the lead strip (h) and the width of gap between there strips (g). In general, a grid ratio of 4 to 16 is desired. Example problem: For a radiographic grid of height 2 mm, with a gap between each of the lead strip being 0.25 mm, find the grid ratio Solution: Given h = 2 mm and g = 0.25 mm, gr = h/g = 2/0.25 = 8 With a rise in grid ratio, the exposure to the X-ray beams also increases, which poses a problem to the subject. However, it is to be noted that as the grid ratio increases, the functionality of the grid also rises and this often

X-ray Source

Primary Radiation

Patient Scattered Radiation

Grid

Detector

h

g

Figure 2.17  Grid positioning to remove the scattered X-ray photons.

Fundamentals of X-Rays  51 results in least scatter radiation. Shown in Figure 2.17 is a depiction of a linear grid.

2.11 X-Ray Visualization X-rays are not visible to the naked eyes due to their nature with respect to the electromagnetic spectrum. Hence X-ray diagnostics are often visualized with the help of photographic films so as to be comprehensive for human visualization after appropriate conversion of the X-ray photons into visible light photons. The photographic films are not sensitive to X-ray photons. Hence these are first converted into visible photons with the aid of image intensifying screens. These screens expose the photographic films to the photons appropriately and also reduce the X-ray dose to the subject. Any motion in the subject during the exposure can also be mitigated by reducing the exposure time accordingly. These intensifying screens are designed such that they can emit light photons perfectly, at the wavelengths at which the photographic films are to be exposed. In general, this process of conversion of X-ray photons into light photons is termed as fluorescence. It is hence apt to consider an intensifying screen as a fluorescent screen as well. Such screens find their use in case of diagnostic fluoroscopy.

2.11.1 Intensifying Screens The components of the intensifying screen are given in Figure 2.18. An intensifying screen houses a phosphor layer of thickness 0.05 mm × 0.3 mm. The phosphor emits light photons when the X-ray photons are incident on the phosphor layer. The screen has a substrate material of about 0.1 mm thickness which allows the X-rays to pass through. The light reflective layer, of about 0.025 mm thickness averts the backward transmission of light photons. Due to the fact that X-ray photons have higher energy than the light photons, it is obvious that a smaller number of X-ray photons are sufficient to result in a huge number of light photons. The protective layer is transparent to light photons. A large number of phosphor-based variants have been used in image intensifying screens. The most common types of such variants are as follows. Calcium Tungstate (CaWO4): Calcium Tungstate has a K edge value of 50.2 keV for which it emits blue light of the visible spectrum region of a wavelength of 250 nm – 580 nm. This light has a peak wavelength of 430 nm. Although this peak value of the wavelength is extremely useful in

52  Medical Imaging X-ray

Substrate Reflective Layer (to light) Phosphor Protective Layer

Figure 2.18  Image intensifying screen.

case of X-ray film exposure, this light is not preferred for visualization. The efficiency of conversion from X-ray photons to light photons is a mere 5% with the usage of Calcium Tungstate. Rare earth screens: rare earth-based phosphor screens provide better performance than Calcium Tungstate at 50 keV to 60 keV range. They emit a narrow band of light in green or blue regions of visible light spectrum and hence the necessary condition in this regard is that the photographic film needs to be sensitive to these regions of light for optimal performance. Further variants such as GadoliniumOxysulfide Phosphor (Gd2O2S) provides an accuracy of 15% while converting the X-ray photons into light photons. The LanthanumOxysulfide Phosphor (LaОBr) gives an accuracy of 12%. The yttrium oxysulfide phosphor (Y2O2S: Tb) gives an accuracy of 18% with regard to the emission of light photons with respect to intensifying screens. The swiftness of an image intensifying screen depends on the following parameters: • • • •

Thickness of the intensifying screen Grain size of the intensifying screen The size of the phosphor layer on the screen The strength of light photons emitted from the screen when X-ray photons are incident

With regard to the thickness of the phosphor layer on the screen, it is evident that a thicker layer of phosphor will result in the absorption of higher number of X-ray photons. This will result in darkening of the screen sooner. Hence this will increase the speed of the intensifying screen.

Fundamentals of X-Rays  53 X-ray Photons

CaWO4 Crystals Light Photons

Intensifying Screen

Film

Figure 2.19  Increase in screen thickness degrades the image quality.

But increase in this thickness results in a higher number of scattering of light photons. This will decrease the sharpness as well as the contrast of the image formed. Furthermore, if the phosphor crystal is too far from the film, a larger area of the film will get blackened. On the contrary, if the crystal is very close, then a much smaller area of the film will be blackened. Hence the distance of the film from the crystal needs to be optimum so as to obtain the required image. The image resolution can also be improved by the addition of a light absorbing dye to phosphor. A typical phosphor layer is shown in Figure 2.19.

2.11.2 Image Intensifiers Image intensifiers are used to increase the brightness of the X-ray image obtained on the X-ray film. This is due to the fact that the conventional X-ray images obtained on the X-ray image intensifying screens are so weak that they can be seen only in dark rooms. Image intensifiers mitigate this issue and increase the brightness of the image for a better visualization of the X-ray images obtained. Image intensifier is a simple vacuum tube housing an input phosphor as well as a photocathode, supported by the focusing plates as well as the anode and the output phosphor. In general, the X-ray photons from the source pass through the subject, and then those X-ray photons coming out of the subject are fed to the fluorescent screen which in turn emits light photons accordingly. These light photons then strike the photocathode which is composed of a photo emissive metal such as that of caesium and antimony. Hence once the light photons strike the photocathode, corresponding electrons are produced. These are focused and accelerated and

54  Medical Imaging Output Fluorescent Screen

Electrons Deflecting Plates

Anode

Glass Enclosure

Input Fluorescent Screen

Photocathode

Figure 2.20  Generic image intensifier tube.

the resulting electron beam is made to strike the output fluorescent screen with the aid of the focussing plates as well as the anode. When a fluorescent screen of about 2 cm diameter is struck by the high-energy electrons, coming out of the anode with an average of 25 kV potential, a brighter image is generated. Thus the generated image is much brighter than the ones generated using a conventional fluoroscope due to the following reasons: • The anode accelerates the electrons and provides adequate energy to them • The input screen is bigger than the output screen in the present case Image intensifiers use Caesium iodide as the input phosphor and Zinc calcium sulphide as the output phosphor. A generic image intensifier is shown in Figure 2.20.

2.12 Detection of X-Rays The most common approaches employed for the detection of X-ray photons are with X-ray films and X-ray detectors. 

Fundamentals of X-Rays  55

2.12.1 X-Ray Film An X-ray film is nothing but a simple photographic film containing a transparent and a plastic substrate coated with a light sensitive emulsion at both the sides. The substrate is generally made up of acetate/polyester. The light sensitive emulsion contains silver halide or silver bromide crystals with a grain size of 0.1 µm to 1 µm. When light photons strike these crystals, a free electron is released which then combines with the silver ion to result in a silver atom. Silver iodide is used to sensitize the film. Due to the fact that the silver atom is black in colour, any point of the film at which the light strikes will become dark. This darkening is directly proportional to the incident light (incident light is in turn dependent on the intensity of light as well as the time of exposure).

2.12.2 Optical Density The optical density, also termed as the photographic density, is useful in the measurement of the blackness created in the film. This is mathematically presented in equation 2.17



I D = Log 10  i  It

  

(2.17)

Where D = Optical density Ii = Incident light intensity It = Transmitted light intensity  This phenomenon is depicted in Figure 2.21. A higher optical density value hints at a lesser transmission of light due to which the film will get more darker. In general, an X-ray film with a density value of say around 0.3 looks bright whereas a value of 2 looks darker, when observed in standard viewing setup. Initially, when the X-ray film is not exposed to the light photons, the density value will be 0.2. This is often termed as the base plus fog density. This value is often seen due to the base material (upon which the emulsion is coated) and the film fog (seen due to the silver halide developed without any exposure to light photons). Brightness is often relevant to the physiological perception of the human eye which is expressed on a logarithmic scale. Hence, the optical density also is expressed on a logarithmic scale.

56  Medical Imaging Ii

Medium

It

Figure 2.21  Optical density.

2.12.3 Characteristic Curve Characteristics curve defines the dependency on the optical density and the X-ray film exposure. This is often called as the H-D curve of the film. A sample H-D curve for an X-ray film with an intensifying screen is shown in Figure 2.22. In this example, it is evident that the density value is not zero for zero exposure due to the film fog and the nature of the base material.

3.5 Shoulder

Optical Density

3.0 2.5 2.0

Linear Region

1.5 1.0 0.5

Toe

Fog Level

0 Log Exposure

Figure 2.22  H and D curve.

Fundamentals of X-Rays  57 At the centre, the optical density and the log of the film exposure is almost linearly proportional to each other. This forms the most important aspect of the curve.

2.12.4 Film Gamma The film gamma is considered to be the maximum slope of the characteristic curve. Film gamma is denoted by equation 2.18 and is illustrated in Figure 2.23, based on which it is evident that the film amplifies the light photons incident when the slope value is higher than 1.

γ=

D2 − D1 Log 10 E2 − Log 10 E1

(2.18)

2.12.5 Speed The speed of an X-ray film is the amount of X-ray exposure needed to achieve a density of 1.0 above the fog density of the film. Note that the

3.5 3.0

Optical Density

2.5 2.0 D2 1.5 D1 1.0 0.5 0

Log10 E1

Log10 E2 Log Exposure

Figure 2.23  Film gamma –a (Film gamma is defined as sleepiest slope in linear region of characteristic curve).

58  Medical Imaging X-ray exposure is measured in terms of Roentgen. This is given by equation 2.19

S=



1 E

(2.19)

Where S = speed E = Exposure The Speed (S) is often relevant when discussed in terms of X-ray intensity (I) as well as the exposure time (E). A film with a higher speed would need a shorter exposure time for a constant intensity to obtain an optical density of 1. But in the real-time world, the speed of the film depends upon various aspects such as those of silver grain size, silver grain content, film development temperature and film development time. However, speed of

3.5

B

3.0 A

Optical Density

2.5 2.0 1.5

DB2 – DB1

DA2 – DA1

1.0 0.5 0 ∆ Log10 E Log Exposure

Figure 2.24  Film latitude - b (Film of larger latitude has lower film contrast).

Fundamentals of X-Rays  59 the film as well as the fog density also rises with a rise in development temperature.

2.12.6 Film Latitude Film latitude is the logarithmic value of the exposure to X-ray beams that result in an acceptable optical density in diagnostic range. Contrast is the variation in the optical density between two neighbouring regions in the film. A larger latitude gives rise to a low film contrast. This phenomenon is depicted in Figure 2.24. Here, film B has a smaller latitude than the film A. However, the film contrast of B ie (DB2 – DB1) is larger than the film contrast of A i.e., (DA2 – DA1), for the same value of Δlog E.

X-ray Cassette Wall Protective Coating Screen Substrate Reflective Layer (to light) Phosphor Light Sensitive Emulsion Film Substrate

Foam Pad

Figure 2.25  Double emulsion film.

60  Medical Imaging

2.12.7 Double-Emulsion Film Coating the X-ray photographic film using a film substrate on both sides of the film ensures that the film does not bend and the film contrast is also increased. In fact, the film will bend if the substrate is coated on a single side. This is when the emulsion dries and shrinks. Such a condition is entirely avoided by double-sided coatings. A generic double emulsion film is depicted in Figure 2.25 in which the emulsion thickness is 0.01 mm and the thickness of the base is 0.15 mm.

2.13 Radiation Detectors Scintillation detectors and ionization chamber detectors are the most common types of X-ray radiation detectors used in diagnostic X-ray technology, as explained below.

2.13.1 Scintillation Detector A scintillation detector is composed of a scintillation crystal which is coupled to a photomultiplier tube. Figure 2.26 depicts a pictorial representation of a photomultiplier tube. The crystal is made up of a combination of sodium iodide and thallium. These sodium iodide emits the light photons, proportional to that of the X-ray photons absorbed. A reflective material X-ray Photon

Collimator

Reflective Layer

Scintillation Crystal Optical Window Photocathode Focusing Grid

Grounded e–

V1 Dynodes

Vn 1200 V

Figure 2.26  Photomultiplier tube.

Anode

Fundamentals of X-Rays  61 coated on the crystal surface collects the light photons. A normal scintillation crystal is made up of an anode, a photocathode (with a coating of a photoemissive material) and multiple dynodes (intermediate electrodes). The photocathode emits electrons when the light photons hit them. The potential of the photocathode is less than the potential of the dynode. In fact, the photocathode is often at ground potential (V1). This makes the electrons emitted from the photocathode to travel towards the dynode. The dynode is coated with appropriate material so as to emit secondary electrons when the electron from the photocathode strikes it. The potentials of the dynodes are V2, ..., Vn. In summary, as the electrons are moving down the tube, they get multiplied. Hence, the overall output current seen is proportional to the strength of the light photons. An overall efficiency of around 85% is seen in such detectors.

2.13.2 Ionization Chamber An ionizing chamber is a gas-filled chamber with xenon being the most commonly used gas. The X-ray photons are found to ionize these gas molecules. The ions thus generated by the gas travel towards the electrodes due to the presence of a voltage difference. This voltage difference is controlled so that a current value proportional to the X-ray photons absorbed is produced. Xenon is the most preferred gas due to its heavy metal as well as the inert nature. However, due to the low density of such gases used inside the chamber, a few of the X-ray photons may travel without being detected at all. This makes such chambers inefficient. However, these chambers are cost effective. This is shown in Figure 2.27.

Voltage Source +

Collimator

Anode

–

X-ray Photon

Current Meter

– +

+

Cathode

Figure 2.27  Ionization chamber.

–

62  Medical Imaging

2.14 X-Ray Diagnostic Approaches Various types of X-ray-based approaches are employed in the field of diagnostic imaging. A few important types of such X-ray-based diagnostic imaging procedures are highlighted in this section.

2.14.1 Conventional X-Ray Radiography Conventional X-ray radiography is one of the most commonly used X-ray diagnostic imaging methods. The advantages of this approach is that it is very basic and conventional, yet delivers the required outputs. The operational procedures are very simple and encompasses a completely automated approach. It does not need any special training sessions to operate this equipment. Hence it is very easy to obtain diagnostic X-ray scans using conventional X-ray radiographs. It provides a higher performance as compared to various other modalities with a better image resolution as well. A depiction of a simple radiographic system is provided in Figure 2.28 from which it is clear that the filter is used to filter out the unwanted X-ray energy beams and also to restrict the beam so as to visualize the required organ only. This also reduces the exposure to the subject. The grids placed behind the subject are useful in the removal of X-ray scatters. The screen/

Anode of X-ray Tube

Filter

Diaphragm

Patient Grid Screen-film Cassette

Figure 2.28  Conventional radiographic system.

Fundamentals of X-Rays  63 film component records the image based on the X-ray beam transmitted across the subject. X-ray attenuation is known to be proportional to the electron density of the tissue. Hence it is obvious to say that when the X-rays travel through the lower density region, they strike the films with a higher density and vice versa. For example, object O in Figure 2.28. Due to this factor, the lower density region will be depicted in a darker shade in the X-ray film. One could hence conclude that the attenuation of the tissues in the path of the X-rays is inversely proportional to the gray levels of the X-ray images formed in the films, as shown in equation 2.9. However, this equation is true for homogeneous medium and a constant attenuation coefficient (β). However, in real time, this is not true as most of the mediums such as those of tissues are heterogeneous in nature.

2.14.2 Penumbra The focal spot in an X-ray beam generator is often of a finite size. This causes a blurring effect when a given object is imaged using X-ray systems. This is shown in Figure 2.29, in which a point P is expected to appear on the film as an ideal case. But due to a finite size of the focal spot (f), the f X-ray Source

Patient

S

P

t

d

Figure 2.29  Blurring effect on the image of the object (Finite aperture of X-ray source causes blurring of image).

64  Medical Imaging point P in the object gets blurred. The blurred point P is denoted by d in the image obtained. This is defined as the penumbra (geometric unsharpness). The relationship between the focal spot and the blurriness is denoted by equation 2.20.

d=



ft S −t

(2.20)

Penumbra can be reduced by reducing f and t and also by increasing S. This would then result in a clearer image with lesser blurring effect seen due to penumbra. When imaging the chest area, the subject is required to lean their chest against the film and the generator is placed away from the subject.

2.14.3 Field Size The X-ray beam diverges as it moves away from the focal spot. This is illustrated in Figure 2.30. If do is the size of the beam restrictor, then the field size d1 which is away from the focal spot at a distance S is given by equation 2.21. Similarly, the field size d2 is given by equation 2.22.

X-ray Source s0 d0

Diaphragm

s1 s2

d1

d2

Figure 2.30  Field size (X-ray beam field size is proportional to distance from source).

Fundamentals of X-Rays  65 (2.21)



S  d1 = do  1   So 



S  d2 = d1  2   S1 

(2.22)

However, penumbra would be relative to the boundaries due to a finite field size.

2.14.4 Film Magnification As shown in Figure 2.31, if the location of the object is O and the same is depicted at a distance t from the film, then the size of the object, Lo is magnified by a factor rm as given in equation 2.23.

Sf L1 = Lo S f − t

r= m



(2.23)



X-ray Source

Sf O

Patient

L0 I

L1

Figure 2.31  Film magnification (X-ray image of object is magnified by ratio of Sf (Sf-t)).

66  Medical Imaging Where L = size of the object S = distance between the focal spot and the location of the X-ray film Equation 2.23 illustrates that if at all multiple objects are to be imaged on the film, then the image so obtained will demonstrate a distortion relative to the distance between the X-ray film on which the image is being formed and the distance between the objects. In order to minimize this distortion, one needs to take adequate care to ensure that Sf> t. X-rays are often the preferred mode of diagnostic imaging for hard tissues such as bones due to the fact that the density of tissues is very different, when compared to other soft tissues of the body. However, X-rays cannot be used when differentiation of soft tissues is required. In such cases, ultrasound and magnetic resonance-based imaging approaches are employed.

2.15 Fluoroscopy A conventional fluoroscope is as shown in Figure 2.32. As compared to the conventional radiography unit, the only variation in fluoroscopy is the inclusion of an assembly of fluorescent screen instead of a standard image intensifier which was seen in the case of conventional X-ray radiography. The fluorescent screen assembly encompasses a grid (to insert an X-ray film), a fluorescent screen as well as a lead glass layer (to absorb the X-ray radiations which pass through the screen). But one major challenge in this modality is the weak images produced. So, to analyse a fluoroscopy image, the analysing environment needs to be dark. Also, the image quality is less. Hence in recent fluoroscopes, an image intensifier is included to amplify the light photons and hence the issue of dark room requirement is averted. Consider an example of the assessment of the digestive tract-based pathology such as those of tumors and ulcers can be ascertained using fluoroscopy. In this aspect, a contrast medium such as that of barium sulphate is provided to the subject orally. Continuous X-ray scans of the region of interest are acquired for the assessment. The challenge in this process is the constant exposure to X-rays which can be harmful to the subjects.

Fundamentals of X-Rays  67

TV TV Monitor

Optics

Image Intensifier

Grid Patient

X-ray Generator

Figure 2.32  Conventional fluoroscope.

2.16 Angiography Angiography is useful in the ascertainment of vascular constrictions and tumours. This approach aids in the provision of a radiography-based visualization of blood vessels. Here, a non-toxic radio-opaque substance like iodine which is considered to be a contrast medium is injected into the artery or vein by the method of catheterization. This bolus dilutes with blood as it gets circulated in the bloodstream. X-ray radiographic images are acquired after the injection of the contrast for better visualization of the blood vessels and to assess if there are any pathologies associated. However, this approach is not without challenges. The most important drawback here is the injection of a foreign object such as that of the contrast. Certain subjects may be allergic to contrast agents such as those of sodium iodide because this is ionic in nature. But introduction on non-ionic contrast agents can address this issue. But again, non-ionic contrast agents are costly. But clinicians still prefer angiography in various pathological assessments such as those of stenosis, thrombosis, etc., due to the fidelity of the images obtained in this process.

68  Medical Imaging

2.17 Mammography Mammograms can be obtained either with the injection of the contrast mediums or entirely without the usage of such agents. However, assessment of the breasts is the confined usage of mammography. Breast is made of soft tissues and for such soft tissues, low energy X-rays are preferred. Hence mammography employs X-rays of about 20 keV using molybdenum (Mo) anode which has an atomic number of 42. Molybdenum is known to provide a peak at 17.4 keV and 19.6 keV and hence can be extremely useful in mammography-based scans. Single emulsion films are used in mammograms due to the fact that microcalcification in breasts can be visualized better with such films. Recent mammography machines are developed to provide a resolution equivalent to 0.125 – 0.2 times the radiation dose as compared to that of the Xeroradiography.

2.18 Xeroradiography Xeroradiography is an X-ray technique which utilizes an energy level of 35 keV to 45 keV only. This also employs an electrostatic approach instead of conventional X-ray films to record the image. Here, a positively charged selenium coated plate is used for the image formation. The X-ray photons striking this plate results in the emission of electrons from the selenium and a part of the positive charge of the plate is mitigated. The region of the plate under thicker body parts retains most of their positive charges whereas the areas of the plate which are under thinner body parts end up losing their positive charge. After this, a negatively charged blue powder is sprayed on the plate. The extent to which this powder gets retained by the regions of the plate will elicit the information about the corresponding X-ray intensity over those respective body parts. While spraying the blue powder, the powder close to the plate area with little positive charge gets attracted to the edge of the nearest area with more positive charge. This results in the formation of a well-defined image of that particular edge. In other words, the edges are very well enhanced in xeroradiography scans. Hence thicker body parts are imaged better than thinner body parts in this method. However, this is not as sensitive as conventional X-ray scans. So, to get an image as similar to that of a conventional X-ray image, a higher patient dose is to be provided in Xeroradiography. The patterns of blue powder are later emulated upon a sheet of plastic-coated paper for ­visualization-based applications. This technique is depicted in Figure 2.33.

Fundamentals of X-Rays  69 Plate Storage Conpartment

Exposed Cassette Plate

Selenium Plate

Spray

Finished Xeroradiogram

Paper Image Transfer

Heater

Blue Toner

Figure 2.33  Xeroradiographic system.

Mammography as well as Xeroradiography requires the compression of the breasts during the scans so as to provide a uniform dose to the breast and to reduce motion artifacts and also to reduce the patient dose to the areas of the breast. However, X-ray based mammograms are known to provide an accuracy of 85% which may result in wrong diagnosis. Also due to the issues pertaining to radiation dose and exposure, other diagnostic modalities such as those of thermograms and magnetic resonance-based scanning methods are being used. Ultrasound-based mammographic scans are being used to ascertain the breasts in the presence of fat and also are successful in the differentiation of tumours from cysts especially in breasts.

2.19 Image Subtraction Image subtraction technique is used to reduce the unnecessary background in the image by digital or photographic approaches with X-ray films. This is extremely useful in angiography to ascertain the blood vessels under examination in the presence of the masked images of soft tissues and bones present around those blood vessels. This method is depicted in Figure 2.34. In Figure 2.34, Figure 2.34 (a) contains more square patterns than Figure 2.34 (b). The difference between these two images is not evident by mere physical examination. Hence in this process of image subtraction, a reversed image of Figure 2.34 (b) is produced and then this is superimposed on Figure 2.34 (a) to obtain the image as shown in Figure 2.34 (c). This is most commonly seen in angiogram-based assessment of blood

70  Medical Imaging R C Bx

R

X

C

C B

C

Bx B

X

B

B

A

A

C

C

(a)

(b)

(c)

Figure 2.34  Schematic representation of image subtraction.

vessels. A major challenge in this technique is the usage of the X-ray films with non-linear characteristics. Hence this issue is handled by performing image subtraction digitally, commonly called as the Digital Subtraction Angiography (DSA).

2.19.1 Digital Subtraction Angiography (DSA) Conventional X-ray film-based image subtraction technique has been fairly successful in the reduction of background noise and also to enhance the region of interest. However, inclusion of additional hardware for digital approaches themselves pose a certain amount of noise. But still, the digital approach is preferred due to the inclusion of further image processing possibility. Also smaller amounts of contrasts can be used thereby reducing the allergy to the subjects. Smaller catheters are sufficient in these intravenous approaches which reduce the risk of arteries. The subject need not get hospitalized and hence, this process can be performed easily. As there

Fundamentals of X-Rays  71 is less discomfort to the patient during injecting the contrast, motion artifacts are reduced. This is cost effective with a higher efficiency as well. But the shortfalls of this approach are that the resolution is poor and the field of view is comparatively smaller. Also multiple views cannot be obtained. Digital Subtraction Angiography hardware is very similar to a digital fluoroscopy unit. But in this case, the video signal is logarithmically amplified before digitizing the feed. This is because, logarithmic compression reduces the dynamic range of the input. This makes the image of the blood vessels more uniform. The so compressed signal is directly proportional to the concentration of the contrast agent in the blood vessel.

2.19.2 Dual Energy Subtraction Dual energy subtraction approach is based on the fact that, in the region of interest where the attenuation coefficient reduces smoothly with increase in X-ray energy, the attenuation coefficients of different materials vary

Soft Tissue Bone

X-ray

Bone

120 keV

Soft Tissue

Gray Scale

Gray Scale

(a)

Soft Tissue

Exposure

(b)

Figure 2.35  Dual energy subtraction.

80 keV

Exposure Bone (c)

72  Medical Imaging differently. For example, attenuation coefficient reduces more swiftly in bone than in soft tissues. Figure 2.35 shows an example for the same. Consider an X-ray beam of around 80keV being used to illuminate a phantom as shown in Figure 2.35 (a). The resultant image is obtained in a digital X-ray unit with a gray scale as shown in Figure 2.35 (b). This phantom is again imaged using a higher order X-ray (say around 120 keV). The change in the gray scale is shown in Figure 2.35 (c) wherein the gray level for the soft tissues is the same as that seen for the X-ray beam of 80 keV. In such a scenario, if one image is subtracted from the other, then the resultant image would not contain any information pertaining to soft tissues and only bones are seen. On similar lines, the vice versa is possible as well. This approach mitigates the motion artifact related issue. However, it reduces the gray level differences between adjacent areas in the image and also increases the complexity of the X-ray generator unit.

2.19.3 K-Edge Subtraction The K-edge subtraction technique incorporates the sudden variations of the attenuation coefficients of the contrast agents like iodine near their K-edge regions. For example, the K-edge absorption occurs at 33.2 keV for iodine. If at all two monochromatic X-ray beams of 33 keV and 34 keV are used to obtain two images of the same region of interest, and then if one image is subtracted from the others, then the resulting image shows a better difference between the structures containing iodine with that of the surrounding regions. This is because bones will look almost the same in these images. But the challenge in this process is that conventional X-ray units produce polychromatic rays. Synchrotron radiation sources need to be used to generate monochromatic X-ray beams which are very costly. Instead, appropriate filters can be used to retain the beams selectively. But to make this possible, one would have to use thick filters which will naturally increase the load on the X-ray tubes. The afore-mentioned X-ray-based approaches pose various challenges in the field of diagnostic imaging. These are two-dimensional scans which result in the loss of information pertaining to the depth. Also subtle abnormalities cannot be ascertained. Soft tissues cannot be differentiated in these methods. Also conventional X-rays cannot quantify the densities of various tissues. Hence a feasible solution to these problems is the incorporation of tomographic imaging technique, often called as the conventional tomography.

Fundamentals of X-Rays  73

2.20 Conventional Tomography X-ray-based tomography is a novel approach which removes the undesired region of interest so as to highlight the required part of the body. This, however, does not improve the resolution of the image, but simply blurs the undesired regions. The working principle of conventional tomography is provided in Figure 2.36. The salient aspects of a conventional tomography is an X-ray tube, the X-ray film and a metal structure rotating about a fulcrum. As the X-ray tube moves, the film synchronously moves in the opposite direction. The fulcrum plane is in sharp focus. The regions below as well as above thus fulcrum points are blurred. As shown in Figure 2.36, if there are two regions, namely a circle and a square, the circle is on the fulcrum. As the tube moves towards the left, the film moves towards the right. So, the circle remains in the sharp focus in the image on the film. The film speed is adjusted so as to ensure that the image of the circle falls on the same spot as the tube gets displaced. The image of the square is blurred because it moves faster than the circle and is hence out of synchrony with the movement of the tube. Due to the fact that the source as well as the detector move linearly in opposite directions, this technique is called as

X-ray Source

Patient Fulcrum Plane

Film

Figure 2.36  Tomographic principle.

74  Medical Imaging linear tomography. Complex movement patterns such as those of circular and elliptical movements are employed to achieve a better resolution and image quality, as required. This approach helps to image a particular plane of the object. But this cannot provide a better sensitivity to soft tissues. However computed tomography-based approaches resolve this issue and provide a better sensitivity of soft tissues and also provide better information about the attenuation of the region of interest.

2.20.1 X-Ray Image Attributes The main goal of X-ray diagnostic imaging is of obtain images of the best possible quality. However, the quality of an X-ray scan is always a tradeoff between the image and the radiation dose to the subject. Hence it is always preferred to achieve a balance between these aspects in radiographic imaging applications. In this regard, the salient attributes defining the quality of X-ray images obtained using X-ray scanning machines are as follows:

2.20.2 Spatial Resolution Spatial resolution is defined as the ability of a given X-ray scanning machine to be able to portray closely placed fine structures, as different components. In other words, this refers to the minimal distance between two points in the object to have them seen as separate points in the image as well. X-ray machines are assessed for their capacity of spatial resolution using a simple bar phantom, as shown in Figure 2.37. A bar phantom is composed of lead strips with varying width. The width of each of these strips are equal to the distance between each strips. A group of these strips portray a band pairs with alternate intensities of white and black patterns, respectively. For instance, a simple bar phantom

Figure 2.37  Bar phantom.

Fundamentals of X-Rays  75 can have 4 lines per mm of space, 6 lines per mm of space and so on. An acceptable X-ray imaging system can resolve upto 8 lines per mm of space. This approach is qualitative and hence, with respect to a linear approach, following are the attributes connected to spatial resolution to be ascertained in X-ray machines.

2.21 Point Spread Function (PSF) A 2-D point spread function is defined as the response of a given X-ray system to an impulse input. In other words, the psf is to be normalized with respect to the point impulse function. It is them termed as a normalized psf function (psf ’). The relationship between them is depicted in equation 2.24.



psf (r ) =

prf ′(r ) ∫∫ prf ′(r )dr



(2.24)

where r = (x, y). Conventionally, a higher spatial resolution is achieved with a narrower psf value. The psf illustrates the spatial resolution of a given X-ray system in the absence of any given noise. The psf is assessed by obtaining an image of a small hole though a lead sheet. The characteristic curve is obtained for this image which is obtained on the X-ray film, based on which the optical density distribution of the image is calculated. This is later converted into the distribution of exposure.

2.21.1 Line Spread Function (LSF) Line spread function (lsf) is defined as the area of the one-dimensional point spread function (psf) in a given direction. This is shown in equation 2.25.

lsf(x) = ∫ psf(r)dy = ∫ psf(x, y)dy

(2.25)

where r = (x, y). For a given X-ray equipment with an isotropic point spread function, the one-dimensional line spread function is calculated to be the same value at any orientation. This also indicates the system response. The line spread

76  Medical Imaging Line Spread Function, lst(x) 1 Fast Film/Screen

Slow Film/Screen

0

Distance, x

Figure 2.38  Line spread function for conventional X-ray radiography.

function is measured by imaging a small slit between a set of two lead sheets. The one-dimensional profile of the distribution of the exposure in a perpendicular direction to that of the slit length gives the line spread function in the corresponding direction. This is indicated in Figure 2.38. The shape of the line spread function elicits a quantitative measure of the spatial resolution oriented behaviour of the X-ray imaging system under consideration.

2.21.2 Edge Spread Function (ESF) The edge spread function is the area under the curve for a given line spread function at a particular direction and is shown by equation 2.26.



lsf (x ) =

d esf (x ) dx

(2.26)

The edge spread function is measured as shown in Figure 2.39. The edge spread function is always considered to be an intermediate approach to ascertain the line spread function and can be extremely useful in the characterization of the edges in X-ray images.

2.21.3 System Transfer Function (STF) The system transfer function is defined as the spatial Fourier transform of a given point spread function. This is useful in the assessment of the X-ray

Fundamentals of X-Rays  77 X-ray Generator

Load Plate

X-ray Film-screen combination

Figure 2.39  Measurement of edge spread function.

systems under consideration. One such assessment is in terms of the modulation transfer function (MTF) which is defined as the magnitude of the Fourier transform of the line spread function and is given by equation 2.27. One such sample assessment of the low line spread functions (which were depicted in Figure 2.38) is shown in Figure 2.40.

MTF(ρ) = |F1{lsf(x)}|

(2.27)

The modulation transfer function indicates the nature of the X-ray machine with regard to its interaction with regard to the spatial frequency content of the distribution of the input. Figure 2.40 shows that most of the X-ray machines permit lower order frequencies and suppress high frequency components, as similar to conventional low pass filters. Hence coarser structures are often blurred. It is hence obvious that the systems with lower spatial resolution or wider line spread function result in a narrow modulation transfer function.

2.22 Image Noise Statistical fluctuations in the detection of X-ray photons as well as the grain size in the X-ray films are the major source of noise in X-ray images obtained. This is quantified in terms of quantum mottle. A wiener power spectrum is useful in a quantitative assessment of image noise. For instance,

Modulation Transfer Function

78  Medical Imaging

1.0 0.8 Slow Film/Screen

0.6 0.4 0.2

Fast Film/Screen

0 1

2

3

4

5

6

7

8

Frequency, Cycles/mm

Figure 2.40  MTF Madulation transfer functions for fast and slow film/screen combination of conventional X-ray radiagraphy.

for finer structures in images, the narrower will be the wiener spectrum. Such noise fluctuations can be mitigated by integrating the wiener power spectrum. The image noises are correspondingly addressed by averaging process.

2.23 Image Contrast Image contrast is yet another important aspect which quantifies the quality of an X-ray image. This is given by equation 2.28



C=

S S −b or S +b S

(2.28)

Where C = image contrast S = signal intensity b = background intensity The fidelity of X-ray detection rises with a higher contrast. Hence the X-ray system is expected to generate a higher image contrast for a given

Fundamentals of X-Rays  79 object contrast. For instance, a lower kVp results in a higher image contrast. But this also increases the image noise due to the attenuation of X-ray photons by the biological tissues. The minimal contrast value needed to ascertain an object of a given size in the presence of image noise is defined as contrast resolution.

2.24 Receiver Operating Curve (ROC) The various aspects discussed above are important under ideal conditions. However, in a real-time situation, there are numerous complicated aspects which are to be considered. In this regard, the Receiver Operating Curve (ROC) has been used to ascertain the performance of a given X-ray machine. Based on the observations of the X-ray image, a standard decision matrix can be constructed, as shown in Figure 2.41. However, this approach poses a few challenges to the user. Decisions are often subjective and the threshold values normally differ from one individual to another during the image analysis. Other non-image-based aspects such as those of the subject history and other relevant evidences are to be analysed before concluding upon the image characteristics. The assessment of an ROC includes the observer to visually verify the given set of X-ray images and then develop a curve as shown in Figure 2.42 by varying the threshold value. Superior imaging equipment will result in a larger area under the curve which depicts the accuracy of the imaging system. In Figure 2.42, I denotes a better performance, as compared to II and III.

2.25 Biological Effects of X-Ray Radiations  It is a known fact for the ionizing radiations to damage the tissues, such as that in case of X-ray radiations. Various aspects like time of exposure, area exposed and the exposure dose are a few determinants used to ascertain such biological effects, as shown in this section.

2.25.1 Determinants of Biological Effects Threshold The extent to which a given tissue can accept the X-rays is not quantified. Hence it becomes tough to determine the exact quantification for a threshold value of the X-ray intensity in this regard.

80  Medical Imaging True Condition The object is there

The object is not there

The object is there

True positive TP

False positive FP

The object is not there

False negative FN

True negative TN

Observer Response

Figure 2.41  Observer decision matrix.

True Positive Frantion or Sensitivity

1.00

0.75

I II

0.50

III

0.25

0 0

0.25

0.50

0.75

False Positive Fraction

Figure 2.42  Receiver operating curve.

1.00

Fundamentals of X-Rays  81 Exposure Time The higher the exposure time, the better is the image quality in most of the X-ray scans. But this also poses a threat of increase in the damage to the tissues. Normally, the tissues recover after getting damaged by such exposure, if the time of exposure is below a definite threshold. However, it is better to give a repetitive exposure rather than a single exposure. Exposure Area The damage to the tissues increases as the body area exposed increases. It is hence a normal approach to shield the rest of the body area other than the region of interest during X-ray scans. Variation in Species and Individual Sensitivity Every species, and for that matter, every individual of the same species has a varying reaction of tissues for a given dose of X-ray radiation. For instance, animals get more damaged than plants by a given X-ray exposure. In terms of the same species, a given tissue reacts differently than an adjacent tissue for the same X-ray dose. Cellular sensitivity For a given subject, the cells that divide rapidly are more sensitive to X-ray exposure than the ones which multiply slowly. Also, specialized cells are less sensitive than non-specialized cells. For instance, muscle cells and nerves are less sensitive as compared to white blood cells which are more sensitive to X-ray dose. Short-Term Effects For an X-ray dose of over 100 rad, given for a short time duration, the irradiations seen over a few hours or a few days are considered to be shortterm effects. These are also called as acute radiation syndrome. A few such symptoms include vomiting and nausea. This can lead to fevers, shocks and ultimately death to the subjects. Long-term effects Long-term effects of X-ray exposure include genetic as well as carcinogenic effects. Hence it is advisable to provide a dose of 0.2 rad per day for the subject being exposed to X-ray radiations constantly for a longer period of time. This can be seen in the technicians conducting the X-ray scans upon the subjects, in general.

82  Medical Imaging

Glossary-Appendix 1. Monochromatic - A single energy level in contrast to white X-rays used in conventional radiation therapy.  2. Permeability - They are quantifiable data which can be candidates for imaging biomarkers in stroke treatment.  3. Photon - An uncharged particle of energy, moving in waves produced by the interaction of high-speed electrons with a target. 4. Ionization - It is the principal means by which  ionizing radiations dissipate their energy in matter.  5. Attenuation - It is the reduction of the intensity of an x-ray beam as it traverses matter. The reduction may be caused by absorption or by deflection. 6. Homogeneous - A structure with similar components. 7. Polychromatic - Relating to radiation that is composed of more than one wavelength. 8. Spectrum - The series of images resulting from the refraction of electromagnetic radiation and their arrangement according to frequency or wavelength. 9. Filament - The filament is the source of electrons (cathode) in x-ray tubes. 10. Helical - The helical path results in a three-dimensional data set, which can then be reconstructed into sequential images for a stack. 11. Anode angle - The anode angle refers to the angle the target surface of the anode sits at in relation to the vertical.  12. Aperture - Diameter of the stop in an optical system that determines the diameter of the bundle of rays traversing the instrument. 13. Diaphragm - Any partitioning structure, such as the iris diaphragm of the eye. 14. Antimony - A trivalent and pentavalent metalloid element with atomic number 51 that commonly occurs in a brittle, metallic, silvery white crystalline form.  15. Emulsion - A mixture of two immiscible liquids, one being dispersed throughout the other in small droplets. 16. Scintillation - A flash of light produced in a phosphor by an ionizing event.

Fundamentals of X-Rays  83 17. Dynodes - A dynode is an electrode in a vacuum tube that serves as an electron multiplier through secondary emission. 18. Photocathode - A  photocathode  is a negatively charged electrode in a light detection device such as the input screen in an image intensifier.  19. Conventional - It is an adjective used to describe things that are normal, ordinary, and following the accepted way.  20. Tomography - Technique for displaying a representation of a cross section through a human body or other solid object using X-rays or ultrasound.

3 X-Ray Computed Tomography 3.1 Introduction to X-Ray Computed Tomography X-ray computed tomography, commonly having an acronym of CT, is useful to obtain cross sectional images of the region of interest, based on the attenuation of X-rays from those areas. In the word tomography, Tomo means to cut/slice and Graphy means to write/reconstruct; this approach is dependent on the X-ray attenuations and hence the name X-ray computed tomography. In CT machines, the X-ray radiations are obtained from conventional X-ray tubes. These X-rays generated strike the subject (at the region of interest) and get attenuated. Thus attenuated X-ray radiations are detected using X-ray detectors. The entire field of view is thus scanned based on a set of lines, in the case of thin X-ray beams. This approach follows either in parallel beam pattern or fan beam pattern. The same process is followed for different angles of measurement, due to which we can obtain the measurement of line attenuation for discrete angles as well as for the distances from the center of consideration. These attenuation values at every point of the region of interest are used to reconstruct a cross sectional image of this region using different reconstruction algorithms. It is to be noted that the reconstruction approaches are similar in the case of other imaging modalities such as Positron Emission Tomography as well as Magnetic Resonance Imaging scans. However, the present section highlights the process of reconstruction based on attenuation coefficient and hence, at times, X-ray computed tomography is also called as attenuation computed tomography. This approach of reconstruction of images is based on the concept of reconstruction of a function by their projections. This was developed by a mathematician, Johann Radon, in 1917. A normal CT machine is as shown in Figure 3.1. Figure 3.1(a) shows a schematic representation of CT whereas Figure 3.1(b) shows a real-time CT machine. Development of novel approaches such as those of helical as well as multi-slice CT technology has aided in 3D volumetric reconstruction H. S. Sanjay and M. Niranjanamurthy. Medical Imaging, (85–120) © 2023 Scrivener Publishing LLC

85

86  Medical Imaging

(a)

(b)

Figure 3.1  CT machine.

approaches of various organs being ascertained. Conventional CT images are of 512 x 512 pixels of late. Before the incorporation of modern CT machines, conventional tomography based on a linear approach as well as an axial transverse approach was being used, as described below and shown in Figure 3.2. 1. Linear tomography: in this approach, the X-ray tube as well as the film detector move at a constant speed, but in opposite directions. This will ensure that one region of interest is always projected on the same position on the film while the other regions are averaged out. 2. Axial transverse tomography: In this modality, the X-ray detector film is placed horizontally in front of the subject, Film

P1

P2

x-ray tube

(a)

Figure 3.2  Linear tomography and axial transverse tomography.

(b)

X-Ray Computed Tomography  87 below the focal plane, and the detector film is made to rotate at a fixed speed around a vertical axis, but the X-ray tube is retained to be stationary. Hence in this case, the focal plane of the subject is retained whereas the rest planes are averaged out.

3.2 CT Number The normal 512 x 512 pixels of the CT images denote the CT number generally defined in terms of Hounsfield units (HU). The linear attenuation coefficient values obtained are in terms of the values relative to that of water, magnified to a larger value by multiplying the normalized difference by a larger integer, called the CT number. The mathematical representation of the CT number is given in equation 3.1



 µ − µw  CT number = k   µw 



(3.1)

where k = an arbitrary constant (This is generally 500 or 1000) μ = Linear attenuation coeffieicnt of a given pixel μw = Linear attenuation coefficient of water For instance, air has a CT number of -1000 HU and water has a CT number of 0 HU. Although bone has a positive value of the CT number, this value ranges between 100 HU to 1000 HU. This variation in the CT number of the bone is seen due to the different types of structure as well as compositions of different types of bone. A gray level or a color scale can be used to represent the CT number of the attenuation coefficient. This flexibility is highly useful when it is required to display the soft tissues in which the attenuation coefficients vary up to a limited range of values. Based on the clinical application, the air-tissue as well as the bone-tissue contrasts vary based on suitable gray level transformations performed by window- or level-based approaches. The window quantifies the width of the gray level interval whereas the level defines the center of the gray level. This is depicted in Figure 3.3. Figure 3.3(a) emphasizes on the visualization of the lungs whereas Figure 3.3(b) highlights soft tissues of the lungs.

88  Medical Imaging

(a)

(b)

Figure 3.3  CT image of chest with different window lengths and levels.

3.3 X-Ray Detectors in CT Machines 3.3.1 Energy Integrating Detectors Most of the detectors used in CT machines are made up of a scintillating crystal with a photodiode. The scintillator is used to convert the X-ray photons into visible photons, often called as scintillations. These scintillations strike the photodiode which produces an equivalent electric current. The scintillators are assembled in the form of a matrix which denote the detector cells. They have a very high absorption efficiency of above 95% and also provide a swift response of a few microseconds. The absorption efficiency of the detector is limited to about 80% due to the finite thickness of septa in the grid used. A multichannel Data acquisition System (DAS) is connected to the photodiode which converts the electrical charges from the photodiode into equivalent voltage value with the aid of a trans-impedance amplifier and also converts the analog signal into its digital equivalent. However, these detectors are prone to electrical noises due to the usage of trans-impedance amplifiers which result in streaks in the images.

3.3.2 Photon Counting Detectors Photon counting detectors are capable of counting the number of X-ray photons directly without any intermediate conversion into light and then

X-Ray Computed Tomography  89 into voltage values. Materials such as cadmium telluride (CdTe) or cadmium-zinc-telluride (CZT) are used to convert the X-ray photons into an equivalent electronic charge value. This has a higher signal ratio as compared to scintillation crystals. This also eliminates the streak noises as seen in scintillation detectors. Electronic noises are removed by setting a predefined threshold value for the photon detection. Also, higher weights are assigned to low energy photons which increases the difference in the attenuation values between two given tissues. Hence the fidelity of this system is higher. This has a higher energy resolution due to its direct conversion of photons into charge values. However, these detectors have the issues of stability as well as the limit of counting rate. Hence these are not used in commercial CT machines as of now.

3.4 CT Imaging Data acquisition and reconstruction

3.4.1 Radon Transform Consider a given two-dimensional function given in Figure 3.4 (a). In this figure, let μ(x,y) represent a 2D function which is the distribution of the linear attenuation coefficient in xy plane. It is to be noted that the subject is made to lie down along z axis and μ(x,y) does not exist outside the circular field of view (FOV). A line running through μ(x,y) is called a ray. The integral of μ(x,y) along this ray is called a ray integral and a set of many such ray integrals is called a projection. These X-ray beams are seen to be existing at an angle θ, with the y axis. The X-ray beam has an intensity of Io when it is not attenuated. Hence a different system with new coordinates (r,s) are obtained by rotating (x,y) by an angle θ. Hence, we define the following transformation relationship, as shown in equation 3.2



 r   cosθ  s  =  − sinθ   

sinθ   x    cosθ   y 

(3.2)

Solving equation 3.2 for obtaining the values in (x,y) coordinate system, we get equation 3.3

90  Medical Imaging



 x   cosθ  = y    sinθ

− sinθ   r   cosθ   s 

(3.3)

For a definite value of θ, the intensity profile measured, in terms of r is depicted in Figure 3.4(b) and is given by equation 3.4 and equation 3.5

Iθ (r ) = I oe − ∫ Lr ,θ µ ( x , y )ds



(3.4)

Replacing (x,y) in equation 3.4 with the relationship shown in equation 3.2, we get equation 3.5, shown below



Iθ (r ) = I oe − ∫ Lr ,θ µ (r cosθ −s sinθ ,r sinθ +s cosθ ) ds

(3.5)

where Lr,θ is the line that makes an angle θ with the y axis at a distance of r from the origin. In fact, the X-ray tube spectrum and the attenuation are related as shown in equation 3.6



∞

Iθ (r ) = ∫ 0 σ ( E )e − ∫ Lr ,θ µ ( E ,r cosθ −s sinθ ,r sinθ +s cosθ )ds dE

(3.6)

In general, X-rays are assumed to be monochromatic in nature. Hence equation 3.5 is used as an approximation and the intensity profile is thus converted into an attenuation profile and is shown in equation 3.7



 I (r )  pθ (r ) = = − ln  θ   Io 

∫

Lr ,θ

µ (r cosθ − s sinθ , r sinθ + s cosθ )ds



(3.7)

where pθ(r) = projection of the function μ(x, y) along the angle θ as seen in Figure 3.4 (c). FOV . Also pθ(r) can be measured It is to be noted that pθ(r) = 0 for |r| ≥ 2 for 0 ≤ θ ≤ 2π. We also know that identical values are obtained for the concurrent beams traversing in opposite direction. Hence corresponding attenuation profiles become redundant. So, for a parallel beam geometry, pθ(r) is measured for 0 ≤ θ ≤ π only.

X-Ray Computed Tomography  91 l0(r) S

θ

y

l0 µ (x, y)

r l0 r

FOV

θ

(b) P0(r)

lg(r) r (a)

(c)

Figure 3.4  Depiction of radon transformation.

θ

r

Figure 3.5  Sample sinogram.

92  Medical Imaging A 2-dimensional dataset pθ(r) is created based on the projections pθ(r) and is called as sinogram. This is shown in Figure 3.5. If the distribution of a single dot is projected, then that projection will take the shape of a sinusoid. Hence the same sinogram. Mathematically, Radon transform denotes the transformation of a given function f(x, y) into its sinogram p(r, θ), as shown in equation 3.8 ∞

p(r ,θ ) = R{ f ( x , y )} = ∫ −∞ f (r cosθ − s sinθ , r sinθ + s cosθ )ds (3.8) 3.4.2 Sampling The previous sections describe the projection data for all values of angles (θ) and distances (r). However, in practice, this is not true. In fact, we see only a limited number of projections (M) and a limited number of samples from the detector (N) as well. Hence a discrete sinogram p(nr, mθ) is to be developed which is to be represented as a matrix of M rows and N columns. Here, r denotes the detector sampling distance and θ represents the rotation interval between the views. FOV . Hence, the minimum number of We know that p(r, θ) = 0, |r| = 2 the detector samples can be found out, for a given beam width s. Figure 3.6 shows the aspects with regard to the number of detector samples required. The projection of the X-ray beam is given in Figure 3.6(a). The Fourier transform of this projection is given in Figure 3.6(b). When a block-shaped beam (shown in Figure 3.6(c)) is convolved with the projection (Figure 3.6(a)), we get a smoothened projection (Figure 3.6(e)). On similar lines, if the Fourier transform of the projection (Figure 3.6(b)) is multiplied with a sinc function (Figure 3.6(d)), then we get the resultant Fourier transform without any high-frequency contents. The smoothened projection (Figure 3.6(e)) is convolved with a pulse train (Figure 3.6(g)) to give a sampled signal (Figure 3.6(i)). This is similar to the convolution of the Fourier transform (Figure 3.6(f)) with the reciprocal of the pulse train (Figure 3.6(h)). The resulting spectrum is given in Figure 3.6(j)). This is obtained by shifting and adding the spectrum shown in Figure 3.6(f)). This also generates a little amount of aliasing. To reduce the aliasing, the contribution of Figure 3.6(f) in Figure 3.6(j) should be as far as possible. If s is the beam width, then the width of the main lobe is s/2. This indicates that the distance between the pulses in Figure 3.6(h) which is 1/r should be atleast 2/s, as shown in equation 3.9.

X-Ray Computed Tomography  93 (a)

(b)

r k

(c)

(d) ΔS

r -1/ΔS

1/ΔS

k

-1/ΔS

1/ΔS

k

(f)

(e)

r

(h)

(g)

Δr

r

(i)

k -1/Δr

1/Δr

(j)

k

r Δr

Figure 3.6  Detector sampling.

-1/Δr -1/Δs

1/Δs 1/Δr

94  Medical Imaging



1 2 Ds ≥ or Dr = Dr Ds 2

(3.9)

Hence one could conclude that the sampling distance should always be less than s/2. Equation 3.9 adheres to the nyquist criterion as well. For example, a field of 50 cm with a beam width of 1 mm needs 1,000 detector channels.

3.4.3 2D Image Reconstruction i.  Back projection Back projection helps to reconstruct the function f(x, y), as shown in equation 3.10 in which, for a given line (r, θ), the values p(r, θ) are assigned to all points (x, y) along the line. This process is repeated for the values 0 ≤ θ ≤ π. π



b( x , y ) = β { p(r ,θ )} = ∫ 0 p ( x cosθ + y sin θ ,θ )dθ

(3.10)

The discrete version of the back projection is given in equation 3.11

= { p(rn ,θm )} ∑mM=1 p(xi cosθm + y j sinθm ,θm )Dθ (3.11) b(xi , yi ) β=

Figure 3.7  Interpolation for discrete back projection.

X-Ray Computed Tomography  95 It is also to be observed that the values (xi cos θm + yj sin θm) do not coincide with the discrete projections rn. This mandates the incorporation of the technique of interpolation, as shown in Figure 3.7, in which a projection line through each of the pixel is drawn for every view. The intersection of the line and the detector array is calculated and the corresponding projection value is interpolated linearly, based on the neighboring values measured. This is called pixel-based back projection with linear interpolation. ii.  Central slice theorem The Central slice theorem relates the Fourier transform and the radon transform. This is a fundamental step in many reconstruction techniques. Alternately, this helps to derive a mathematical expression of the inverse radon transform, as shown in equation 3.12

f(x, y) = R−1{p(r, θ)}

(3.12)

Equation 3.12 is supported by the projection theorem as shown below. Statement Let F(kx, ky) be defined as the 2-dimensional Fourier transform of f(x, y), as shown in equation 3.13 ∞



F (kx , k y ) = ∫∫ −∞ f ( x , y )e

−2π i ( kx x + k y y )

dx dy

(3.13)

Let Pθ(k) be the one-dimensional Fourier transform of pθ(r), as shown in equation 3.14 ∞



Pθ (k ) = ∫ −∞ pθ (r )e −2π i ( kr )dr

(3.14)

If θ is considered to be varying, then Pθ(k) is regarded to be a 2-­dimensional function of P(k, θ). Then the central slice theorem can be mathematically expressed as shown in equation 3.15

P(k, θ) = F(kx, ky)

(3.15)

96  Medical Imaging where



kx = k cos θ , k y = k sin θ and k = kx2 + k y2

(3.16)



It is hence possible to calculate f(x, y) for every point (x, y) based on the respective projections pθ(r) with 0 ≤ θ ≤ π. Proof A 2-dimensional Fourier transform of f(x, y) is given by equation 3.17 ∞



F (kx , k y ) = ∫∫ −∞ f ( x , y )e

−2π i ( kx x + k y y )

dx dy

(3.17)

Equation 3.16 in equation 3.17 gives rise to equation 3.18 ∞



F (kx , k y ) = ∫∫ −∞ f ( x , y )e −2π i ( k cosθ x +k sinθ y ) dx dy

(3.18)

For any given value of θ, equation 3.12 and equation 3.3 can be used with the Jacobian determinant J (as shown in equation 3.19), to obtain the polar coordinates from cartesian coordinate system with respect to r and s, as shown in equation 3.20.

J=

Cos θ

− sinθ

sinθ

cosθ

=1

(3.19)



∞

F (kx , k y ) = ∫∫ −∞ f (r cosθ − s sin θ , s cosθ +

r sinθ ) e −2π i ( k cos θ (r cosθ −s sinθ )+k sin θ ( s cos θ +r sin θ ))ds dr



(3.20)

Also, we know that

cos2θ + sin2 θ = 1



(3.21)

Substituting equation 3.21 into equation 3.20 and simplifying, we get equation 3.22 ∞



F (kx , k y ) = ∫∫ −∞ f (r cosθ − s sin θ , s cos θ + r sin θ ) e −2π i ( kr )ds dr

(3.22)

X-Ray Computed Tomography  97 The function e−2πi(kr) does not depend on the variable s and hence can be taken out of the inner integral thereby giving rise to equation 3.23



F (kx , k y ) =

∞

  −∞ 

∞

 f (r cosθ − s sin θ , s cos θ + r sin θ )ds  e −2π i ( kr ) dr −∞ 

∫ ∫

(3.23)

From equation 3.8, it is evident that the inner integral resembles the projection p(r, θ) due to which equation 3.23 can be written in the form of equation 3.24 ∞

F (kx , k y ) = ∫ −∞[ p(r ,θ )] e −2π i ( kr )dr



(3.24)

The RHS of equation 3.24 is the one-dimensional Fourier transform of p(k, θ) and can be written as shown in equation 3.25

F(kx, ky) = P(k, θ)

(3.25)

Equation 3.25 is nothing but the proof of equation 3.15 and thereby proves the projection theorem. The projection theorem hints that if we have a set of all the projections of a two-dimensional function, called as the cross section, then we can reconstruct the image of that cross section.

3.4.4 Direct Fourier Transform The following approach can be employed to calculate f(x. y), on the basis of equation 3.25 Step 1

Calculate the one-dimensional Fourier transform of all projections pθ(r) as shown in equation 3.26

F1{pθ(r)} = Pθ(k)

(3.26)

When all the given projections are processed, we obtain a 2-dimensional Fourier transform on a polar grid.

98  Medical Imaging Step 2

Include all the values of this one-dimensional function Pθ(k) onto a polar grid so as to obtain a two-dimensional function P(k, θ), as shown in Figure 3.8(a). The data points are supposed to be interpolated to a cartesian grid so as to arrive at F(kx, ky), as shown in Figure 3.8(b). Interpolation yields an approximation to the two-dimensional Fourier transform of an image of cross section on a rectangular grid.

Step 3

Calculate the two dimensional inverse fourier transform of F(kx, ky) as shown in equation 3.27

F2−1{F (kx , k y )} = f (x , y )



(3.27)

This inverse value helps to recover the image. A major source of error in this method is due to the process of interpolation. The density of the radial points becomes sparse as one gets farther away from the centre. Also interpolation error grows at that instant. In other words, the error is greater in the calculation of higher frequency components in an image which results in image degradation.

3.4.5

Filtered Back Projection (FBP)/Convolution Back Projection (CBP)

This approach is an alternative to the direct Fourier method. This is based on the inverse radon formula. And it is quite accurate when a larger number ky

ky P(θ, k)

F(kx, ky)

k θ

kx

kx

(a)

Figure 3.8  Interpolation process.

(b)

X-Ray Computed Tomography  99 of projections are available. The implementation of FBP is efficient as well as fast. Consequently, most of the practical CT machines use this approach as shown mathematically in equation 3.28



f (x , y ) =

∫

π

0

p*(r ,θ )dθ

(3.28)



Proof The 2-dimensional Fourier transform in cartesian system is as shown in equation 3.29 ∞



F (kx , k y ) = ∫∫ −∞ f ( x , y )e

−2π i ( kx x + k y y )

dx dy

(3.29)

Transforming the equation 3.29 into polar coordinate system, and taking inverse, we obtain the 2-dimensional inverse Fourier transform in polar form as shown in equation 3.30 π



∞

f ( x , y ) = ∫ 0 ∫ −∞ P(k ,θ )|k|e i 2π kr dk dθ

(3.30)

where r = x cos θ + y sin θ

Let P*(k, θ) = P(k, θ)|k|

∞

P *(r ,θ ) = ∫ −∞ P *(k ,θ )e i 2π kr dk

(3.31) (3.32)

Then equation 3.30 can be rewritten as shown in equation 3.33 π



f ( x , y ) = ∫ 0 p*(r ,θ ) dθ

(3.33)

From equation 3.33, it is evident that the function f(x, y) ca be reconstructed by back projecting p*(r, θ) which is the inverse Fourier transform of P*(k, θ) and hence proves the back projection theorm. The function P*(k, θ) is obtained by the ramp filter |k| and hence the name filtered back projection. Also, Fourier transform is equivalent to convolution in time domain. Hence p*(r, θ) can be rewritten as shown in equation 3.34 ∞



p*(r ,θ ) = ∫ −∞ p(r¢ ,θ ) q(r¢ − r¢ )

(3.34)

100  Medical Imaging where q(r) is the convolution kernel given by equation 3.35 ∞

q(r ) = F −1 {|k|} = ∫ −∞ |k|e i 2π kr dk



(3.35)

The overall reconstruction process can be summarized into different steps as follows: Step 1

Filter the sinogram p(r, θ) For all values of θ, we have

* p= pθ (r ) ∗ q(r ) θ (r )



(3.36)

Hence we have

Pθ* (k) = Pθ (k) |k|

Step 2

(3.37)



Back project the filtered sinogram pθ* (r ,θ ) π

f (x , y ) = ∫ 0 p*(x cos θ + y sin θ ,θ ) dθ (3.38) Due to the divergent nature, a continuous filter |k| does not exist. However, from Figure 3.6(j) we can infer that for discrete projection data, 1 1 the Fourier content is limited to frequencies less than kmax = = . Ds 2Dr Hence a ramp filter |k| with a cutoff at kmax can be incorporated. This is

kmax

–kmax

kmax

–kmax

Ip/mm (a)

Figure 3.9  Ram Lak filter.

kmax

–kmax

Ip/mm (b)

Ip/mm (c)

X-Ray Computed Tomography  101

kmax

–kmax

(a)

kmax

–kmax

Ip/mm

(b)

Ip/mm

Figure 3.10  Ramp filter multiplied by smoothing windows (hamming and hanning).

shown in Figure 3.9(a). Such a filter, called the ram-lak filter is obtained after subtracting a triangular filter from a band pass filter, as shown in Figure 3.9(b-c). The frequencies below kmax are prone to noise and aliasing effect which are mitigated by the usage of a smoothing window such as those of hanning, hamming, shepp-logan and butterworth. One such instance with the usage of a hamming (α = 0.54) and hanning (α = 0.5) window is shown in equation 3.39



  πk   α + (1 − α )cos   kmax  H (k ) =   0 

for |k| < kmax for |k| ≥ kmax

(3.39)



Figure 3.10 provides a pictorial depiction of the product of a ramp filter with these filters.

3.4.6 Fan Beam Projections The reconstruction approaches mandate the X-ray beams to be in parallel beam approach, as seen in first- and second-generation CT machines. However, the recent CT scanners adopt a fan beam approach, as shown in Figure 3.11 (a) in which the fan beam-based coordinates (γ, β) are related to the parallel bean-based coordinates (r, θ) and the X-ray detectors follow the circular arc pattern where β = the angle between the X-ray source and the y-axis

102  Medical Imaging ?

β L θ

R

(x, y) r

γ

(a)

(b)

Figure 3.11  Fan beam reconstruction.

γ = angle between the ray through (x, y) and the central line of the associated fan beam projection with which the fan angle is observed to be formed. Figure 3.11(b) shows that a few of the line measurements in fan beam geometry are not included for 0 ≤ β ≤ π. For instance, when the X-ray tube starts at β = 0, and goes clockwise until β = 180°, then the line denoted by “?” in Figure 3.11 (b) is not measured. This can be addressed by having 0 ≤ β ≤ 2π. This can be reconstructed by either rebinning (which reorders the data into parallel beam-based data by interpolation) or by using an adaptive approach for filtered back projection equation. Substituting equation 3.34 into equation 3.33 and limiting )ŕ in the inteFOV FOV  , , we arrive at equation 3.40, as shown below gration to  − 2 2   fov



1 2π 2 f ( x , y ) = ∫ 0 ∫ fov p(r¢ ,θ ) q( x cosθ + y sinθ − r¢ )dr¢ dθ − 2 2



(3.40)

X-Ray Computed Tomography  103 1 mitigates the variation of the integration limits 2 from 0 to 2π. For the fan beam geometry, as shown in Figure 3.11(a), the following coordinate transformations are used Inclusion of the factor

θ = γ + β and r = R sin γ



(3.41)

where R = distance from the top of the fan beam source until the centre of the FOV. Incorporating equation 3.41 into equation 3.40, we get equation 3.42



f (x , y )=

1 2

2π

+

∫ 0 ∫−

fan angle

p(γ¢ , β ) q(x cos(γ + β ) + y sin(γ + β ) − R sin γ¢ ) R cos γ¢ d β

2 fan angle 2



(3.42)

Equation 3.42 is simplified to obtain the fan beam reconstruction formula as shown in equation 3.43

f (x , y ) = ∫

2π 1 2 0 L

∫

fan angle 2 fan angle − 2 +

2

1  γ − γ′  [R cosγ¢ P(γ′ , β )]   q(γ − γ′ )d γ′ dβ 2  sin(γ − γ′ ) 



(3.43)

where L = distance of the image point (x, y) from the top of the fan. A similar equation can be developed for a line perpendicular to the central line of the fan (as shown in Figure 3.12) with coordinates (t, β), given in equation 3.44. where t = distance from the origin to the ray through (x, y) measured parallel to the detector array

f (x , y ) =

∫

2π

0

1 2 U   R

∞

R   −∞  R 2 + t¢ 2

∫

 1 q(t − t¢ )dt¢ d β 2 

(3.44)



104  Medical Imaging β θ U R

r

(x, y) t

Figure 3.12  Fan beam projections with (t, β) coordinate system.

where U = projection of the distance between the source to the point of interest onto the central ray of the fan beam. In cardiac CT and related dynamic applications, motion blurriness can be reduced by having shorter scans. However, equation 3.43 and equation 3.44 mandate the scans to be from 0 to 360°; this cannot be used for cardiac CT scan. Instead, 0 to 180° + fan angle scans are used and for downweight projections, parker weighting is performed with measurements obtained twice.

3.5 Computer Tomography-Based Diagnostics 3.5.1 Single Slice Computed Tomography The simplest approach in CT is to obtain multiple scans of the region of interest using circular rotations of source and detectors. In this regard, if Nyquist criterion is satisfied, then a complete 3-dimensional dataset can be obtained. The distance between consecutive slices depend on the effective slice thickness. An extension of this approach is to follow a helical pattern instead of a conventional circular pattern. As the source rotates around the subject, the subject is moved forward into the gantry. Hence the tube

X-Ray Computed Tomography  105 traverses in a helical pattern. The missing points are interpolated in this approach.

3.5.2 Multislice Computed Tomography Of late, the CT machines are equipped with a matrix of detector assembly so that multiple slices can be measured for every rotation of the X-ray tube. Multiple detectors are combined with longitudinal focal spot wobble providing interlaced slices. For instance, a 32-row detector can then provide 64 slices per rotation. By tilting the plane of the image, axial slices can be interpolated, and this is called titled plane reconstruction. Artifacts in the reconstructed image become more prominent with an increase in the number of detectors, in which case, complete 3-dimensional reconstruction is recommended. Thicker slices provide a higher SNR. These can be achieved by convoluting the projection values along the z axis with a smoothing filter, and this is called as z-filtering. Reconstruction using thinner detector arrays for thicker slices reduce nonlinear partial volume effects. A comparison between the single slice and multislice CT approach is shown in Figure 3.13.

(a)

Figure 3.13  Single slice vs. multislice computed tomography.

(b)

106  Medical Imaging selected cardiac phase

z-interval of multidetector array

z

t~β

Figure 3.14  Cardiac CT obtained by helical scan.

3.5.3 Cardiac CT Helical scans or axial scans can be used to obtain the image of the heart. Dynamic 3-dimensional images of the heart can be reconstructed in synchrony with the different phases of the cardiac cycle with the aid of the corresponding ECG signals acquired simultaneously. In axial scan, adjacent volumes of the selected phases of the cardiac cycle are obtained and later reconstructed at the rate of one slab per heartbeat. This kind of acquisition is also called as the step-and-shoot method. If the X-ray beam is large enough to cover the entire organ in a single rotation, then this reduces the X-ray exposure time to the subject as well. Figure 3.14 shows the cardiac CT acquired by the helical scan approach. Here, a particular phase of the cardiac cycle is selected in the ECG signal and the corresponding projection data are used to reconstruct the image of the heart.

3.5.4 Dual Energy Computer Tomography Dual energy CT approach captures two energy spectra so as to achieve tissue characterization. In general, different spectra can be obtained by a conventional CT scanner by performing two consecutive rotations at different energy levels. Alternately, a dual source CT machine can be used which would have two X-ray tubes positioned in perpendicular to each other, operating in different energy levels. Alternately, a suitable detector

X-Ray Computed Tomography  107 with two separate layers (top layer and the bottom layer) of scintillators can be used to detect the two different spectra. The top layer detects low-energy photons and the bottom layer detects the high-energy photons. This approach provides the tissue specific coefficients for each pixel value from which the monochromatic images at any energy can be calculated. Dual energy CT scans are used to eliminate the artifacts seen due to beam hardening as well as for automated segmentation approaches. They help in specific tissue characterization as well. However, dual energy CT mandates energy separation as well as co-registration. For an effective material decomposition to be achieved, the measurements have to occur at different effective energy values. If these energy values are similar, then this will amplify the noise. Also, the field of view is smaller if the second detector is small in dual energy CT scans.

3.6 Image Quality 3.6.1 Resolution The spatial resolution of a CT image is relative to the following factors. a) F  ocal spot: Focal spot is the area of the anode at which the electrons strike and this is the place from which the X-ray photons are emitted. The focal spot is often a small angle, relative to the imaging plane so that the thermal length (physical) can be much larger than the optical length (projected) in order to spread the heat production over a larger thermal area. b) Detector channels: The size of the detector channel and the - between the channels have a sizable effect on the spatial resolution. c) X-ray beam width: The focal spot size affects the beam width if the location is very close to the focal spot. If the location is closer to the detector, then the size of the detector cell affects the beam width. d) Rotation of tube/detector: A constant rotation of the X-ray tube as well as the detector result in azimuthal blur and this increases with the distance from the centre of rotation. This is why the azimuthal blur is higher at the boundaries of the FOVs.

108  Medical Imaging e) R  econstruction kernel/convolution filter: This can be tuned to reduce the effects of noise and aliasing by suppressing the high-frequency components and enhancing the high-frequency components of sharpest images. f) Interpolation: A good interpolation process depends upon factors such as those of the channel size, the helical pitch, the detector offset and the focal spot wobble.

3.6.2 Noise The most common types of noise seen in CT are quantum/statistical noise, electronic noise and roundoff/quantization noise. The most prominent among them are the quantum noise seen due to the statistical nature of X-rays. The noise often depends upon the total exposure and the type of reconstruction approach used as well.

3.6.3 Contrast The contrast between the background as well as the object depends on the attenuation properties as well as upon various physical factors such as those of the X-ray tube spectrum, beam hardening and the non-linearities in the process of X-ray detection. The gray level transformation post-image formation affects the image contrast at lower levels.

3.6.4 Image Artifacts i.

Undersampling Undersampling is seen when there are an inadequate amount of detector samples or views. In this regard, if the number of detector samples are less, then sharp edges will not be approximated correctly which will result in a high-frequency damped oscillations around the edges. During reconstruction, this error results in aliasing artifacts. This can be addressed by increasing the number of detector samples or by increasing the beam width. Also, if the number of views are small, then alternating white and black streaks are seen in the peripheral image areas where the sampling density is small. ii. Beam hardening As the X-ray beam traverses through the tissues, it gets hardened and this reduces the attenuation. Every X-ray

X-Ray Computed Tomography  109

iii.

iv.

v.

vi.

beam passing through a given tissue follows a different path. Hence every beam is hardened to different levels which results in having different attenuation values of the same tissue. This causes beam hardening artifact in the form of a reduced attenuation towards the centre of the object (which is called cupping), and the ones with stronger attenuation values are seen as streaks. Scattering Although ideally, the X-ray photons travel from the X-ray tube and reach the detector in straight path, this is practically not true. Over 25% of such X-ray photons get scattered which results in an underestimation of the attenuation values of a given X-ray beam and also in relative error during projection. Scattering is seen as streak artifact in the reconstructed image. Nonlinear partial volume effect The width of the X-ray beam is always finite and the measured value is relative to the intensity averaged over this beam width which is later used to calculate the linear attenuation along the beam. But in fact, this is not precisely the same as the integrated average value of attenuation. This difference results in streaks tangent to the edges in the reconstructed images and is called as the non-linear partial volume artifact. Motion artifact Any motion of the subject during the CT scan results in inconsistent measurement and is seen as streaks which connect the object and the position of the X-ray tube at the moment when the subject had moved and also a streak that connects the subject and the X-ray tube at its initial position. Gradual movements such as those seen in cardiac motion result in blurred images of the parts in motion. Stair-step artifact Longitudinal interpolation is seen in the case of a 3-­dimensional surface in helical CT scans. Stair-step artifacts are seen when the helical pitch is very big or when the reconstruction interval is too small. This artifact is seen in longitudinal reslices as regular stair-step disruptions along the inclined edges. In 3-dimensional images, this is seen as black/white helical winding along the inclined surfaces.

110  Medical Imaging

3.7 CT Machine – The Hardware Aspects CT machines are an extension of X-ray modules with an incorporation of various advance features with each of its modules having specific functions. Although every manufacturer has their own specifications of CT machines, most of them have a scanning gantry, an X-ray generator unit, a computer system, and a console panel as well as a viewing console. Recent machines also include a printer for printing the images on the film. The workstation takes care of viewing the images and for electronic achieving. The gantry and the patient table are responsible for image creation. The image processing module includes data acquisition, image reconstruction and image display unit. A schematic representation of a CT machine is shown in Figure 3.15. The components are described as below. The Gantry The gantry is a ring-shaped component of the machine. It holds the components responsible for the production as well as the detection of X-ray beams which are mounted on a rotating scan frame. An aperture of about 80 cm is normally provided here. The gantry can be tilted forward or backwards as required to facilitate the scanning of different regions of interest. A normal tilt of up to 30o is possible at the gantry. Control panels are provided at either side of the gantry unit which are used by the technicians to control various aspects such as those of the alignment, gantry tilt and table movement. These aspects can be controlled from the console at the X-ray tube Filter Collimator

Detector array

Gantry

Figure 3.15  CT machine – a hardware perspective.

X-Ray Computed Tomography  111 operator end as well. The gantry also has a microphone for the communication between the technician at the console and the subject at the table during the scanning process. Slip rings Recent CT machines include slip rings, which are electromagnetic devices with a brush kind of apparatus to facilitate continuous electrical power to the rotating gantry and also for the signal transfer from the detector. Slip rings ensure a continuous rotation of the gantry unit for circular as well as helical scans. Cooling Systems The cooling mechanisms present in the gantry ensure that the components are not affected by fluctuations in temperature. These can be in the form of filters, devices or oil circulation units. Generators CT machines include high-frequency generators which are small enough to be placed inside the gantry and produce high voltages which are transmitted to the X-ray tubes. The kV and mA settings of the CT machines depend on the power capacity of the generators. Beam intensity is increased by producing high kV and also reducing the heat load on the X-ray tube. X-Ray Tubes X-ray tubes are used to produce the X-ray photons which are used to develop the CT scans. This is a modified version of a standard rotating anode tube, as seen in conventional radiography. Tungsten is the anode material used due to the fact that it produces a higher intensity X-ray beam. CT scan tubes have multiple-sized focal spots, the most common ones being 0.5 mm and 1 mm. Smaller focal spots produce sharper images due to reduced penumbra, similar to that of X-ray machines. A CT scan tube is under huge stress with CT scans requiring long exposures and generate huge amounts of heat. This heat is normally dissipated by cooling paradigms. Filtration The X-ray beams are generally shaped by using compensating filters which reduce the patient dose and also minimize image artifacts. The X-ray radiations which are initially polychromatic, have multiple energy radiations which are reduced by the filters appropriately thereby resulting in a uniform beam intensity which improves the CT images. Different filters are used for different scanning protocols.

112  Medical Imaging Collimation Collimation limits the X-ray beams to a predefined specific region and reduces scatters which improves the image quality with an improvement in the contrast resolution and an increase in the radiation dose to the subject. Collimation can narrow or widen the X-ray beam and hence control the slice thickness. The source collimator is placed near the X-ray tube which controls the X-ray beam before it passes through the subject. The source collimators are small shutters with adjustable openings which are used to determine the slice thickness. Predictor collimation, as seen in a few CT machines are located below the subject and above the detector array. This ensures that beams of appropriate width enter the detector and also prevents the scatter radiations from reaching the detector. Detectors A detector acquires the information about the X-ray beams attenuated by the region of interest. Different organs attenuate X-rays to a different level. CT machines house detector arrays which are placed in an arc or ring and each of the detector elements measures the intensity of the transmitted X-ray beam after being attenuated by the subject, as the X-ray beam passes through the subject. The efficiency of the detectors depends on various factors such as stopping ability of the detector material, scintillation efficiency, change collection efficiency and scatter rejection. Xenon gas detector and solid-state crystal detectors are the most common types of detectors used in CT machines.

3.8 Generations of CT Machines The first CT machine was developed during the 1970s and since then, these machines have evolved with improvements in technology and requirements. In this regard, the following section describes six generations of CT machines. 1.  First Generation: Rotate/translate approach-pencil beam Electric and Musical Industries Ltd., along with Godfrey Hounsfield, are credited for the development of the first CT machine during the 1970s. These machines were initially used for head scans. They used a rotate-­ translate mechanism with a single X-ray beam technology with parallel beam geometry approach, called as the pencil beam approach, as shown in Figure 3.16. A pin-hole collimator was used to provide a single beam of X-ray during the scan.

X-Ray Computed Tomography  113 X-ray tube

Detector Translate

Rotate

Translate

Figure 3.16  First-generation CT machines.

These machines housed two X-ray detectors located at the opposite side of the X-ray tube. These detectors were able to provide two slices of the region of interest being scanned. In order to obtain multiple slices, the tube-detector setup was moved linearly and then rotated accordingly, to obtain the images at various projection angles. This process continued until the rotation angle achieved a complete 180o rotation with respect to the projection angles. The main advantage of this system was the usage of pencil beam X-ray geometry. Also, the usage of a two detector setup ensured that the scattered radiations were not detected, thereby achieving significant scatter reduction during the process of detection. However, these machines needed a significant amount of time to acquire the images and then reconstruct them. 2.  Second-generation CT machines: Rotate/translate-narrow fan beam The very first enhancement made to the first-generation machine was to reduce the can time by incorporating a narrow fan beam of about 10o which resulted in a linear array of about 30 detectors. As the fan beam was narrow, this still required translate and then, rotate approach to encompass the entire region of interest; the time required for translated scan was much less, as shown in Figure 3.17. This was about 15 times faster than the first-generation machines. But the issue in these machines was the increase in scattering due to the usage of narrow fan beams. Due to the rise in the

114  Medical Imaging

Figure 3.17  Second-generation CT machine.

number of detectors, which were exposed to these scattering, the resolution of the images was less. Due to the time taken by first-generation and second-generation CT machines, these were limited to head and brain scans. When body parts with intrinsic movements such as the abdomen were imaged, the reconstructed images were prone to motion artifacts.

Figure 3.18  Third-generation CT machines.

X-Ray Computed Tomography  115 3.  Third-generation CT machines: Rotate/rotate-wide fan beam The drawbacks of translational motion seen in first-generation and second-generation machines limited the usage of CT scans for certain body parts only. Hence to image the body parts such as abdomen and lungs, it was imperative to develop a technology which could complete the entire imaging process with the subject holding their breath. In this regard, a wide aperture fan beam was developed so as to avoid the translational movement completely. The X-ray tube and detector setup was made to rotate freely at every projection angle without pausing to acquire multiple slices per projection angle. But this required a longer linear detector array setup with about 1,000 detector elements. This approach needed just 5 seconds of time per projection angle. This is shown in Figure 3.18. However, addition of multiple detector elements increased the overall cost of the hardware. Also, due to such a large number of detectors, ring artifacts were produced in the reconstructed images. 4.  Fourth-generation: Rotate/stationary The fourth-generation machines were developed to reduce the ring artifacts seen in their previous counterparts by synching the detector elements. The calibration was achieved by placing the detector array in a stationary ring, all across the ring area instead of placing them on the rotating gantry. This further increased the number of detector elements. A fan-shaped X-ray beam was processed with individual detectors as the vertex of a fan.

Figure 3.19  Fourth-generation CT machine.

116  Medical Imaging The fan beam data was acquired using one detector over the time it took for the X-ray tube to rotate from one side of the fan arc angle to the other side. This is shown in Figure 3.19. The X-ray tubes were able to rotate inside or outside the detector ring. 5. Fifth-generation CT machine: Electron beam scanner-stationary/ stationary These machines were developed specifically for cardiac imaging and are also called as cine-CT or electron beam scanners. These were able to acquire moving organs such as the heart due to their shorter acquisition times. These machines had stationary parts. Instead of a rotating X-ray tube, these machines consisted of a large X-ray tube inside which the subject lies down during the scan. An electron beam behind the subject ejects the electron which is deflected down, away from the patient and makes contact with a large tungsten ring target encircling the patient. This interaction between the electrons and the tungsten generates the X-ray beams

Data acquisition system Detectors

Electron Gun

Focus cell

X-ray beam

Detection Cell

Patient

Electron beam

Target rings

Figure 3.20  Fifth-generation CT machine.

X-Ray Computed Tomography  117 which traverse through the heart area and are detected by a detector ring located on the opposite side. This is shown in Figure 3.20. This approach permits a very high-speed image acquisition thereby producing CT movies of the beating heart. Due to the incorporation of such complex hardware, these scanners are very costly and are confined to cardiovascular imaging only. 6.  Sixth-generation CT machine: Helical The previous types of scanners required the gantry to stop after every slice. So, data acquisition was discrete and not continuous. But for better image acquisition, constant supply of power is essential for the tube-detector setup which was not possible using wires for power supply. This was resolved using the slip ring technology which allows the electricity to be passed to the rotating components without any stopping of the tube-detector assembly. Hence the gantry was able to rotate continuously across all the patient slices and hence resulted in shorter scan times. The sixth-generation systems incorporated the technology of third- as well as fourth-generation approaches, with a slip ring technology. This was called as the helical CT. This is shown in Figure 3.21. However, because the data was collected by helical approach, full slice of data are not collected. This is mitigated by reconstruction approaches.

Table translation

Figure 3.21  Sixth-generation CT machine.

118  Medical Imaging

3.9 Biological Effects and Safety-Based Aspects Radiation dose to the subjects in CT is about 100 times greater than that in conventional radiography. Hence when the tradeoff is between the radiation dose and the image quality, it is ideally preferred to reduce the dose as much as possible, by the incorporation of optimal conditions such as those of a low tube current and a limited scan range. The dose can also be reduced by using a larger tube current for a higher attenuation and vice versa. Regular calibration of the machine will ensure the optimal conditions and the verification of image consistency can be done by using appropriate phantoms. Generally, there are two types of phantoms, head phantom (radius of 8 cm) and body phantom (radius of 16 cm). The dose absorbed by a cylindrical acrylic phantom for a 360o rotation of the tube is called as the CT dose index (CTDI) and this is to be checked before the actual scans.

Glossary-Appendix Attenuation - The process of making something less or weaker, the reduction of the amplitude of a signal, electric current, or other oscillation. Ascertained - Find (something) out for certain; make sure of. Hounsfield units (HU) - The Hounsfield unit (HU) is a relative quantitative measurement of radio density used by radiologists in the interpretation of computed tomography (CT) images. Scintillating crystal - A scintillator is a material that exhibits scintillation, the property of luminescence, when excited by ionizing radiation. Scintillation - Scintillation is a flash of light produced in a transparent material by the passage of a particle (an electron, an alpha particle, an ion, or a high-energy photon). Trans-impedance - Trans-impedance amplifier (TIA) is a current to voltage converter, almost exclusively implemented with one or more operational amplifiers. Monochromatic - Containing or using only one colour. Sonogram - A graph representing a sound, showing the distribution of energy at different frequencies. Nyquist criterion - A criterion for determining the stability or instability of a feedback system. Radon transform - The Radon transform is an integral transform whose inverse is used to reconstruct images from medical CT scans.

X-Ray Computed Tomography  119 Jacobian determinant - A determinant which is defined for a finite number of functions of the same number of variables and in which each row consists of the first partial derivatives of the same function with respect to each of the variables. Radial points - Radial refers to the pattern that you get when straight lines are drawn from the centre of a circle to a number of points round the edge. Sparses - Present only in small amounts, less than necessary or normal especially. Convolution kernel - In image processing, a kernel, convolution matrix, or mask is a small matrix. It is used for blurring, sharpening, embossing, edge detection, and more. Shepp-Logan - The Shepp-Logan phantom is a popular mathematical model of a cranial slice, made up of a set of overlaying ellipses. Rebinning - Rebinning, or averaging, is the practice of reducing the size of a dataset by bunching of data points. Helical scans - Helical scan is a method of recording high-frequency signals on magnetic tape. Step-and-shoot method - Step-and-shoot scanning utilizes prospective gating to determine exactly what point in the heart cycle the picture is taken. Crosstalk - Unwanted transfer of signals between communication channels. Stair step artifacts - Volume-rendered CT image demonstrates “stair step” artifact. Pinhole collimator - A pinhole collimator is a cone-shaped lead shield, whicch tapers into a small aperture perforated at the center of the tip at a distance.

4 Ultrasound Imaging 4.0 Ultrasound Ultrasound waves are sound waves which are above 20KHz frequency. Their physical properties are very similar to conventional sound waves, but they cannot be heard by human beings due to the limitations of human auditory systems. Devices incorporating ultrasound technology operate in the frequency of 20 KHz to several GHz of range. Ultrasonic devices are often used to detect the objects as well as in applications related to the measurement of distances. Ultrasound-based imaging has been extremely useful in the case of diagnostic imaging in clinical applications since 1970s, after the implementation of gray scale ultrasound imaging approach.

4.1 Basics of Acoustic Waves Ultrasound waves are progressive longitudinal in nature and are often termed to be compressive as well. For such longitudinal waves, the particle displacement in the medium is found to be parallel to the direction in which the corresponding wave moves. For waves of compressive nature, the local displacement in the wave particles results in the generation of high particle density as well as low particle density, as shown in Figure 4.1 in which the high pressure areas correspond to the compression regions and low pressure areas are denoted by the rarefaction areas. The elasticity as well as the property of inertia of the medium results in waver propagation. Any given local compression seen is mitigated by the property of elasticity due to which the wave returns to the equilibrium. However, due to inertia, this return will be very large, which gives rise to a local rarefaction which is again countered by the elasticity. This continues for a multiple number of iterations. The wave gets damped with every such iteration. So, after a few iterations, an equilibrium is achieved. This is how a compression wave propagates. Sound is generally categorized into subsonic (frequency H. S. Sanjay and M. Niranjanamurthy. Medical Imaging, (121–150) © 2023 Scrivener Publishing LLC

121

122  Medical Imaging Bob Spring Equilibrium

Acoustic rarefaction

compression

Acoustic

Figure 4.1  Representation of longitudinal waves.

of less than 20 Hz), sonic (frequency of 20 Hz to 20 KHz) and ultrasonic (frequency of more than 20 KHz).

4.2 Propagation of Waves in Homogeneous Media When an acoustic wave traverses through a homogeneous medium, various physical aspects are observed which are discussed in this section. Equation 4.1, as shown below, can be used to describe such a plane progressing wave

Z = ρc

(4.1)

Where Z = Specific acoustic impedance of the acoustic wave (in general, Z is a ratio of the acoustic pressure p and the particle velocity response v ie Z = p/v) ρ = mass density c = the velocity of the acoustic wave in the medium

4.3 Linear Wave Equation Consider the waves of small acoustic pressure (p) and of small amplitude, traversing through an acoustically homogeneous and a non-viscous medium for which the linear equation is shown in equation 4.2



∇2 p −

1 ∂2 p =0 c 2 ∂t 2

(4.2)

Ultrasound Imaging  123 Where ∇2 = the laplacian operator In general cwater ≈ csoft tissue ≈ 1500 ms−1 cair ≈ 300 ms−1 cbone ≈ 4000 ms−1 Equation 4.2 can be considered as a basic differential equation representing the propagation of wave. A general solution to this in one dimension is given in equation 4.3

p(x, t) = A1 f1(x – ct) + A2 f2(x + ct)

(4.3)

4.4 Loudness and Intensity The intensity (I) of an acoustic wave is defined as the average energy of a given wave per unit time seen across a unit area which is perpendicular to the direction of the propagation of the wave. This is represented mathematically in equation 4.4 T

I = T1 ∫ 0 p(t )v(t )dt



(4.4)

Consider a sinusoidal plane wave as shown in equation 4.5



p( x , t ) = po sin

 2π x 2π t   2π  − = po sin ( x − ct )  λ    λ T



(4.5)

The acoustic intensity of this wave is as shown in equation 4.6



I=

1 ZT

∫

T

0

p 2 (t ) dt =

po2 ZT

∫

T

0

sin 2

p2  2π x 2π t  − dt = o (4.6)  λ T  ZT

Where x = direction in which the acoustic wave propagates λ = wavelength of the acoustic wave T = Period (c = λ/T)

124  Medical Imaging The sound level (L) is given as follows



L = 10 log10

I where I o = 1012W /m2 Io

(4.7)

Substituting equation 4.6 in equation 4.7 gives rise to equation 4.8



L = 10 log10

P where Po = 20 µ Pa Po

(4.8)

Where Io = threshold value at 1000 Hz of human hearing Note that the absolute silence for human beings is at 0 dB. When the value of intensity is increased to 10 dB, it is perceived as double the loudness in human beings. The wave frequency affects the perceived loudness of sound. This is mitigated using the phon scale. Phon denotes the perceived loudness level for pure tones.

4.5 Interference Given a large set of acoustic wave sources with a constant phase shift and similar frequency, we generally observe a complex interference phenomenon which is termed to be diffraction, which is known to rely upon the geometry of the acoustic wave. Consider the situation shown in Figure 4.2. Figure 4.2 depicts the process of interference of two waves at point P. This interference can be obstructive or constructive, depending upon the difference in the distance travelled by these waves with regard to the wavelength. In general, when the observation point is away from the source and is placed on its symmetry axis, the interference of the wavelets are constructive due to their negligible phase difference. Also, the variations in the maximal pressure occur very slowly. This far field approach is called constructive interference. But when the observation point is close to the source, the wavelets interfere in a complex manner due to a significant phase difference which results in a faster variation in the maximal pressure. This near field approach is called destructive interference.

Ultrasound Imaging  125 P O1

O2

δ

Two coherent point sources, originating from positions O1 and O2 respectively, travel in all directions, but only the direction towards position P is shown. When the waves meet in P, they can amplify each, i.e., interface constructively, or depress each other, i.e., interfere destructively. Maximal construvctive interference is the case when δ = nλ with λ the wavelength, while complete 1 )λ. destructive interference happens when δ = (n + 2

Figure 4.2  Depiction of two coherent sources.

4.6 Attenuation When an ultrasound wave propagates through a given medium, it loses its acoustic energy. This phenomena is called as attenuation. If the medium of interest through which the ultrasound travels is the tissue, then as they are travelling, the acoustic energy is converted into heat due to the viscous nature of the tissue which is seen as an exponential decay of the amplitude of the wave. The attenuation depends on the wave frequency and is as shown in equation 4.9, expressed in terms of nepers per centimeter (Np/cm). n



H ( f , z ) = e −α z = e −α o f z

(4.9)

Where f = frequency of the ultrasound wave as it is traversing through the medium

126  Medical Imaging z = distance traversed by the ultrasound wave across the medium with an attenuation coefficient α

4.7 Nonlinearity Equation 4.2 is derived based on the hypothesis that the acoustic pressure p is nothing but an infinitesimal disturbance of the static pressure for which the linear equation derived depicts that any wave can traverse across a medium without changing its shape. But when the acoustic pressure increases, the waveform gets distorted. This is seen in frequency domain at the higher level of harmonics. Also due to such distortion, the propagation distance is increased. Different medium has a varying rate of generation of harmonics for a constant pressure value. Such a non-linearity of the

Schematic representation of Huygens’ principle. The concentric lines in this figure represent the wavefronts, i.e. surfaces where the waves have the same phase. Any point on a wavefront can be considered as the source of secondary waves and the surface tangent to these secondary waves determines the future position of the wavefront.

Figure 4.3  Huygen’s principle.

Ultrasound Imaging  127 medium is described for different biological tissues by the standard nonlinearity parameter B/A which is directly proportional to the non-­linearity of the medium. .

4.8 Propagation of Waves in Non-Homogeneous Media The previous description of wave propagation was in an homogeneous media which is often not the case seen. Instead, the tissue itself is non-homogeneous in nature. Under such circumstances, along with those aspects seen in homogeneous media, additional aspects are to be considered as per the Huygen’s principle. This is shown in Figure 4.3. Huygen’s principle considers any given point on a wavefront (a surface wherein the waves have the same phase) as a source of secondary wave and the surface tangent to the secondary wave determines the future position of the wavefront.

4.9 Reflection and Refraction Consider a wave propagating with a density ρ1 with a velocity c1 in a medium incidents on a similar wave with a density ρ2 with a velocity c2 in another medium. This will result in a part of the wave energy to be reflected and the rest to be transmitted, as shown in Figure 4.4 and Figure 4.5, respectively. The frequency remains the same throughout the process. Then, using Huygen’s principle, it can be proved that the angles of travelling waves with l1

lr

θr

θ1

reflected wavefront

c1 = λ1.f c2 = λ 2.f

incident wavefront c1

1

2

3

4

Schematic representation of reflection of an incident wave at a planar interface of two different media. The relationships between the angles θ1.

Figure 4.4  Reflection of the wave.

c2

128  Medical Imaging l1

c1 = λ1. f c2 = λ2. f θ1

1

2

3

incident wavefront c1

4

c2

refracted wavefront θt

lt Schematic representaion of refraction of an incident wave at a planar interface of two different media. The relationships between the angles θ1.

Figure 4.5  Refraction of the wave.

respect to the planar interface are related as per Snell’s law, as shown in equation 4.10



sinθ i sinθ r sinθ t = = c1 c1 c2

(4.10)

Where θi = Angle of incidence θr = Angle of reflection θt = Angle of transmission Due to the fact that the transmitted wave may not traverse in the same direction as that of the incident wave, it is generally called as the refracted wave. On simplifying equation 4.10, we obtain the following relationship to ascertain the phase of the incident and reflected waves



c  cos θ t = 1 −  2 sin θ i   c1 

2



(4.11)

Ultrasound Imaging  129 The incident wave and the reflected wave are considered to be out of phase if c2 > c1 in equation 4.11. On similar lines, the amplitudes of the incident and the reflected waves are as follows:



T=

2 Z 2 cosθ i At A Z cosθ i − Z1 cosθ t = and R = r = 2 Ai Z 2 cosθ i + Z1 cosθ t Ai Z 2 cosθ i + Z1 cosθ t

(4.12)

Where Ai = Amplitude of the incident wave Ar = Amplitude of the reflected wave At = Amplitude of the transmitted wave Z1 = Acoustic impedance of the first medium Z2 = Acoustic impedance of the second medium This results in equation 4.13, given as follows

R = T – 1

(4.13)

Where R = reflection coefficient T = Transmission coefficient With respect to the reflection seen in case of ideal ultrasonic waves, they occur at perfectly smooth surfaces and are called as pure specular reflections. However, in practice, this is not true. Instead, reflections are significant in a cone centered around θr. Hence in case of ultrasonic waves, a single transducer is used for transmission as well as for the measurement of the ultrasonic waves as well.

4.10 Scattering Reflections occur at every part of the tissue and not just at their boundaries due to their inhomogeneous nature seen because of the variations in density and compressibility of their sub-tissues. Such scattered reflections are often seen in the acoustic signals traversing through the tissues and such smallest possible scattering is called a point scatterer which diverges the incident wave in every possible direction. Such scattered points seen in the

130  Medical Imaging t

P

P

t

t t t t

t

(a)

t

(b)

Figure 4.6  Concept of scatterer in acoustic wave.

direction opposite to the direction of the incident wave is called back scatter. Every point scatterer diverges (retransmits) the incident wave in every possible direction which in turn interferes with each other and results in a scattered pulse. This interference often depends upon the size and shape of the scatterer. If the scatterer is of a very small wavelength, then we see a constructive interference which does not depend upon the shape of the scatterer and the point of observation P, as shown in Figure 4.6(a). But if the wavelength is large enough, then there is a phase shift between the divergent wavelets, and then the interference pattern depends upon the point of observation (P) as well as the shape of the scatterer, as shown in Figure 4.6(b).

4.11 Doppler Effect in the Propagation of the Acoustic Wave When an acoustic wave traverses, relative to the observer, the frequency of the wave being transmitted as well as the frequency of the observer are not the same. This is called the Doppler effect. Statement Consider a situation as shown in Figure 4.7, of that of a transducer transmitting an acoustic pulse at a frequency of fT and the presence of a point scatterer which will reflect the acoustic pulse at a frequency fR with the scatterer moving away from the transducer which is stagnant, with an axial velocity (va), as shown in equation 4.14.

Ultrasound Imaging  131



 va = |v |cosθ

(4.14)

Then the Doppler frequency fD in this case is given by equation 4.15



f D = f R − fT =

−2 va fT C + va

(4.15)

Equation 4.15 can be proved as follows Proof Let the starting point of the transmitted pulse at time t, be given as follows

Ps(t) = ct

(4.16)

Where c is the velocity of sound in the medium and t is the time since the pulse is transmitted. Then the position of the scatterer P(t) can be written as shown in equation 4.17

P(t) = do + vat

(4.17)

Where do is the distance between the transducer and the scatterer at time t = 0. The initial point of the ultrasonic pulse meets the scatterer at time tis at which instance, we can write Ps(t) = P(t). Then, from equation 4.16 and equation 4.17, we can write as follows



ctis = do + vatis ⇒ tis =

do c − va

(4.18)

If the acoustic pulse has a wavelength λ and if the period of the transmitted pulse is T, then the position of the end point Pe(t) is given as shown in equation 4.19

Ps(t) = ct – λ = c (t – T)

(4.19)

When the initial point meets the scatterer at time tie, then Pe(tie) = P(t) = P(tie)

132  Medical Imaging Equation 4.19 in equation 4.17 results in the following equation



c(tie − T ) = do + vatie ⇒ tie =

do + cT c T = tis + c − va c − va

(4.20)

The scatterer reflects back the incident pulse back to the ultrasound receiver. The point Ps meets the scatterer at Ps(tis) and the point Pe meets the scatterer at Pe(tie). After meeting the scatterer, the point Ps takes a time of trs to travel back to the transducer, which is given in equation 4.21

trs =



Ps (tis ) = tis c

(4.21)

On similar lines, the point Pe takes a time of tre to travel back to the transducer, which is given in equation 4.22

tre =



Pe (tie ) = tie − T c

(4.22)

The overall travel time back and forth of Ps and Pe are depicted as ts and te and given as follows

ts = tis + trs = 2tis & te = tie + tre = 2tie – T

(4.23)

Based on equation 4.20, the duration of the received acoustic pulse is given as follows:



TR = te − t s = 2

c  c + va  T −T =  T  c − va  c − va

(4.24)

1 1 &T = in equation 4.24 results in the final equafR fT tion of the doppler frequency, as shown in equation 4.25 (which is the same as equation 4.15) Substituting TR =



f D = f R − fT = −

2va fT c + va

(4.25)

Ultrasound Imaging  133 Generally, the velocity of the scatterer is very small, when compared to the velocity of sound and hence equation 4.25 is approximated as given in equation 4.26



 2|v |cosθ fD ≈ − fT c

(4.26)

The above approximation is often used as the standard notation for the Doppler frequency at small scatterer velocity.

4.12 Generation and Detection of Ultrasound A piezoelectric crystal can be used to generate as well as detect the ultrasound waves. This is due to the fact that this crystal not just deforms under the influence of an electric field, but induces an electric field when subjected to a deformation as well. Such a crystal is housed inside a transducer. Polymers such as those of Lead zirconate titanate (PZT) and polyvinylidene fluoride (PVDF) are the most commonly used piezoelectric materials. When driven with a sinusoidal electric signal, the surface of the piezoelectric crystal moves and generates a compression wave of the corresponding frequency. This wave propagates across the surrounding media. A part of this gets reflected inside the crystal and travels back towards the opposite surface inducing electric field which interfere with the driving electric signals. Also, when the wavelength of the induced wave is double the thickness of the crystal, the amplitude of the vibration is seen to be maximum. This is called resonance and the corresponding frequency is called as the fundamental resonance frequency. Usage of appropriate materials as the backing at the opposite surface ensures that most of the acoustic energy generated emerges from the crystal through the surface on the image side. At the front part of the crystal, most of the energy needs to be transmitted into the medium which is hampered by the acoustic impedance. This is resolved by the usage of matching layer with the required impedance value. In practice, if Zc is the acoustic impedance of the crystal and Zt is the acoustic impedance of the tissue, then the acoustic impedance of the matching layer is expected to be Zc Zt to solve the issue of acoustic impedance.

134  Medical Imaging

4.13 Ultrasonic Transducer An appropriate piezoelectric material is chosen for ultrasound generation based on their stability as well as the strength. Quartz is a highly stable piezoelectric material, but requires a high electric field strength to produce higher output values. Ceramic materials can provide higher outputs with less field strength, but they are not as stable as quartz. Also, ceramics exhibit a lower input impedance at higher frequency values. A generic single element ultrasonic transducer is shown in Figure 4.7. The piezoelectric crystal is placed near the face of the transducer. The crystal is generally either gold coated or silver coated. The exterior part is often grounded to avert any plausible electric shock to the subjects. The housing is either plastic or metallic in nature. An acoustic insulator is placed between the housing and the crystal to avoid ringing of the housing due to the crystal vibrations. For the crystal to provide the desired outputs, the crystal should operate at its resonant frequency. Else, the intensity of the beam reduces, as per the Q factor of the resonant circuit, which is defined as given in equation 4.27.

Q=



fo f 2 − f1

(4.27)



Connector

Housing

Electrode Protective Layer

Figure 4.7  Generic single element ultrasonic transducer.

Backing Material Piezoelectric Element

Relative Amplitude

Ultrasound Imaging  135

1.0 0.707 0.5

f1

f0

f2

Frequency

Figure 4.8  Frequency response of the transducer.

Where fo = resonant frequency f1 and f2 = the frequencies at which the amplitude drops by -3 dB relative to the maximum value (as depicted in Figure 4.8). Piezoelectric transducers are electromechanical devices. So, it is obvious to consider both electrical Q factor as well as the mechanical Q factor for the assessment of the transducer functionality. In continuous doppler flowmeter, where maximal output is preferred without any bandwidth restrictions, the Q factor of the corresponding transducer is expected to be large. However, in case of pulse echo doppler flow meters, where the output is pulsed in nature, the Q factor needs to be small. Such a variation in the Q factor can be achieved by electrical matching or mechanical matching.

4.14 Mechanical Matching A transducer resonates at its resonant frequency when it is excited by an electric source. The transducers are air-backed for continuous wave applications in which most of the energy is irradiated in the forward direction. Because of the mismatch in the acoustic impedance between the air and the piezoelectric material, the acoustic energy is reflected in forward direction thereby resulting in much less loss of energy. But this mismatch also results in the ringing effect in case of pulsed applications which is an artifact. The ringing effect can be damped by using backing materials to absorb the vibrations at the backside and also reduce the mismatch in the acoustic impedance. The most commonly used backing is a mixture of tungsten powder with rubber in epoxy resin.

136  Medical Imaging

4.15 Electrical Matching Matching the electrical characteristics of the ultrasonic transducer to that of the electrical source as well as the amplifier also results in an increase of energy transmission as well as a rise in the bandwidth. In such cases, the circuit components are placed between the transducer and the external electrical devices.

4.16 Ultrasound Imaging 4.16.1 Gray Scale Imaging 4.16.1.1 Data Acquisition Pulsed ultrasound signals are generated which are useful to obtain the spatial information from the region of interest. After the ultrasound pulses are incident upon the body part to the images, the corresponding data acquisition is achieved by three modes as given below.

4.16.1.2 Amplitude Mode (A-Mode) The A mode approach incorporates the usage of the amplitude of the ultrasound echo as a function of the depth of penetration. Figure 4.9 represents a block diagram of an A-mode scanning system.

Display

Display Vertical Axis

Display Synch

Pulse Generator

PreAmplifier

Transducer

Amplifier

Skin Surface

Tissues

Figure 4.9  A-mode ultrasound scanning system.

Signal Processing

Ultrasound Imaging  137

Voltage

As shown in Figure 4.9, the ultrasound transducer is excited by a pulse generator (which is capable of generating a high-voltage pulse train with a peak-to-peak voltage of greater than 100 V) with a repetition rate of about 1 KHz. The pulse-echo systems use a single transducer as a trans-­ receiver and hence, when a pulse is transmitted from the transducer, this pulse needs to strike the region of interest and an echo needs to be elicited from these regions which are to be detected by the transducer. Until then a new pulse cannot be transmitted. Hence the depth of penetration limits the pulse repetition rate in such cases. A conducting aqueous gel is used to transmit the ultrasound pulse into the subject. A low-noise preamplifier is used as a buffer due to the fact that the transmitted pulse is of large amplitude and the echo is very weak. The amplifier has excellent overload capacity with a short recovery time and a dynamic range. The output from the amplifier is rectified, filtered and envelope detected. The processed signal is displayed on the monitor. A-mode scans are typically used in case of ophthalmic applications (eye tumors), to localize the midline structures of the brain and to assess liver cirrhosis and myocardial infarctions.

Transmitted Pulse

Echo from Skin Surface

Echo from Organ Front Face

Echo from Organ Back Face

t - 2d/c

Time

(a) d Transducer

Water

Organ

Skin Surface (b)

Figure 4.10  A-mode scan (a) A-mode display of (b) organ situated beneath skin surface.

138  Medical Imaging Voltage A Mode

Depth of Penetration B Mode

Figure 4.11  A-mode vs. B-mode scan.

A sample A-mode scan of the organ under the skin surface is shown in Figure 4.10. Figure 4.10(a) shows the ultrasound scan and Figure 4.10(b) depicts the organ under the skin which is being imaged.

4.16.1.3 Brightness Mode (B-Mode) The A-mode scan shown in Figure 4.10 can be performed using B-mode approach as well. This is shown in Figure 4.11. In this approach, the amplitude of the echo signal is used to modulate the electron beam intensity of the CRT. In case of bistatic B-mode display, the electron beam is on when the amplitude of the echo rises above a certain threshold value during which the image is displayed. In case of gray scale B-mode scan, the electron beam resulting in the display of the image is proportional to the amplitude of the echo which is in turn dependent upon the depth of penetration. Multiple lines of the same region of interest obtained by translating the ultrasound probe manually can be used to obtain a two-dimensional image of the region of interest. A generic representation of a B-mode scanner is given in Figure 4.12. The echoes returning from the region of interest are amplified by the preamplifier. The variable gain amplifier takes care of the time-gain compensation as well as the logarithmic compression. Thus the compressed signal is demodulated for envelope detection and then filtered to remove the carrier signal. A scan convertor converts these signals into a format which can be displayed on the screen. This is also post-processed by further smoothening, filtering and thresholding operations by a computer. These scanners are called as static B-mode scanners and take a few minutes to construct the image. Hence, they cannot be used to image any moving structures. Real-time B-mode scanners mitigate the shortfalls of the static

Ultrasound Imaging  139

Sync Pulser

Monitor

Preamplifier

Articulated Arm

Variable Gain Amplifier

Log Comp/ Demodulation

Z

Scan Converter

X Y Transducer

Tissue

Figure 4.12  B-mode scanner.

B-mode scanners by producing images faster so as to image the moving parts as well. These machines are less dependent on the operator and use mechanical as well as electrical real-time systems for scanning process. B-mode scans are commonly used in fetal monitoring and for the assessment of cardiac conditions.

Display c b c ab a Y-axis

X-axis Z-axis

Signal Processing

Receiver

Pulser

Transducer

Figure 4.13  M-mode scanner.

a

b

c Water

Ramp Generator

140  Medical Imaging

4.16.1.4 Motion Mode (M-Mode) Motion mode scanners are an enhanced version of Amplitude mode scanners with a modified display unit. A block diagram representation of M-mode scanner is given in Figure 4.13 with the X-axis depicting the time units and the Y-axis depicting the distance of the echo from the transducer. In general, the ultrasound wave signal detected after it strikes the region of interest is generally called the radio-frequency signal (RF signal) due to the fact that the frequency range of these detected signals is similar to the frequencies of the Radio waves (MHz) of the electromagnetic spectrum.

4.17 Image Reconstruction The ultrasound wave-based information is processed so as to obtain a pictorial representation of the region of interest, as seen on a display screen by appropriate reconstruction approaches, as given below. Step 1: Filtering: The detected RF signals are filtered so as to remove the high-frequency noise components. However, in second harmonic-based imaging, even the transmitted low frequencies are filtered thereby retaining only the received high-frequency components. Step 2: Envelope detection: This step helps to remove the high-­frequency components represented by the rapid fluctuations in the detected RF signal using a quadrature filter / Hilbert transform approach. Step 3: Attenuation correction: Similar structures in the region of interest normally are represented by the same gray values and hence, ideally, one should have the same amplitudes for the reflected waves. But due to the depth factor, the amplitude of the reflected wave is less than that of the incident wave for similar regions because the acoustic energy of the ultrasound wave gets attenuated as the depth increases. Hence the actual amplitude is often estimated with the aid of the attenuation correction approach by time-gain-compensation. This gain factor can be modified manually in most of the ultrasound machines at different depths. Step 4: Log compressions: The scattered reflections are not always visible due to the dynamic difference in the amplitudes of specular reflection and scattered reflection. This is mitigated by incorporating a suitable graylevel transformation approach such as that of a logarithmic function using which the scatter can be perceived easily. Step 5: Scan conversion: If the ultrasound image is obtained by tilting the transducer and not by translating it, the samples are obtained on a polar grid. This is later converted into a rectangular grid by interpolation and is called as scan conversion.

Ultrasound Imaging  141

4.18 Schlieren System A schlieren system is used to visualize the ultrasonic field. This is an optical system which relies upon the ray of light getting diffracted from its initial path when it passes through a medium with a refractive index being normal to that of the light beam. This system depends upon the fact that the density of a given medium varies when the ultrasound waves travel across the same. A transparent medium supporting an ultrasonic wave diffracts the light because of the variation of its density, in relation to that of the ultrasonic wave. A generic schlieren system is shown in Figure 4.14. Here, a light beam passes across a transparent medium such as that of water in which the ultrasound field is supposed to be ascertained. The light is focused to an obstruction so as to ensure that it does not reach the observer when the optical field is undisturbed. But when the ultrasound wave varies the refractive index of the medium, the path of the light gets disturbed and a schlieren image is obtained which can be displayed on the screen or photographed. The intensity of these images is directly proportional to the intensity of the ultrasound. But for a quantitative mapping of this aspect, non-directional micro-probes with a broad bandwidth are used.

4.19 Doppler Imaging Approaches Doppler-based approaches are incorporated in ultrasound imaging so as to visualize the velocities of the moving tissues. These are generally used to monitor the fetal heart rate, to detect the cardiac output and in case of Transducer Water Tank Light Souce

Screen Stop

Lens Water

Figure 4.14  Schlieren system.

Lens

142  Medical Imaging stenosis in blood vessels. There are three approaches in this regard, namely, continuous wave Doppler system, pulsed wave Doppler system and color Doppler system.

4.19.1 Continuous Wave Doppler System In these systems, a continuous sinusoidal wave is transmitted by a piezoelectric crystal and the reflected wave is detected later by a second crystal. However, both these crystals are housed inside a single transducer element. A block diagram of a continuous Doppler system is given in Figure 4.15. From Figure 4.15, it is evident that the received signal is amplified and mixed with the reference frequency. The demodulator houses the doppler frequency. The signal is lowpass filtered and then audio amplified so as to be heard from an audio output device. Continuous Doppler systems are often incapable of ascertaining the source of the echo which can lead to wrong assessment when the vessels overlap. This can be resolved by using pulse wave Doppler systems.

4.19.2 Pulse Wave Doppler System Pulsed Doppler waves are transmitted along a predefined line of strike across the region of interest at a constant pulse repetition frequency (PRF) in the form of short coherent sinusoidal bursts. One sample of each of the reflected pulse is obtained at a predefined time interval and Output Audio Amplifier

Receiver

Demodulator

Transmitter

Transmitting Element

Transducer

Figure 4.15  Continuous wave Doppler system.

Receiving Element

Ultrasound Imaging  143 the corresponding information from a particular spatial position is reconstructed. This is depicted in Figure 4.16. Figure 4.16 depicts a pulsed wave Doppler system in which a series of pulses are generated by the pulse generator at the PRF (around KHz) which modulates the oscillator. The reflected echoes from the region of interest are amplified and gated with an adjustable time delay of the gate and then demodulated by a demodulator. This output is sampled by a sample-andhold circuit. This is then lowpass filtered and the resultant waveform is audio amplified and provided to an audio device for hearing. The PRF is often limited by the depth of penetration due to which the echoes from the region of interest are received before the transmission of the next pulse.

4.19.3 Color Doppler Flow Imaging The color Doppler flow systems are similar to the B-mode scans with an exception that several pulses are transmitted instead of a single pulse to obtain a line in the image. Many such lines are processed to result in a 2D image based on the autocorrelation function of the Doppler frequency values wherein the velocity is indicated by colors which are superimposed onto the conventional grayscale image. A block diagram of a color Doppler flow system is shown in Figure 4.17.

Oscillator

Pulse Generator

Receiver

Transducer

Time Delay

Gate

Demodulator

Sample & Hold Sample Volume Low Pass Filter Audio Amplifier Output

Figure 4.16  Pulsed wave Doppler system.

144  Medical Imaging Conventional Doppler Signal Processor

Low Pass Filter

Array

AutoCorrelator

Digital Scan Converter

Color Processor

Velocity & Variance Calculator Display 2-D B-mode Images

Figure 4.17  Color Doppler flow system.

The color Doppler system shown in Figure 4.17 uses the autocorrelation approach and uses a probe for the simultaneous acquisition of Doppler information as well as for the B-mode scan acquisition. A separate conventional Doppler data is again obtained using a third channel. The Doppler shift is depicted in terms of colors and the B-mode image is shown in gray scale. In general, red color depicts the flow towards the transducer, and the flow away from the transducer is shown by blue color. The shades of these colors vary with the velocity. The lower the velocity, the darker is the shade. The variance is denoted by yellow or green color. This approach takes less time for imaging. The flow mapping helps to ascertain the problematic areas initially after which these areas are marked for further imaging.

4.20 Tissue Characterization Due to the interaction of the ultrasound waves with the biological tissues, a quantitative characterization of such tissues can be obtained. The gray scale images provide information about the texture patterns and the echogenic aspect of the tissues. For example, a solid tumor is more echogenic than a fluid containing cyst. Conventionally, the following parameters are used to characterize the tissues of the region of interest with regard to ultrasound imaging.

Ultrasound Imaging  145

4.20.1 Velocity The velocity of ultrasound waves differs with respect to the pathology of the region of interest. One of the approaches to assess the velocity of the ultrasound beam returning from the tissues is based on the image misregistration concept using a B-mode scanning approach. Here, the region of interest is located by the scanner by placing the probe at a particular location. Then the image of this target is obtained by placing the probe at a different location because the image of the target would be displaced from the true location as the assumed velocity and the true velocity are often not the same. The true velocity is then calculated based on these scans. Both the images are often matched by cross-correlation techniques. For instance, the velocity of a fatty liver is observed to be less than that of a normal liver.

4.20.2 Absorption The absorption of ultrasound waves differs with pathology in case of normal and abnormal tissues, especially in organs such as liver and spleen. This information can be obtained by the averaged value of the data over a large volume of the region of interest. Conventional two probe-based approaches (with one for transmission and the other for reception) cannot be used in this scenario. This is mitigated by the loss of amplitude approach (which uses the drop in the echo amplitude as a function of the penetration depth in A-mode to ascertain the attenuation coefficient) or using frequency shift approach (which measures the spectral difference).

4.20.3 Scattering In general, an ultrasound image is formed due to the reflected echoes (at the tissue boundaries) and the diffusely scattered echoes (by the tissue parenchyma). The most important aspect, however, is the intrinsic scattering property of the tissue which is important from a diagnostic perspective. An abnormal tissue can be differentiated from a normal tissue by quantifying the gray levels of the echogenic aspects of the tissue considered. Better information can be obtained by analyzing the detected signals for aspects such as those of back scatter coefficient, the frequency dependency of the back scatter and the average backscattered signal. Although tissue characterization seems an easy task, various technical issues need to be mitigated in this regard. Aspects such as the correction of

146  Medical Imaging the effects of intervening tissues and the correction of transducer diffraction effects pose a major challenge in this approach.

4.21 Ultrasound Image Characteristics 4.21.1 Spatial Resolution Spatial resolution helps to analyze the lateral resolution (resolution perpendicular to the axial direction within the image plane), the axial resolution (the resolution in the direction of wave propagation) and the elevation resolution (resolution perpendicular to the image plane). The lateral resolution can be reduced by reducing the beam width and consequently by increasing the central frequency and the band width of the transmitted pulse. Gray scale images have a better lateral resolution as they are acquired with shorter pulses. Also the pulsed Doppler systems have a better lateral resolution than the continuous wave Doppler systems as they have a smaller bandwidth.

4.21.2 Image Contrast Strongly reflecting structures such as those of calcifications result in bright reflections and are considered to be echogenic as compared to the structures such as blood with weak reflections, known to be hypogenic. Such received signal is due to the scatter as well as specular reflection and the difference between these two results in a large dynamic range. This is mitigated by the usage of a logarithmic function.

4.21.3 Ultrasonic Texture Ultrasonic texture, also called as speckles in B-mode ultrasound-based images are similar to laser speckles seen due to the interference between the echoes arriving at the transducer from various parts of the tissue. This depends upon the tissue properties as well as the equipment characteristics. The presence of speckles results in the degradation of the spatial resolution of the device. Hence approaches related to frequency compounding and spatial compounding are employed to reduce the speckles in the images. These approaches rely upon the incoherent averaging of images with varying speckle patterns. In spatial compounding, the images obtained at different spatial locations are averaged whereas in frequency compounding, the images obtained at various frequencies are averaged.

Ultrasound Imaging  147

4.22 Biological Effects of Ultrasound 4.22.1 Acoustic Aspects at High Intensity Levels There are various non-linear effects seen at high ultrasonic intensities. The most important of them are cavitation and wave distortion.

4.22.2 Cavitation Cavitation illustrates the behavior of gas bubbles in ultrasonic field. There are two types of cavitation seen, namely, transient cavitation and stable cavitation.

4.22.3 Transient Cavitation In this type of cavitation, with a decrease in the pressure, the bubbles in the medium get expanded, and then these bubbles collapse and disappear at which point the internal pressure of the bubbles becomes high, as they collapse. This can decompose the water into chemically active acidic components causing serious biological effects.

4.22.4 Stable Cavitation At lower intensities, the bubbles will not collapse, as seen in the case of transient cavitation. Such bubbles are stable in nature. Cavitation can be reduced by raising the external pressure which is applied to the system by degassing the liquid.

4.22.5 Wave Distortion The sinusoidal pressure wave gets distorted with the rise in the pressure levels of the acoustic wave. So, in regions with a higher pressure, the propagation velocity is high and during such instances, the sinusoidal waveform looks similar to a sawtooth waveform, and a large amount of energy is transferred to the higher harmonics of the wave which in turn results in a higher absorption.

4.22.6 Bioeffects (Thermal and Non-Thermal Effects) These effects are seen due to cavitation. Continuous high intensity ultrasound (say above 100 mW/cm2) wave provided for an extended period of

148  Medical Imaging ultrasound exposure is known to be fatal to biological tissues with thermal effects. However, all diagnostic ultrasound approaches are well within these ranges and hence can be regarded as safe for usage. Cavitation itself can be avoided if the ultrasonic field is less than the threshold intensity. On the positive side, such attributes are used in clinical applications as well. For instance, heating effect seen due to a higher exposure of ultrasound waves can be used in ultrasound surgeries to burn malignant tissues. Similarly, lithotripters which are used to destroy the kidney stones depend on the phenomena of cavitation with high-pressure ultrasonic waves.

Glossary-Appendix Ultrasound - Ultrasound is sound waves with frequencies higher than the upper audible limit of human hearing. Elasticity - The ability of an object or material to resume its normal shape after being stretched or compressed. Inertia - A property of matter by which it continues in its existing state of rest or uniform motion in a straight line, unless that state is changed by an external force. Homogeneous - Of the same kind Constructive interference -  When the maxima of two waves added together are in phase.  Destructive interference - When the maxima of two waves are 180 degrees out of phase and cancel each other. Harmonic - A signal or wave whose frequency is an integral (whole-number) multiple of the frequency of some reference signal or wave. Transducer - A device that converts variations in a physical quantity, such as pressure or brightness, into an electrical signal, or vice versa. Frequency - The rate at which something occurs over a particular period of time or in a given sample. Wavelength - The distance between successive crests of a wave, especially points in a sound wave or electromagnetic wave. Piezoelectric crystal - A crystal, such as quartz, that produces a potential difference across its opposite faces when under mechanical stress. Amplitude - The maximum displacement or distance moved by a point on a vibrating body or wave measured from its equilibrium position. Ophthalmic - Relating to the eye and its diseases. Liver cirrhosis - Chronic liver damage from a variety of causes leading to scarring and liver failure. Myocardial infarction - A blockage of blood flow to the heart muscle.

Ultrasound Imaging  149 Radio frequency - A frequency or band of frequencies in the range 104 to 1011 or 1012 Hz. Quantitative - Relating to, measuring, or measured by the quantity of something rather than its quality. Echogenic - Reflecting ultrasound waves.

5 Radionuclide Imaging 5.1 Radionuclide Imaging – A Brief History Henri Becquerel, a French scientist, discovered Radioactivity in 1896 with phosphorescent materials. Initially, these radiations were assumed to be similar to X-rays. However, with further research by Pierre and Marie Curie, it was proved to be different and much more complex than considered initially. Earnest Rutherford discovered that these elements decay as per the exponential relationship which resulted in the transmutation of one element into another. Further, Kasimir Fajans and Frederick Soddy formulated the process of alpha and beta decay. The research work pertaining to radium is considered to be the start of modern nuclear medicine. With the advent of technology in terms of cyclotrons and particle accelerators, nuclear medicine is gaining more importance in the field of modern diagnostic imaging. Benedict Cassen developed the first rectilinear scanner with calcium tungstate crystal coupled to a photomultiplier tube in 1949. He was successful in obtaining an image of the uptake of 131I in the thyroid. He incorporated a lead collimator and a scanning mechanism for this application. Hal Anger developed the scintillation camera (gamma camera/Anger camera) in 1957 which is considered the most important milestone in the field of radionuclide imaging. This housed a large sodium iodide crystal with an array of photomultiplier tubes which facilitated swift acquisition of radionuclide images without any mechanical scanning motion. John Keyes developed the Single Photon Emission Computed Tomography (SPECT) approach in 1977 which provided enhanced images in terms of contrast as compared to conventional radionuclide images, which was possible due to the usage of stationary camera setup. The development of Positron Emission Tomography (PET) gained importance in the late 1970s, based on the detection of the coincidence of two photons emitted in opposite directions following the obliteration H. S. Sanjay and M. Niranjanamurthy. Medical Imaging, (151–178) © 2023 Scrivener Publishing LLC

151

152  Medical Imaging of an electron and a positron. The PET systems housed multiple scintillation detectors placed around the subject with each of these detectors being coincident with those on the opposite direction of the subject. The detection of coincidence provided the projection data for the reconstruction of the positron emitting radionuclide distribution within the subject. The radionuclides were labelled with different pharmaceuticals to form radiopharmaceuticals, which were injected or orally provided to the subject so as to reach the designated tissues. Since the development of this technique, radionuclide imaging has evolved as one of the best approaches for various applications for the assessment of physiological functions of the human body which cannot be achieved with other imaging approaches such as that of ultrasound or CT. Advances in radiopharmaceuticals have aided in this process as well.

5.2 An Insight Into Radioactivity 5.2.1 Nuclear Particles In general, many radioactive isotopes disintegrate, giving rise to either nuclear particles or radiations or both. The most common types of such radiations are Alpha, Beta and gamma radiations. The proton neutron ratio present inside the nucleus often determines its stability. When the number of protons and neutrons are equal (as seen at lower atomic numbers), the nuclei are stable. However, at higher atomic numbers, for the nuclei to be stable, the proton-neutron ratio is supposed to be 1:1.5. Otherwise, such nuclei will disintegrate into a stable nucleus by spontaneous emission of the extra nuclear particles and will get back their stable ratio. For example, a neutron rich nucleus undergoes the conversion, as shown below



n yields  → p + + e − + ve + energy



(5.1)

Where n = neutron p+ = proton e− = electron ve = anti-electron neutrino On the contrary, a proton-rich nucleus undergoes the conversion as shown below

Radionuclide Imaging  153



p + yields  → n + e + + ve + energy

(5.2)

Where e+ = positron ve = electron neutrino A positron has the same mass as the electron, but has a positive charge. In equation 5.1 and equation 5.2, the total rest mass of the particles on both sides are not the same and hence the additional energy is given out to balance these equations. An element of a given atomic number has a fixed number of protons, but the neutrons in the nucleus may be different. Such elements with the same number of protons but a different number of neutrons are called as isotopes. The isotopes used in radionuclide imaging are artificially produced and are radioactive and are hence called as radioisotopes or radionuclides. The technetium isotope (99mTc, with a γ emission and a photon energy of 0.14 MeV with a half-life of 6 hours) is commonly used in radionuclide imaging due to its high penetrating γ emission.

5.2.2 Radioactive Decay Radioactive decay is a process in which an unstable nucleus transforms into a more stable daughter nucleus, by releasing a photon and nuclear energy. For instance, in case of electron capture, a proton-rich nucleus transforms into a stable state by capturing its orbital electron which then combines with a proton to form a neutron and a neutrino. The energy released is in the form of the kinetic energy of the neutrino. For example, in electron capture, a proton-rich nucleus may transform to the stable state by capturing one of its own orbital electrons. The electron combines with a proton to form a neutron and a neutrino. The transition energy is released as kinetic energy of the neutrino. Approximately 90% of electron capturing involves the K shell electrons which are closer to the nucleus. When the electron vacancy is filled up, the additional energy is released in the form of characteristic X-rays and auger electron. In case of isomeric decay, the metastable radionuclide decays by emitting γ rays. One such example is the 99mTc, which decays by emitting the gamma photons with 140 KeV of energy. In case of a positron decay, when a positron collides with an electron, both particles are crushed to form two 511 KeV protons which move in opposite directions. This forms the principle of Positron Emissions Tomography (PET).

154  Medical Imaging Radioactive decay is quantified as shown in equation 5.3

N(t) = Noe−λt

(5.3)

Where No = Radionuclide at time zero N(t) = Radionuclide at time t e−λt = the amount of the radionuclide remaining after time t (decay factor) λ = the decay constant The decay constant is related to the half-life of the radionuclide (T1/2) and is defined as the time required for half of the radionuclides to decay by a factor of T1/2 and is given by equation 5.4

T1/2 =



0.693 λ

(5.4)

The activity of radionuclide (A) is defined as the average decay rate and is given by equation 5.5



d N (t ) A(t ) = − = λ= N (t ) λ N oe − λt dt

(5.5)

Nuclear activity is normally measured in terms of curie and becquerel. 1 curie (Ci) is defined as 3.7 x 1010 decays per second (dps). The SI unit of activity is becquerel (Bq) which is defined as one decay persecond. Hence 1 Ci = 3.7 x 1010 Bq.

5.2.3 Specific Activity Specific activity is defined as the ratio of the activity to the mass of the radionuclide. Normally, the radionuclide may contain a stable isotope of the element which are often called as the carrier. A carrier-free radionuclide always has the highest specific activity which is given in equation 5.6



1.3 x 108 Acf = AmT1/2

(5.6)

Radionuclide Imaging  155 Where Acf = carrier free specific activity (Ci/gm) Am = mass number T1/2 = Half-life of the radionuclide (in days) A smaller dose of the tracer would yield a higher nuclear activity if the specific activity is high and such tracers are often preferred in radionuclide imaging. For instance, 131I has a specific activity of 1.2 x 105 Ci/gm and 99m Tc has a specific activity of 5.3 x 106 Ci/gm.

5.2.4 Interactions Between Nuclear Particles and Matter 5.2.4.1 Alpha Particles An alpha particle is a helium nucleus with two neutrons and two positively charged protons. The radionuclides decaying by emitting alpha particles have a larger nuclei with an atomic number greater than 82. Such emitted alpha particles possess an energy of 3-9 MeV. Because of two positive charges and a large mass, the alpha particles have a higher interactive power and lose their energy by ionizing (exciting) the other particles (atoms). The mean range of the alpha particle in air is given by equation 5.7



Rm = 0.325 Ea 3/2



(5.7)

Where Rm = Mean range of the alpha particle in air Ea = energy of alpha particles (MeV) For mediums other than that of air, the mean range of alpha particles is given by equation 5.8



Rmm =

ηa ( Amm )1/2 ηm ( Ama )1/2

Where Rmm = mean range of alpha particles, for mediums other than air ηa = density of air ηm = density of the medium Amm = mass number of the medium Ama = mass number of air

(5.8)

156  Medical Imaging

5.2.4.2 Beta Particles The interaction of the beta particles and matter is similar to that of the X-ray generators which produce X-ray photons when the electrons strike the anode material. In fact, when beta particles interact with the matter, both white X-rays as well as characteristic radiations are produced. The range of beta particle is directly proportional to its energy, but inversely proportional to the density of the medium. Also, we find a normalized range of beta particles in different media if their densities are similar.

5.2.4.3 Gamma Particles Gamma particles are very similar to X-rays. But the gamma particles are intranuclear whereas the X-rays are extranuclear in nature. The interaction between the gamma particles and matter are similar to that seen in case of X-rays. But for gamma rays carrying an energy of above 1.02 MeV, we see pair production and photo disintegration interactions. In pair production, the total photon energy is converted into the rest mass of the electron-­ positron pair when the gamma ray photon travels near a large electric field surrounding the nucleus. The energy higher than 1.02 MeV is converted into kinetic energy of the electron and positron. This interaction is shown in Figure 5.1. Annihilation is seen when the positron combines with the electron and results in two photons each of 511 KeV being emitted in opposite directions.

e–

γ (0.511 MeV)

e+

γ (>1.02 MeV) γ (0.511 MeV)

Figure 5.1  Pair production with gamma rays.

Radionuclide Imaging  157 In case of photo disintegration, the gamma ray photon is absorbed by the nucleus and a neutron and a proton (or an alpa particle) is ejected from the nucleus. The attenuation of gamma rays across the medium is given by equation 1.9

I = Ioe−βx

(5.9)

Where I = Intensity of the transmitted gamma rays Io = Intensity of the incident gamma rays x = thickness of the medium β = Linear attenuation coefficient Similar to that of X-rays, β is a function of the density of the medium as well as the energy of the gamma photon.

5.2.5 Properties of Radionuclides Various aspects, in terms of both physical as well as the biological nature of radionuclides are expected in ideal circumstances in case of medical imaging. This section highlights few such factors to be satisfied in case of ideal radionuclides.

5.2.5.1 Physical Properties Physical half-life The physical half-life of an ideal radionuclide material should be short enough to have a substantial amount of radioactive decay before the material is excreted by the body, into which it is injected initially. Also, the half-life should be sufficient enough for imaging and also to transport the material from the generator to the patient location. The 6-hour half-life seen in case of 99mTc suits both these requirements and hence this material is commonly used as a radionuclide material for medical imaging purposes Emission Giving the patients a lesser radiation dose is a major concern in radionuclide imaging. The charged particles produce ionization which contributes towards this radiation dose and hence such emissions are not desired. Also, the radiation detectors used in radionuclide imaging are developed to detect the gamma rays. For optimal imaging, these gamma ray photons

158  Medical Imaging should have an energy substantial for them to escape from the subject. But this energy should be less enough to be detected by the scintillation detector without a greater penetration across the collimators. This condition is satisfied by 99mTc for ideal dose and imaging aspects. Specific activity The radionuclides with a higher specific activity are preferred in radionuclide imaging. Preparation Preparation approaches of radionuclides need to be easy with a better yield. 99m Tc can be produced by portable generators.

5.2.5.2 Biological Properties Biological half-life Biological half-life is defined as the time required by the body to excrete half of the radionuclide administered to the body. This excretion process follows an exponential decay and the effective half-life of the radionuclide is given by equation 5.10



(T1/2 )eff =

(T1/2 ) p (T1/2 )b (T1/2 ) p + (T1/2 )b

(5.10)

Where (T1/2)eff = effective half-life of the radionuclide (T1/2)p = physical half-life of the radionuclide (T1/2)b = biological half-life of the radionuclide Hence one could say that the biological half-life of a radionuclide is lesser than its physical half-life and the biological half-life needs to be long enough to permit adequate nuclear activity, but short enough to minimize the radiation hazards. Differential uptake The radionuclide needs to be taken by the normal/abnormal tissue with a high specificity so as to provide best quality images during radionuclide imaging. Toxicity The ideal radionuclide is always non-toxic.

Radionuclide Imaging  159

5.3 Generation of Nuclear Emission 5.3.1 Nuclear Sources Most of the naturally occurring radioactive isotopes cannot be used in radionuclide imaging due to their long half-life and charged particle emission properties. Hence artificial radioisotopes are produced keeping in mind these criteria so as to aid in radionuclide imaging. Stable isotopes are artificially bombarded with high energy protons after which these stable isotopes convert into radioisotope and then again transform into another stable isotope by radioactive decay thereby resulting in artificially produced radioisotope. These can be produced by nuclear reactors or by charged particle accelerators. In nuclear reactors, neutrons from nuclear fission are captured by the nuclei of target material. The neutron activation process results in the generation of new radioisotopes. The most common neutron activation processed are (n, γ)& (n, p) reactions. 14C, 24Na and 32P are the most commonly produced artificial radioisotopes which emit beta particles and also have low specific activity. Charged particle accelerators are used to accelerate the charged particles such as protons to a very high energy. These particles are then made to strike the target materials thereby resulting in radioisotopes. The most common charged particle accelerators are as follows: • Van de Graaff accelerators • Linear accelerators • Cyclotrons The radionuclides 11C, 13N, 15O and 18F, produced by cyclotrons are extremely useful in PET imaging. These are produced with a high specific activity and can function as physiological tracers as well. However, they have a short half-life. Also, not every PET imaging site can house a cyclotron manufacturing setup due to cost constraints. This is one of the shortfalls of PET imaging as well.

5.3.2 99mTc Radionuclide Generator A radionuclide generator is an equipment containing parent-daughter radioisotope. This equipment separates and extracts the daughter isotope from the parent. A schematic representation of this generator is provided in Figure 5.2.

160  Medical Imaging Saline

Evacuated Collecting Device

Air In

Lead Shielding

Eluted 99mTc

Alumina 99Mo

Lead Shielding

Figure 5.2  99mTc generator.

The parent 99Mo is absorbed upon an alumina column or alumina beads. The parent 99Mo has a half-life of 2.5 days and decays as per the reaction given in equation 5.11



99

Mo yields  → 99mTc + e − + ve



(5.11)

Where e− = electron ve = anti electron neutrino The daughter isotope 99mTc is metastable with a 6 hours of half-life and decays to form a stable nuclei 99Tc by emitting gamma radiations at 140 KeV. Also due to the fact that 99mTc cannot bind with alumina, it is eluted from alumina with saline after which the 99mTc activity is replenished within a few hours from the decay of 99Mo. Certain breakthrough issues are seen in this regard, which can be averted so as to reduce the patient dose and also to ensure the purity of the daughter isotope.

5.3.3 Detection of Nuclear Emissions Often, three categories of detectors are employed for the process of the detection of nuclear emissions resulting due to radioactive decays, namely

Radionuclide Imaging  161 • Ion collection detectors • Scintillation detectors • Semiconductor detectors

5.3.3.1 Ion Collection Detectors A pictorial representation of a generic ion collection detector is given in Figure 5.3. An ion collection detector houses the cathode and anode electrodes separated by a volume of gas (with a high atomic number) such as that of xenon. When an external voltage is applied to the electrode, the gas acts as an insulator until it gets ionized by the radiations incident upon the detector which cause a short pulse of electric current in the detector circuit. A graphical representation of this electric current as a function of the external voltage is given in Figure 5.4. When the applied voltage is zero, there current is zero as well, even though the ion pairs are formed due to the radiations. This is due to the fact that the ion pairs do not possess enough energy to separate and hence, they recombine to form a neutral atom (region 1 of Figure 5.4). With the increase in the applied voltage, more electrons acquire enough energy to reach the anode, resulting in a rise in the current value. With a further rise in the applied voltage, the electrons and the positive ions acquire enough energy to ionize the gas molecules. Hence a steeper increase in current is observed (region 2 of Figure 5.4). When the applied voltage increases beyond region 2, at a certain point, all gas molecules get ionized after which any rise in the applied voltage will result in a small rise in the current. Further increase in Current Meter

Photons

Id

– Cathode –

+

Gas Anode

Figure 5.3  Ion collection detector.

V +

Voltage Source

162  Medical Imaging

Simple Ionization

Gas Amplification

Current, Id

Region 1 Region 2

Region 3

Saturation

Applied Voltage, V

Figure 5.4  Discharge current of an ion collection detector as a function of the applied voltage.

the applied voltage, beyond the region 3 (of Figure 5.4) causes spontaneous ionization within the detector volume. The current will rise again and this region is called the spontaneous discharge region. This, however, provides no useful information and is best avoided. The detectors operating in the region 1 (of Figure 5.4) are called as ionizing chambers and are used to detect high intensity radiations. The current produced in these chambers are directly proportional to the intensity of the radiations at a certain voltage. The detectors operating in region 2 (of Figure 5.4) in which the current is proportional to the incident radiations are called as proportional counters. The Geiger-Muller (GM) counters functions in region 3 (of Figure 5.4) and are used to detect very small radioactivity due to the fact that a single event will result in an avalanche ionization across the gas irrespective of the type of nuclear radiation. Ion collection detectors are not efficient in the detection of high energy γ rays. Their response time is longer than the other types of radiation detectors. Hence these detectors are not widely used in radionuclide imaging.

5.3.3.2 Scintillation Fetectors A scintillation detector houses a scintillation crystal such as that of NaI(TI) which is used to convert high energy gamma ray photons into visible light

Radionuclide Imaging  163 photons. The NaI(TI) is most commonly used crystal due to a high density (3.69 gm/cm3), a faster response time, ease of handling as well as due to its low cost. The lead shielding reduces the detection of background radiations by the crystal. When the gamma ray photon gets absorbed by the crystal, the intensity of the light scintillations (number of visible light photons) which are generated, is proportional to the energy of the absorbed gamma ray photon. These visible light photons are then converted into electrons by a photocathode. The photomultiplier tube (PMT) houses multiple dynodes at increasingly higher electric potential. The electrons from the photocathode are accelerated towards the anode via stages of synods, each of which increases the number of secondary electrons. Overall, a 10 stage PMT portrays an electron multiplication factor of 610. The magnitude of the final electric pulse from the PMT is proportional to the number of light photons incident upon the PMT. This electric pulse is then amplified by a suitable amplifier, analyzed by a pulse height analyzer (PHA) to ascertain the energy of the absorbed photons. A schematic depiction of the scintillation detector is given in Figure 5.5. In the PHA, by specifying a threshold, only the required pulses with the height of more than the threshold value can be selected. Due to the fact that the pulse height is proportional to the energy of the absorbed photons, the pulse height window is called as the energy window. Appropriate selection of the energy window is essential for the rejection of scatterred radiations. Another important type of scintillation detector is the well counter which is used to measure the radiations from small radioactive sample and is given by Figure 5.6. Photomultiplier Tube

Nal(Tl) Crystal

Lead Collimator

Figure 5.5  Scintillation detector.

Amplifier

Pulse Height Analyzer

Scaler or Counter

164  Medical Imaging

Sample Nal(TI)

Lead Shield

Photomultiplier Tube

Figure 5.6  Well counter.

Well counters are highly efficient and are preferred for the detection in case of weak radiation sources. Here, the radioactive sample is mixed with the scintillation liquid due to which the radioactive sample interacts directly with the scintillation material which results in a very high detection efficiency.

5.3.3.3 Solid State Detectors In the case of solid state detectors, at reverse bias scenario, a depletion region is seen because of the absence of any free charges near the p-n junction on the semiconductor. Commonly used semiconductors in these detectors are either silicon or germanium. A gamma ray photon interacts with the semiconductor and results in electron/hole pair. When the bias voltage is applied, the reverse current increases and the magnitude of this is proportional to the absorbed radiation energy. A schematic of the solid state detector is given in Figure 5.7. The semiconductors have a better energy resolution and a fast response time as well. But they are of small size and are also costly to use. They are used in charged particle and gamma ray spectrometers. Silicon-based detectors can operate in room temperature. However, a germanium-based detector requires a very low operating temperature of -196°C.

5.3.3.4 Collimator A collimator is employed to limit the field of view in the radiation detector. There are two types of collimators, namely, single-hole focused collimator

Radionuclide Imaging  165 Radiation

p-n Junction

–

p type

n type

+

Depletion Region

–

+

Ir

Battery

Figure 5.7  Solid state detector.

and multiple-hole focused collimator. The single-hole focused collimator is used to detect the gamma rays from a huge volume of radioactive source. The multiple-hole focused collimator can detect the localized region of radioactivity. This is shown in Figure 5.8. The dashed lines in this figure indicate the shape of the field of view. These collimators are used in rectilinear scanner

PMT

Nal (TI) Crystal Lead Shield 100% 40% 20%

Figure 5.8  Single-hole and multiple-hole focused collimator.

166  Medical Imaging systems in radionuclide imaging and are capable of determining the spatial resolution and the detection efficiency of the system.

5.4 Radionuclide Detection 5.4.1 Rectilinear Scanning Machines Rectilinear scanning machine were the first hardware equipment used for radionuclide imaging. A simple schematic of a rectilinear scanning machine is given in Figure 5.9. A conventional rectilinear scanning machine houses a mechanical scanning device, scintillation detection mechanism with a focused collimator and a recorder module. The collimator allows the passage of required gamma radiations through the collimator hole so as to interact with the crystal. The rest of the gamma radiations are blocked by the lead shield (septa) of the collimator. The incident gamma radiations are detected as they are attenuated and a two-dimensional image is formed based on this detected data. This image is either displayed on a CRT or is archived for further processing. The image quality depends upon the rate of counting of the distribution of the radioactivity and the speed of scanning. The spatial resolution of the image as well as the detection efficiency depends upon the collimator. An acceptable tradeoff between these two aspects is achieved by using a multi-hole

Positioner

X Amplifier PHA Preamplifier PMT Collimator Scintillation Crystal

Organ of Interest

Figure 5.9  Rectilinear scanning machine.

Y

Counter Z

CRT

Radionuclide Imaging  167 focused collimator approach. The spatial resolution can be increased either by reducing the focal length or by increasing the thickness of the collimator. At times, to detect high energy photons, single-hole focused collimators are used to reduce the penetration of the photons through the septa of the collimators. Rectilinear scanner systems often use a linear array of detectors instead of a single detector setup so as to achieve a better image quality with lesser scanning time. These are employed in a few special SPECT machines.

5.4.2 Scintillation Camera (Gamma Camera) Scintillation camera or gamma camera (Anger camera), developed by Hal Anger in the late 1950s, does not incorporate the rectilinear scanning approach; instead, the radioactivity from a larger area of the body is imaged simultaneously with a better efficiency. This also provides the functional imaging of the uptake/washout of radioactivity. The gamma camera is composed of a camera head and the electronic processing unit. The camera head houses a collimator and the scintillation crystal.

5.4.2.1 Collimator The collimator consists of parallel holes to provide a one-to-one connection with the size of the object distribution and the image formed. This is shown in Figure 5.10. X+

X–

Y+

Y–

Preamps, Summing Network & Amp

PMTs Scintillation Crystal

Radiation

Figure 5.10  Gamma camera.

168  Medical Imaging

5.4.2.2 Scintillation Crystal This is about 40 cm in diameter in a modern camera and about 50 cm in jumbo cameras. The detection efficiency of the incident photons and the intrinsic resolution of the camera are always a tradeoff and depend upon the thickness of the scintillation crystal. These crystals detect 99mTc labelled pharmaceutical with a 140 keV low energy gamma photon emissions. The best tradeoff is achieved by a crystal of thickness 9.5 mm.

5.4.2.3 Photomultiplier Tube The photomultiplier tubes (PMTs) are located in the form of a hexagonal array behind the scintillation crystal. This setup is shown in Figure 5.11. The intrinsic resolution of the camera depends upon the number of PMTs present. In general, the Low FOV cameras house a minimum of 61 closely packed PMTs. The PMTs are coupled to the crystal with light pipes. The output of each of the PMTs is provided to a preamplifier for pulse amplification and shaping. The signals from the preamplifier are combined

Summing Network

Y+

X–

Nal Crystal 1 5

Summing Network

16

6 11

17 23

7 12

18 24

29

9

13

25

14 20 27 32

36

15 21

26 31

35

4 8

19

30 34

3

Summing Network

10

2

22 28

33

37

PMTs

Summing Network

Figure 5.11  PMTs located in the gamma camera.

Y–

X+

Radionuclide Imaging  169 into four composite signals, namely X+, X-, Y+ and Y- and are then amplified by summing amplifiers and the output of the amplifiers is adjusted as per the requirement by attenuators. At this juncture, each of these four composite signal is further divided into two separate signals. One of the paths sums up the four signals and the amplitude of this summed signal is proportional to the intensity of the energy of the absorbed photons (scintillations). This summed signal is then fed into the pulse height analyzer with a preset energy window. If the amplitude of this signal is within the energy window, then the summed signal will switch on a gate which further triggers the line amplifiers and wave shaping circuits. The summed pulse is fed into the pulse height analyzer with a preset energy window. If the amplitude of the summed pulse is smaller or larger than the preset energy window, no further processing will occur. If the amplitude falls within the From Scanner Head Summing Networks X+

X–

Y+

Y–

Attenuator

Delay Lines

Lines Amps

Summing amplifier

Wave Shaping Circuits X+

X–

Y+

Y–

DA

PHA Z Pulse

Z Pulse

DA

Energy Correction

Gate

Y

X

Monitor Counter

Figure 5.12  Electronic processing unit of gamma camera.

Z

170  Medical Imaging energy window, the summed pulse will turn on a gate that triggers the line amplifiers and wave-shaping circuits.The wave-shaping circuits shapes and lengthens the narrow composite pulses. These processed pulses are then given to the differential amplifiers which calculate the change in positions in the display monitors. This would indicate the location of the absorbed photons. The change in positions in x and y axis are given as follows



g Dx = − ( X + − X − ) Z

(5.12)



g Dy = − (Y + − Y − ) Z

(5.13)

A block diagram of the electronic processing unit is provided in Figure 5.12. Spatial resolution and field uniformity are two major factors in this type of imaging. Ideally, the spatial resolution should be good. Also, the camera response should be uniform for uniform irradiations. But practically, there is a variation of around 10% in this aspect. Also the stationary scintillation cameras provide better resolution than the rectilinear scanning machines. Scintillation cameras, combined with computers, can provide functional images of specified time sequences. Such approaches are extremely useful in renal imaging as well as cardiac diagnostics.

5.4.3 Longitudinal Section Tomography (LST) In the longitudinal section tomography (LST) approach, a rectilinear scanner is used with a focused collimator. The obtained image is successful in focusing upon the regions which fall in the focal plane of the collimator and also blurs out the regions that are outside the focal plane. The usage of a slant hole collimator is depicted in Figure 5.13. As shown in Figure 5.13, the angle of the slant hole with respect to the collimator axis (θ) determines the projection of the object upon the image plane. As the θ varies, the position of the projection moves as well. The speed of this movement is more if the distance between the object plane and the camera is larger. As observed in conventional X-ray tomography, longitudinal section tomography too suffers from reconstruction problems related to limited angle. Even though the contributions of the plane of interest is highlighted and all the others are blurred, it may still lead to

Radionuclide Imaging  171 Scintillation Crystal Collimator

Direction of Rotation

θ Plane Plane

Image on Camera

V1

V2

Figure 5.13  Longitudinal section tomography with a slant-hole collimator.

overall degradation of the image at lower image contrast. This is addressed in transverse section tomography (TST) wherein the projections from all the 360o views around the subject are used for image reconstruction, similar to that of X-ray CT reconstruction methods.

5.4.4 Single Photon Emission Computer Tomography (SPECT) The Single Photon Emission Computer Tomography (SPECT) considers small voxels of the matrix of the transverse section and the radioactivity of each of the voxel is computed by the projections from all the 360o views around the subject. The projection data is obtained by a multidetector approach (using an array of multiple detectors) or by a camera-based approach (by using multiple scintillation cameras). This is depicted in Figure 5.14. In principle, in case of SPECT, a suitable radioactive pharmaceutical is administered to the body. This radioactive pharmaceutical binds itself to certain molecules with certain biological properties and then accumulates in the target regions in the body. For example, glucose, labelled with fluorine, accumulates in the brain region as well as in tumors. After this accumulation, these radioactive pharmaceuticals begin to emit photons due to radioactive decay process. These emitted photons are detected and

Count Rate

172  Medical Imaging

Projection Functions

Count Rate

Figure 5.14  Projections of radioactivity in the body at different angles.

processed to produce the images of the desired activity. In SPECT, one photon is detected per emission and hence the name. SPECT systems have a higher count rate and hence are expensive. Single slice imaging is possible in these systems due to single photon detection. SPECT can house either single of multiple scintillation detectors. The reconstruction aspects of SPECT are similar to that of X-ray CT. But the X-ray CT depends upon the attenuation coefficient whereas the SPECT depends upon the emission coefficient and also uses a camera-based setup for reconstruction which is often two-dimensional which can hence provide multiple transverse images. The SPECT images are often limited by the amount of radioactivity that can be safely administered to the subjects. A higher detection efficiency results in a poor spatial resolution and vice versa. This tradeoff is addressed by using a fan beam approach or a cone beam approach for reconstruction with multiple cameras. However, SPECT has a better image contrast as compared to conventional nuclear medicine-based images. SPECT is majorly used in the detection and the assessment of tumors. Generally, SPECT requires about 30 minutes of scan time for a single camera-based system. The shortfalls of SPECT are addressed in the case of Positron Emission Tomography (PET) machines.

Radionuclide Imaging  173

5.4.5 Positron Emission Tomography (PET) Positron Emission Tomography (PET) is based upon the fact that most of the elements present in the human body contain positron emitting radioisotopes. One could ascertain the functional aspects by labelling such active body constituents with the positron emitters. In PET approach, a suitable radioactive pharmaceutical is administered to the subject and a certain waiting period is to elapse so as to allow the radioactive pharmaceutical to accumulate at particular regions, after which the radiations are emitted which are further detected using suitable detector setup. The information pertaining to the detected radiations are used for reconstruction of the image. The total number of events detected along each of the lines defined by the detector geometry will yield the projection of the radioactive pharmaceutical distribution concentrated along that particular line. Using the set of all the line integrals along the possible lines specified by the detector geometry, the images of the distribution of the radioactive pharmaceutical can be obtained using conventional reconstruction algorithms. The most common non-idealities seen in this approach is that of the random co-incidences as well as the variations between the point of origin and the point of detection of the radioactivity. This results in a blurring effect in the reconstructed image. Also, random coincidences can be mitigated by using shorter coincidences. Also, sufficient time is required to obtain good-quality images which is a tradeoff

Detector

511 keV

Coincidence Circuit

511 keV

Detector

Figure 5.15  Detection of coincidence in PET.

174  Medical Imaging with respect to the coincidence resolving time. Image resolution also depends upon the size of detectors. The process of detection is shown in Figure 5.15. Advantages of PET over SPECT • Positron emitting isotopes (carbon, nitrogen and fluorine) occur naturally in many compounds of biological interest which is not the case in SPECT. • In PET, the radioactive decay results in the emission of a positron which almost immediately results in the emission of two photons that traverse in almost opposite directions. • Usage of electronic collimation in PET provide higher accuracy in terms of collimation which results in a better sensitivity and hence in a better SNR and also in a better image quality. But in case of SPECT, the lead collimator absorbs many photons and hence results in a reduced sensitivity. Attenuation correction Attenuation of photons are seen when they are emitted from the radioactive decay in any emission computer tomography (SPECT or PET). This has an undesirable effect on the image quality. In emission computer tomography attenuation, the correction must be incorporated as a part of the image reconstruction approach. A major issue in PET imaging approach is the short half-life of the positron emitters. Hence the radio-nuclides need to be produced at the site of imaging itself. This is achieved by cyclotron units which can produce positron emitters at the hospital sites. However, these cyclotron units are costly and complicated to maintain as well.

5.5 Diagnostic Approaches Using Radiation Detector Probes The radiation detector probes are used in various clinical applications. A few of them are explained in this section. These probes encompass a single scintillation detector system without any scanning mechanisms. Monitoring and evaluating the radioactivity from the region of interest as a function of time provides important functional information of that particular organ. A few such examples are provided below.

Radionuclide Imaging  175

5.5.1 Thyroid Function Assessment The evaluation of the functional aspects of the thyroid gland can be obtained by the assessment of the uptake of radioactive iodine by the thyroid gland. A conventional scintillation detector system is used here for the process of detection. Thyroid needs iodine to produce hormones so as to regulate the body metabolism. In the case of hypothyroid or hyperthyroid, the concentration of iodine in the thyroid is abnormal. The thyroid function test begins with the oral intake of about 300 kBq of 131I in the form of a liquid or capsule. After 24 hours, the amount of 131I is detected by counting the gamma particles emitted by the radioactive iodine per minute. A reference counting happens for the same amount of time by using a neck phantom. The ratio between these two values provides the 24-hour uptake of iodine for thyroid. For normal subjects, this ratio is around 20% whereas hyperthyroid subjects demonstrate a ratio of 60% and this ratio is found to be less than 10% for hypothyroid subjects.

5.5.2 Renal Function Test The 131I labelled hippuric acid is injected into the bloodstream and the excretion of this radio labelled hippuric acid by the kidneys is assessed by the radiation detector which provides an insight into the time-­activity curve of the detected radiations from the kidney (renogram). This is achieved by positioning the radiation detector over the kidney.

5.5.3 Blood Volume Assessment Dye dilution approach is incorporated by injecting about 200 kBq of radioactive 131I labelled albumin. After a waiting period of 15 minutes, a blood sample is drawn from the vessel and counted which provides an insight into the blood volume.

5.6 Radionuclide Image Characteristics The most common parameters of a radionuclide images are spatial resolution, image contrast and noise.

5.6.1 Spatial Resolution The spatial resolution of a radionuclide image is mostly dependent upon the nature of collimator used in the radionuclide equipment. Other aspects

176  Medical Imaging such as the photon energy, system uniformity and the patient motion also affect the spatial resolution of the image. A bar phantom is used to assess the spatial resolution of the equipment being used. Spatial resolution is quantified in terms of point-spread function, line-spread function, edge spread function, optical transfer function and modulation transfer function.

5.6.2 Image Contrast Factors such as the distribution of the radionuclide, scattered radiations and the penetration across the septa of the collimator are found to affect the image contrast. The contrast efficiency function is used to quantify the image contrast. Contrast efficiency is comparatively better in emission computed tomography approach due to the reduction of the overlying as well as the underlying structures.

5.6.3 Image Noise Magnitude and texture components can be used to characterize the image noise. The noise magnitude is seen due to the random noise fluctuations due to the statistical nature of the radiation detection. This is reduced by increasing the number of counts detected or by using smoothing approaches. The noise texture depends upon the recording device and the image processing techniques being employed. For instance, a device with a smaller density results in sharper noise texture. This is mitigated using smoothing filters.

5.7 Biological Effects of Radionuclides Radiations emitted during radioactive decay process (alpha, beta and gamma radiations) are capable of ionizing the atoms and molecules and are hence termed as ionizing radiations. These radiations cause harmful effects to the body when exposed to high dosage. Hence it is important to understand the biodistribution of the radionuclides in various tissues before determining the required dose of radiation to the subject.

Radionuclide Imaging  177

Glossary-Appendix 1. I sotope: Elements with the same number of protons but a different number of neutrons 2. Radioactive nuclide: An isotope with an unstable nucleus which decomposes readily and results in the emission of radiation and or nuclear particles 3. Radioactive decay: The process by which an unstable is transformed into a more stable daughter nucleus 4. Half-life: The time required for half of the radionuclides to decay 5. Activity: Average decay rate of the radionuclide 6. Specific activity: The ratio of activity to the mass of the radionuclide sample 7. Carrier: The stable isotopes of the element 8. Alpha particles: Helium particles consisting of two neutrons and two positively charged protons 9. Specific Ionization: Number of ions produced per unit length 10. Linear Attenuation co efficient: A function of the density of the medium and the energy of the gamma photon 11. Biological Half-life: The time required for the body to excrete half of the amount of the administered radionuclide 12. Radionuclide generator: An apparatus that contains a parent-daughter radioisotope pair 13. Collimator: A device used to limit the field of view of a radiation detector 14. Single-hole focused collimator: To detect the gamma rays from a huge volume of radioactive source. 15. Multiple-hole focused collimator: Detect the localized region of radioactivity

6 Magnetic Resonance Imaging

The concept of Nuclear Magnetic Resonance (NMR) was discovered by E. Purcell and F. Block in 1946 for which they were awarded Nobel Prize in 1952. Since then, the concept of NMR has been widely used in spectroscopic applications. NMR has been used for medical imaging-related applications since the 1970s as Nuclear Magnetic Resonance Imaging (Nuclear MRI) due to its ability to penetrate the air filled as well as bony structures of the body with less attenuation and artifacts. Due to the fact the MRI does not incorporate any kind of ionizing radiation (it uses radiofrequencies and its interaction with the nuclear magnetic moment is ascertained) and its minimally invasive nature, it provides a high-quality image of soft tissue contrasts in different planes. With the advent of technology, functional MRI (fMRI) is gaining more popularity for various neurological assessments with respect to the physiology as well.

6.1 Basics of Nuclear Magnetic Resonance The MRI images are formed based on the signals received from the nuclei of the hydrogen atoms. As a matter of fact, the hydrogen atoms encompass a nucleus which contains a single proton and a single electron orbiting the nucleus due to which the hydrogen atom is electrically neutral. MRI concentrates on this proton for imaging applications. This setup is depicted in Figure 6.1. The proton being positively charged (and the electron being negatively charged), also demonstrates a spin (which is an intrinsic attribute of almost every elemental particle). Hence, the proton rotates about its axis resembling a spinning top. Such a proton possesses two important attributes, namely angular momentum and magnetic moment, as explained below.

H. S. Sanjay and M. Niranjanamurthy. Medical Imaging, (179–218) © 2023 Scrivener Publishing LLC

179

180  Medical Imaging

Figure 6.1  The nucleus of the hydrogen atom.

• Angular momentum (M): the proton being a rotating mass of m, possesses an angular momentum similar to a spinning top and has a spatial orientation about its rotational axis, as shown in Figure 6.2. • Magnetic moment (B): As the proton is a simple rotating mass with an electrical charge, it has a magnetic moment (B) and acts like a magnet. This is shown in Figure 6.3. Hence the proton gets affected by external magnetic field and can induce a voltage in the receiver when it is set into motion. One needs to also remember that the spin of a proton exists always with the same magnitude and never accelerates or decelerates. In other words, the proton always is spinning and is never stagnant. This is due to the fundamental property of the elementary particles. Hence one could infer that the proton spins always.

M

m

Figure 6.2  Angular momentum of the proton.

Magnetic Resonance Imaging  181 B

N

+ + + + + ++ + + S

Figure 6.3  Magnetic moment of the proton.

To understand the behavior of the spin of the proton when subjected to a magnetic field, consider the same example of the spinning top. When an external force such as that of the gravity (G) acts upon the spinning top, the orientation of its rotational axis varies, resulting in the wobbling of the top. This process is called precession. Simultaneously, the rotation of the top slows due to the friction at the point of contact due to which the inclination of the axis increases and eventually, the top falls. This is depicted in Figure 6.4. On similar lines, when the protons are exposed to the magnetic field (Bo), the magnetic moment (spin) aligns in the direction of the field and also undergo precession as similar to the spinning top. This is shown in Figure 6.5.

G

Figure 6.4  Falling of the spinning top.

182  Medical Imaging

B0

Figure 6.5  Precision in hydrogen protons.

6.2 Larmor Frequency The characteristic speed of the precession of the nuclei is found to be proportional to the strength of the applied magnetic field and is called the Larmor frequency. Hence one could define the Larmor frequency as “the rate at which the spins wobble when placed in a magnetic field”. The Larmor frequency is directly proportional to the strength of the magnetic field (Bo) and is governed by the larmor equation as shown in equation 6.1



ωo = γoBo

(6.1)

Where ωo = Larmor frequency γo = a constant, specific to a particular nucleus (gyromagnetic ratio) Bo = Strength of the magnetic field in tesla (T) The spin system becomes stable by relaxing, the longitudinal magnetization (Mz) increases in the z-direction due to the fact that the magnetic vectors of the individual magnetic moments add together. When this value is large enough, then the MR signals can be obtained. In this context, the spins align in parallel and anti-parallel directions to the magnetic field. The parallel alignment is preferred because it represents the spins at favorable

Magnetic Resonance Imaging  183 energy state. Eventually, the parallel and anti-parallel magnetization cancels and the net value is the excess parallel magnetization which denotes the measurable net magnetization vector (NMV). The longitudinal magnetization is found to increase with the magnetic field strength. An electromagnetic wave with an energy equal to that of the Larmor frequency of the proton can result in the introduction of an energy into a stable spin system. This is called “resonance condition”. Such an electromagnetic wave can be generated with the aid of a radio transmitter and is applied to the organ which is to be imaged in the MRI machine using an appropriate antenna coil. The proton absorbs this energy from the electromagnetic wave and is called as the excitation of the spin system. This in turn results in the movement of longitudinal magnetization away from the z-axis and towards the transverse plane (xy axis) and in a direction perpendicular to the main magnetic field. A radio frequency pulse (RF pulse) often called as the 90o RF pulse, is then applied until the longitudinal magnetization rotates into the transverse plane (rotation by 90o). The net magnetization is denoted by Mxy as this lies in the xy-plane and is called as the transverse magnetization which precesses about the z-axis with an effect of an electrical generator inducing an alternate voltage of the frequency equal to that of the Larmor frequency in the receiver coil and is called as the MR signal. This signal is acquired and processed to generate MR images. This is shown in Figures 6.6 – 6.9.

Figure 6.6  Protons without any external magnetic field.

184  Medical Imaging B0

Figure 6.7  Production of longitudinal magnetization Mz.

Figure 6.8  Exposure of the protons to the RF pulse.

Magnetic Resonance Imaging  185

Figure 6.9  Generation of transverse magnetization and reduction of longitudinal magnetization.

6.3 Relaxation After the protons are excited by the RF waves, the magnetization rotates onto the xy-plane from the z-plane and is hence termed to be transverse magnetization (Mxy). This rotation of the magnetization results in the MR signal to be detected by the receiver coil. But as a matter of fact, this MR signal deteriorates due to two processes, namely spin-lattice interaction and spin-spin interaction which in turn causes T1 relaxation and T2 relaxation, respectively. This eventually reduces the transverse magnetization and reinstates the original status of the proton (as it was before excitation).

6.3.1 T1 (Longitudinal Relaxation) Once the transverse magnetization begins to decay, the magnetic moments gradually align themselves with respect to the z-axis of the main magnetic

186  Medical Imaging

Mz

Mxy

Figure 6.10  T1 relaxation process.

field (Bo). The transverse magnetization begins to decrease slowly and the MR signals starts to fade correspondingly. With this, the longitudinal magnetization (Mz) is restored. This process is called as longitudinal relaxation (T1 recovery). Such a return to the ground state is often associated with the dissipation of the excess energy by the nucleus to the surrounding, i.e., the lattice and hence this process is also called as the “Spin-lattice relaxation”. T1 denotes the time constant required for such a recovery and depends upon the strength of the external magnetic field (Bo) and the Brownian motion (internal motion of the molecules). This process is shown in Figure 6.10.

6.3.2 T2 (Transverse Relaxation) After the excitation of the protons, a part of the spin precess in synchrony. Such spins have a phase of 0o and are hence termed to be in-phase. This is

Mxy

Figure 6.11  T2 relaxation.

Magnetic Resonance Imaging  187 called “phase coherence”. The phase coherence does not stay for long as some spins fall behind in their path of precession due to which the individual magnetization vectors start to cancel each other instead of adding together. The resulting vector sum, which is nothing but the transverse magnetization, reduces and eventually disappears, thereby resulting in the loss of MR signal as well. This is shown in Figure 6.11. Transverse relaxation can be considered as a decay of transverse magnetization due to dephasing of the spins. However, in this case, the spins do not dissipate energy, as seen in the case of longitudinal magnetization, but instead there is an internal exchange of energy with each other. The spins can lose their coherence due to the following reasons: • Energy transfer between the spin due to the local variations of the magnetic field: These fluctuations are seen due to the fact that the spins are associated with small magnetic field which randomly interact with each other. The precession of spin is slow or fast based on the magnetic field variations they experience. Overall, this leads to a loss of phase due to the spin-spin interaction. Dephasing is seen due to the time constant T2 and not due to the strength of the external magnetic field (Bo). • Time independent homogeneities of the external magnetic field (Bo): These are the intrinsic homogeneities seen due to the magnetic field generator and result in the dephasing which eventually results in the signal decay, much faster than that seen due to the time constant T2. This instead, occurs with the time constant T2* (which is much shorter than T2). This effect is predominantly seen at the tissue borders, at air-tissue interfaces. The loss of MR signal due to T2* is called “Free induction decay (FID)”. The effects of T2* can be mitigated by spin-echo sequences. In other words, T2 denotes the process of energy transfer between the spins and T2* denotes the effects of additional field inhomogeneities contributing to dephasing. The T1 and T2 relaxations are independent of each other, but occur in synchrony (almost simultaneously). For instance, the decrease in the MR signal due to T2 relaxation is seen within the first 300 msec whereas the complete recovery of the longitudinal magnetization (Mz) due to T1 relaxation takes up to 5 seconds of time.

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6.4 Image Contrast The following features affect the brightness of an MR image and therefore the image contrast: • Proton density: the number of excitable spins per unit volume affects the maximum signal that can be obtained from a given tissue. Proton density depends upon T1 and T2. Such images are called as proton density images. • T1 time: The T1 time of the tissue refers to the time taken by the excited spins to recover and be ready for the next excitation. T1 affects the signal intensity and can be varied. The images with T1-based contrast variations are called as the T1 weighted images (T1w). • T2 time: The T2 time emphasizes the quickness at which the MR signal deteriorates, post excitation. The images with T2 based contrast variations are called as the T2 weighted images (T2w). The above-given aspects are the intrinsic features of the biological tissues and can vary from each other. The MR sequence and the tissue contrasts can differ, based on the organ being imaged. Hence MRI can provide excellent soft-tissue differentiation and score better than CT scans and does not need the administration of any kind of contrast medium as well.

6.5 Repetition Time (TR) and T1 Weighting Generation of an MR image requires the excitation of the slice and then recording the signal for multiple iterations. The Repetition time is defined as the interval between the two successive excitations of the same slice. It is the length of the relaxation period between two excitation pulses. A longer TR results in more number of excited spins to revert back to the z-plane and result in the regrowth of longitudinal magnetization. A higher value of the longitudinal magnetization can be excited with the next RF pulse, due to which a larger MR signal can be seen. Instead, if the repetition time is short (say, less than 600 msec), then the image contrast is strongly affected by T1, during which the tissues with shorter T1 relax faster and result in a larger signal after the next RF pulse and hence appear bright on the image. But tissues with a longer T1 undergo less relaxation before the next RF

Magnetic Resonance Imaging  189 Mz Short T1 90°

Long T1

TR A: 500 msec

Time

TR B: 2000 msec

Figure 6.12  Relation between TR and T1 contrast.

pulse and hence lesser longitudinal magnetization is seen when the next excitation pulse is applied. Such tissues appear darker. The image obtained with a shorter TR is often T1 weighted because it contains T1 information. If a longer TR is selected (say around 1500 msec), then more tissues (even those worth longer T1) can return back to equilibrium and hence give similar signals resulting in less T1 weighing. Hence the T1 weighted information can be controlled by varying the TR (i.e., short TR results in strong T1 weighting and long TR results in low T1 weighting). This is shown in Figure 6.12. In other words, the tissues with a shorter T1 appear bright as they regain most of their longitudinal magnetization during the TR interval and hence produce a stronger MR signal. On the other hand, the tissues with a longer T1 appear dark as they cannot regain much of their longitudinal magnetization during the TR interval and hence produce weak MR signals.

6.6 Echo Time (TE) and T2 Weighting Different gradients used in MR imaging induce magnetic field inhomogeneities which are required to encode the spatial origin of the MR signal. But these gradients also result in spin dephasing. Such effects are mitigated by applying a refocusing pulse before the MR signal is obtained. The signal induced in the receiver coil after the restoration of the phase coherence is called as spin-echo can be measured. The Echo Time (TE) is defined as the interval between the application of the excitation pulse and the collection of the MR signal. The TE provides the information about the influence of T2 on the image contrast. One needs to remember that T2 is much

190  Medical Imaging shorter than T1. A shorter TE results in a smaller differentiation between the tissues as T2 relaxation would have just begun and hence a minor decay would be seen during the collection of the echoes. This results in a low T2 weighting. Longer TE results in a better depiction of the tissues with different signal intensities in the resulting MR image. Tissues with shorter T2 appear dark and the tissues with a longer T2 produce a stronger signal and hence appear bright. Appropriate selection of TE can vary the extent of T2 weighting on the image. In other words, shorter TE results in a low T2 weighting and a longer TE results in a strong T2 weighting. Hence the tissues with a short T2 appear dark on T2 weighted images and the tissues with a longer T2 appear bright on T2 weighted images. Figure 6.13 shows the relationship between the T2 and the T2 weighted images. Figure 6.13 demonstrates the relationship between TE and T2 contrast. When TE is very short (A), there is virtually no signal difference between two tissues with different T2 times whereas clear differences become apparent when TE is longer (B): a tissue with a short T2 rapidly loses signal and becomes dark while a tissue with a long T2 retains its brighter signal for a longer time. The MR images obtained with a combination of T1 and T2 effects are called as proton density weighted images (PD images) and are known to have a higher SNR than conventional T1 or T2 weighted images. This is due to the fact that a longer TR allows the recovery of longitudinal magnetization and a shorter TE minimizes the reduction of the signal seen due to the decay of transverse magnetization. PD images are used for evaluating the organs with low signal intensities (for example, bones and connective

Signal

90°

Long T2 Short T2 TE A: 20 msec

TE B: 80 msec

Figure 6.13  Relationship between TE and T2.

Time

Magnetic Resonance Imaging  191 tissues). PD weighting also provides excellent resolution images. These are used for imaging of the brain, spine and musculoskeletal system.

6.7 Saturation at Short Repetition Times A shorter TR results in smaller components of longitudinal magnetization which is restored and available for the next excitation process. This results in the decrease of the MR signal. As this degradation of the MR signal continues, eventually, the MR signal becomes more and more weak after subsequent excitation. This is referred to as saturation. This is depicted in Figure 6.14. Saturation is of prime importance in fast/ultrafast MR imaging during which the MR signal becomes very weak due to short repetition times. This is depicted in Figure 6.15.

Mz

90°

1st excitation

90°

2nd excitation

3rd excitation

Figure 6.14  Mechanism of saturation.

Mz 90° Equilibrium

TR

Figure 6.15  Longitudinal magnetization at short repetition times.

Time

192  Medical Imaging

6.8 Flip Angle/Tip Angle Flip angle-based approach is extremely useful to reduce the saturation and hence to achieve the required MR signal with a very short repetition time (TR). A smaller flip angle deflects the magnetization by a fraction of the standard 90o (say for instance, 30o). This results in a lesser transverse magnetization value with the individual MR signals being smaller, but a larger longitudinal magnetization being available for the next excitation despite a shorter TR, thereby resulting in a larger overall signal (as compared to the one obtained with a 90o flip angle). A much less flip angle is sufficient to prevent excessive saturation if the TR is shorter. The value of the flip angle which increases the MR signal for a given TR and TE is called as the Ernst Angle.

6.9 Presaturation Presaturation aids in the modulation of the image contrast. This approach makes use of an initial 90o or 180o inverting pulse which is delivered to the proton before the MR signal is obtained. A presaturation pulse, often called as the prepulse, can be combined with other basic pulse sequences. In general, the fast gradient echo sequences often have a poor image contrast due to shorter repetition times which result in homogeneous saturation of different tissues. The images thus obtained are weak T1 weighted. Although a stronger T1 weighting can be achieved by having a larger flip angle, this would still not be useful as larger flip angles would increase the saturation as well. Hence presaturation is used to enhance the T1 contrast. A higher T1 effect can be seen with a 180o inverting pulse, rather than with a 90o inverting pulse due to the fact that all the longitudinal magnetization can be inverted using a 180o pulse. Also, the time interval between the 180o pulse and the excitation pulse (i.e., the inversion time TI) can be varied to modulate the T1 effect. TI can be selected so as to eliminate the signal contributions from a certain set of tissues by applying the excitation pulse when the tissue has no magnetization. For instance, a short TI can suppress the signals from fat and a long TI can suppress the signals from CSF.

6.10 Magnetization Transfer In general, the protons considered in the preceeding sections are free protons, i.e., protons in free water which contribute towards the generation

Magnetic Resonance Imaging  193 Signal free

bound

free

bound Frequency (Hz)

Figure 6.16  Magnetization transfer.

of MR signal. However, biological tissues house a specific pool of protons bound in macromolecules, usually proteins, which cannot be directly visualized due to their very short T1. They have a wider range of Larmor frequencies, as compared to the water protons. Hence the macromolecular protons can be excited by the RF pulses with a different frequency than that of the Larmor frequency of hydrogen protons. This permits us to selectively excite the tissue with a larger pool of macromolecular protons, without affecting the protons in free water. But repeated delivery of the magnetization pulses saturates the magnetization of the macromolecular protons from where it gets transferred to the free protons around them. This also results in a decrease in the signal depending upon the macromolecules and their interaction with free water. This is called as the magnetization transfer. This is depicted in Figure 6.16. Such a reduction of signal intensity is higher in the case of the magnetization transfer in solid tissues and lower in the case of fluids and fatty acids. This approach can improve the image contrast with the process of Magnetization Transfer Imaging (MTC). For instance, MTC can be used to improve the contrast between the synovial fluid and the cartilage in the case of cartilage imaging, due to the fact that the synovial fluid contains few bound protons and hence shows less magnetization transfer, whereas the cartilage contains huge amounts of bound protons and hence depicts a larger magnetization transfer.

6.11 Slice Selection MR imaging provides a cross sectional imaging of the region of interest and hence, the excitation pulse is provided only that part of the body which

194  Medical Imaging is to be imaged. For example, consider a cross section through the body. The magnetic field generated by the MR equipment is directed along the body axis of the subject, commonly denoted as the z axis, i.e., the direction of the main magnetic field. The magnetic field gradients are denoted by wedges with thick side indicating a higher field strength and the tips indicate a lower field strength. It is indeed the Larmor frequency being proportional to the magnetic field strength which results in the excitation of a specific slice during imaging. This is possible due to the fact that the protons are excited by the RF pulse only if the frequency of the RF pulse is equal to their Larmor frequency. If a uniform field of identical strength is generated across the body, then all the protons would have the same Larmor frequency due to which all the protons would get excited by a single RF pulse simultaneously. So, to excite the desired slice selectively, the magnetic field is made to be inhomogeneous in a linear pattern along the z direction with the help of gradient coils. In general, the magnetic field strength has a smooth gradient with the gradient being smoothest at the head of the subject and strongest at the feet. Hence the Larmor frequencies vary gradually across the z axis and each slice has a unique frequency, and corresponding RF frequency pulse (matching its Larmor frequency) can be used to excite the protons within the slice of interest and the rest of the body is unaffected. This is depicted in Figure 6.17.

Z

Figure 6.17  Slice selection by z gradient.

Magnetic Resonance Imaging  195 Field strength or frequency Strong gradient

Weak gradient

Same RF pulse

Thinner slice (in same position)

a

Distance

Figure 6.18  Gradient and slice thickness.

Field strength or frequency

Gradient

Higher frequency

Selection of more distal slice

Figure 6.19  Slice selection.

Distance

196  Medical Imaging Gradient coils generate an additional magnetic field, generally known as the gradients which add up or reduce the main magnetic field. The protons along these gradients are temporarily exposed to this extra magnetic field and hence demonstrate a variation in their frequency of precession. A steep gradient results in a thinner slice while a shallow gradient provides a thicker slice. This is shown in Figure 6.18. Variations of the center frequency of the RF pulse can help to select the position of the slice. This is depicted in Figure 6.19.

6.12 Spatial Encoding After selecting the position and thickness of the slice with the aid of an appropriate slice-select gradient, one can identify the spatial position of the MR signal. This can be done by spatial encoding which requires additional gradients to alter the magnetic field strength along the x axis and y axis. Spatial encoding involves two stages, namely, phase encoding and frequency encoding.

6.13 Phase Encoding In this process, once the spins are excited and precess in the xy plane, a gradient is switched on in the y direction (top to bottom) which varies the Larmor frequencies of the spins with respect to their location along the gradient. This results in a phase difference between the spins with the

y

Figure 6.20  Phase encoding by y gradient.

Magnetic Resonance Imaging  197 ones at the top having a faster phase shift and the ones at the bottom of the scanner having a slower phase shift. This is shown in Figure 6.20. The extent of phase shift depends upon the amplitude and the duration of the phase encoding gradient. Once the gradient is switched off, all the spins return to their initial phase due to which the phase is seen to vary along the y axis linearly within the slice.

6.14 Frequency Encoding The second spatial dimension of the MR signal can be related to the changes in frequency in x axis at which a frequency encoding gradient is applied. This gradient provides a magnetic field which increases the strength from right to left. Hence, the corresponding Larmor frequency varies and the spins at the right side precess faster than those on the left side. The MR signal obtained with frequency encoding gradient encompasses an entire frequency spectrum and not a single frequency. The high frequency components are on the right side and the lower frequency components are seen

x

ω0

Frequency

Figure 6.21  Frequency encoding at the x axis.

ω0

Frequency

198  Medical Imaging at the left side. Every frequency denotes a column of the slice. This is shown in Figure 6.21. It is hence evident that the spatial identification of each of the volume element, often termed as the voxel, can be achieved with a combined incorporation of phase encoding and frequency encoding. The MR signal thus obtained provides the frequency information (in the x axis) and the phase information (in the y axis). The frequency information can be processed using frequency analysis to decompose the frequencies in the x-axis and hence to detect the individual frequencies of the composite signal. The phase information of each of these frequency signals denote the origin location of the origin of the respective signal component in y axis. The echoes of varying phase coded spatial information is obtained by applying the fourier transform in the y axis. Hence, in spatial encoding, the Fourier analysis is performed twice, along x axis and y axis, respectively. This is nothing but a 2D Fourier analysis. For an MR machine to perform such a complicated analysis, an array processor is incorporated, which is a dedicated computer for such calculations. Repetitive measurements can be obtained with specific temporal delay. Also, the image quality improves with multiple phase encoding. However, this increases the scan time and hence is always a tradeoff. An additional phase encoding gradient along z-axis provides a third dimension which can be processed along with the x-axis and y-axis–based information using a 3D Fourier analysis to obtain a 3-dimensional spatial encoding which can then image an entire volume rather than the individual slices. Such an approach will increase the scan time further, but will nonetheless provide excellent volume imaging, such as those seen in the case of MR angiography.

6.15 K-Space The data acquired from the signals are stored in a mathematical domain called as the k-space which has two horizontal axes, as shown in Figure 6.22. Here, the kx represents the frequency information and the ky denotes the phase information. A k-space is a graphical matrix of digitized MR data before performing the Fourier analysis. Each line of the k-space denotes one measurement and a line is acquired for each phase encoding. The central line includes the data which is not effected by the phase encoding gradient. Once the k-space is filled up with the raw data, the entire matrix is subjected to 2D Fourier analysis so as to obtain the MR image. The data at

Magnetic Resonance Imaging  199 K-space ky (phase)

Measurement 2 Measurement 1 kx (frequency)

Figure 6.22  K-space.

the centre of the k-space corresponds to the contrast of the image and the peripheral data of the k-space denote the spatial information.

6.16 Image Noise The MR signal and the noise of the MR image are quantified in terms of the signal-to-noise ratio (SNR) which is quotient of the intensity of the MR signal measured in the Region of interest (ROI) and the standard deviation of the signal intensity outside the ROI. In general, image noise in an MR image can be seen due to various factors, as mentioned below: • Issues pertaining to image processing • MR system issues ◦◦ Thermal noise from the RF coils ◦◦ Magnetic field inhomogeneities ◦◦ Nonlinearity of signal amplifiers • Patient related factors ◦◦ Body movement ◦◦ Respiratory movement The SNR of the MR image depends upon the following factors: • Selection of the coils: Usage of appropriate RF coils can improve the SNR without varying the voxel size or even without increasing the scan time. Normally, the RF coil should be closer to the region of interest to obtain better

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•

•

•

•

•

• •

signals. The various types of RF coils such as those of volume coils, surface coils, intracavity coils and phased array coils are used as per the requirement so as to improve the SNR. Image size: The MR image houses a matrix of pixel values. Each of these pixels correspond to the signal intensity. Each pixel relates to the information on a corresponding 3D volume element called the voxel. The voxel determines the spatial resolution of the image. The finer the matrix, better the resolution and lesser the SNR. Field of view: When the size of the matrix is constant, the field of view (FOV) determines the pixel size. A smaller FOV results in a smaller pixel if the size of the matrix is not changed. With the same FOV, a finer matrix can improve the spatial resolution. On the contrary, a coarser matrix reduces the spatial resolution at a constant FOV. Hence, a larger matrix can contain more pixels. But the SNR reduces with the voxel size. Slice thickness: For an optimal image resolution, thin slices with a high SNR are desirable. But thinner slices induce higher noise and hence, lesser SNR. The SNR, however, improves with the increase in slice thickness. But a thicker slice also increases the partial volume effects. Hence the poor SNR in the case of thinner slice is mitigated by increasing the number of acquisition or by having a longer TR. But this in turn will increase the acquisition time. Receiver bandwidth: The receiver bandwidth is a range of frequency collected by the MR system. A wider bandwidth results in a faster acquisition and reduces the chemical shift artifacts, but also reduces the SNR due to the inclusion of noise. A narrow bandwidth results in a higher chemical shift and motion artifacts. Magnetic field strength: A higher magnetic field strength increases the longitudinal magnetization due to the fact that, in such a scenario, a greater number of protons align along with the main axis of the main magnetic field. This in turn improves the SNR. Number of excitations: Higher number of excitations improve the SNR of the image. But such a process also increases the scan time. Scan parameters: Imaging parameters such as those of Repetition time (TR) and Time to Echo (TE) and the flip angle affect the SNR. The SNR increases with a higher TR,

Magnetic Resonance Imaging  201 but this also results in the loss of T1 effect. The SNR reduces with a higher TE wherein the T2 contrast is lost. Overall, in T1 weighted images, reduction of TE improves the SNR.

6.17 The MR Scanning Machine The major components of an MRI machine are a strong magnet, a gradient system, a radio frequency transmitter, additional coils, computers and other peripheral modules. A block diagram representation of an MR system is given in Figure 6.23.

x-gradient amplifier

MR scanner

y-gradient amplifier

Transmit/receive coil (body coil)

z-gradient amplifier

Surface coil (receive only) Switch Transmit amplifier

Receiver amplifier

Control computer

Peripheral devices

Host computer

Operator’s console

Figure 6.23  MR scanning machine - hardware.

Array processor

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6.17.1 The Magnet The magnet is used to generate the main magnetic field and should ideally have an adequate strength (of about 0.1 to 3T), without any fluctuations in the field strength and the best possible homogeneity in terms of a uniform strength across the entire field. There are three types of magnets associated with MR machines, as given below.

6.17.2 Permanent Magnet Permanent magnets are made of ferromagnetic substances and can create a magnetic field without any external power supply. These magnets are very heavy and cannot generate a higher magnetic field strength (not more than 0.5T) and depend upon the external temperature as well.

6.17.3 Resistive Magnets Resistive magnets are simple electromagnets which depend upon a high power supply to create a magnetic field. These magnets cannot create a higher magnetic field as well (not more than 0.3T). Their operating costs are very high due to the power requirements. They also have a poor field homogeneity. However, these magnets can be turned off instantly during emergency situations.

6.17.4 Superconducting Magnets Superconducting magnets encompass a coil made of niobium-titanium (Nb-Ti) alloy which has a nearly zero resistance to the flow of current, which is achieved by the usage of coolants called as cryogens such as liquid helium. Hence, once the magnetic field is established, it is maintained at the same levels without any additional power requirements. These magnets can generate a strong magnetic field (up to 18T). But a regular maintenance of liquid helium is necessary in these magnets. Also, these magnets cannot be instantly switched off. Most of the current MR machines incorporate these superconducting magnets for their operation. The maintenance of the magnets involves three important processes, namely, quenching, shimming and shielding, as mentioned below.

6.17.5 Quenching Quenching is a scenario where a sudden loss of the absolute zero temperature is seen in the magnet coils. This reduces the superconducting capacity

Magnetic Resonance Imaging  203 of the magnets, due to which the magnets in turn become resistive and therefore the magnetic field is reduced. This results in the escaping of the helium from the cryogen bath rapidly into the surrounding atmosphere. Quenching can result in severe, irreparable damage of the superconducting coils. Quenching is also seen during accidental fires in the scanning areas. A manual quench is, however, performed during routine servicing of the machine.

6.17.6 Shimming Shimming in MRI refers to the process of reduction of the magnetic field inhomogeneities so as to achieve an optimal homogeneity for obtaining MR images of better SNR. Field inhomogeneities can be seen due to the intrinsic magnetic properties as well as due to the surrounding environment of the MR magnets (i.e., nearby electrical wires and metallic structures). Shimming is of two types, namely, active and passive shimming. Active shimming uses shim coils which cancel the field gradients in the main field. Passive shimming involves the usage of ferromagnetic pellets or metal sheets which are attached within the bore of the MR scanner.

6.17.7 Shielding Magnetic shielding isolates or blocks the magnetic field of the MRI magnet so as to prevent the unwanted interference from the MR magnet or from the nearby electronic devices (like those of pacemakers). The entire environment around the MR magnet needs to be shielded from magnetic fields. This is done by including steel or copper in the walls of the magnet room. These components can cancel or block the magnetic field and redirect them so that the environment is shielded. But such approaches are not cost effective and also increase the overall weight of the walls. Alternately magnets with integrated (active shielding) are used. The active shielded magnets have a set of double windings in which the inner core creates the field and the outer core provides a return path for the magnetic field lines thereby shielding the surrounding environment.

6.17.8 The Gradient System Magnetic field gradients are useful in the process of slice selection and spatial encoding. Three gradient coils with individual amplifiers are present in the MR machines to vary the magnetic field strength in the x axis, y axis and z axis whether separately or in a synchrony so as to define the required

204  Medical Imaging size of the region of interest. When the gradients are switched on, a typical banging sound is heard during the MR scan known as the noisy clanging, and also small amounts of magnetic fields are generated. Any instability in the gradient coils lead to image distortions. The performance of the gradients are quantified by the maximum gradient strength, the rise time (time to maximum gradient amplitude) and the slew rate (the maximum gradient amplitude per rise time).

6.17.9 The Radiofrequency System The radiofrequency (RF) system includes a powerful RF generator and a sensitive receiver. Spatial encoding depends upon the frequency and phase of the signal and hence, the RF generator and receiver need to be stable. Any phase rotation seen due to the receiver results in a blurred image. Effective RF shielding of the MR room prevents the interferences from external sources and therefore result in an adequate detection of weak MR signals as well. RF shielding is achieved by housing the entire magnet in a closed conductive structure, called the Faraday cage. The RF system also includes transmitting and receiver coils such as that of the body coil which is integrated into the scanner. These coils contain cages of copper windings put around the subject. The RF transmitter also delivers the pulses corresponding to the resonant frequency of the hydrogen atoms. Similarly, many other RF coils can be used to vary the SNR. Selection of suitable coils can help to optimize the image quality.

6.17.10 The Computer System The computers of the MR machines are useful to coordinate and control various intermediate processes involved with the MR scanning and also help with regard to image processing and other software-based aspects in MR scans. They can display the images and also store or transmit the images to other locations in the network.

6.18 Pulse Sequences Various types of sequences are used in MR imaging such as those of Spin Echo sequence, Inversion Recovery sequence and the Gradient Echo sequence. These sequences are explained in detail below.

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6.18.1 Spin Echo Sequence The Spin Echo (SE) sequences utilize a slice selective 90o RF pulse to excite the spins after following which, the transverse magnetization decays with T2*. A few spins precess faster than the others due to static magnetic field inhomogeneities, due to which dephasing is seen to occur. Hence, after the elapsing of half of the echo time (TE), a 180o RF pulse is given to refocus the spins, after which the spins that were behind will catch up because they are still exposed to the same field inhomogeneities that had resulted in the phase difference initially. So, all the spins get in phase once again, after the elapsing of the TE interval. At this moment, echoes are formed. This is shown in Figure 6.24. The 180o refocusing pulse reduces the effects of static magnetic field inhomogeneities (T2*), but cannot address the issues of variable field

90°

180°

RF pulse

Z-gradient (slice) Y-gradient (phase) X-gradient (frequency) Signal Echo Echo time (ET) 1

1) Steady state: no magnetization in xy-plane

2

3

4

2) After 90° RF pulse: 3) Decay of signal all magnetization due to spin precessing in dephasing xy-plane (T2 and T2*)

Figure 6.24  SE sequence.

5

4) 180° refocusing pulse after ½ TE interval: spin reversal

5) After full TE interval: spin rephasing and full recovery of magnetization (echo)

206  Medical Imaging inhomogeneities seen with spin-spin interaction (T2). Hence, the magnetization decay (being a function of T2) that is seen after the excitation is slower. Due to this decay, the transverse magnetization is smaller at the time when the echo is collected. But the image quality is very good due to the reduction of the effects of static magnetic field inhomogeneities. But this also results in a longer scan time and thereby is prone to motion artifacts. This approach is used to acquire T1 weighted images and PD weighted images.

6.18.1.1 Black Blood Effect The black blood effect, also called as the outflow effect, is seen as a natural high contrast between the flowing blood and the tissues. This is seen in SE sequence due to long echo time, during which the flowing blood does not provide any signals and hence appears black because most of the blood would have left from the slice of the image in the region of interest during the long TE, because of which the spins are not affected by the 180o refocusing pulse. The black blood effect is also seen in the case of turbulent blood flow in which there is a signal loss due to phase dispersion. One could hence conclude that the normal flowing blood is black. So, if the blood flow is very slow, then the excited blood remains in the slice and produces a signal. In cases of thrombosis, a bright signal is seen due to a fresh thrombus and an older thrombus will appear darker in the image.

6.18.2 Inversion Recovery Sequence Inversion Recovery (IR) sequence is used in case of T1 weighted and fat suppressed imaging. However, IR sequences can also be used for T2 weighted imaging. IR sequence is an SE sequence with an extra 180o inversion pulse that is given before the normal 90o excitation pulse and the 180o rephasing pulse. This inversion pulse is used to flip the conventional longitudinal magnetization (Figure 6.25a) to a negative z axis after which the longitudinal magnetization points downwards (Figure 6.25b). With the onset of relaxation, the inverted longitudinal magnetization moves towards the transverse plane and starts to return to its original position (Figure 6.25 c,d). Midway during this relaxation process, a 90o pulse of the SE sequence is applied. The time interval between this 90o RF pulse and the 180o RF pulse is called the inversion time (TI). This process is shown in Figure 6.25. Varying the TI can manipulate the image contrast. A short TI, i.e., the delivery of the 180o inversion pulse and immediately delivering the 90o excitation pulse results in the flipping of all the negative longitudinal

Magnetic Resonance Imaging  207 (a)

Mz

(b)

Mz

(c)

Mz

(d)

Mz

Figure 6.25  Inversion recovery sequence.

magnetization onto the transverse plane and hence a stronger signal. A longer TI results in a lesser flipping of longitudinal magnetization onto the transverse plane and hence a weaker signal. But if the TI is long enough to allow complete relaxation of the negative longitudinal magnetization, then the signal becomes stronger again. IR approaches are used for the generation of short TI inversion recovery (STIR) sequences and fluid attenuated recovery (FLAIR) sequences, in diagnostic imaging.

6.18.3 Short TI Inversion Recovery (STIR) Sequences STIR sequences can eliminate the signal from fat, at all the given magnetic field strength and hence are used for fat suppression. The STIR sequence inverts the longitudinal magnetization of both water and fat with the delivery of the 180o pulse. The fat signal is suppressed by adjusting the TI (for a few hundreds of milliseconds) such that the 90o RF pulse is delivered exactly when the fat passes through the zero. For instance, the TI for fat suppression is around 150ms for a field strength of 1.5T.

6.18.4 Fluid Attenuated Recovery (FLAIR) Sequences FLAIR sequence is an inversion recovery approach with long TI values at which the signals from CSF are entirely suppressed and the signals from brain tissues, tumors and fat are detected. FLAIR is hence useful in the assessment of lesions with poor contrast in the surrounding brain tissues.

6.18.5 Gradient Echo Sequence Gradient Echo (GRE) sequence, also called as the Fast field Echo (FFE) sequence use gradient coils to produce the echo and not the RF pulses. Initially, a frequency encoding gradient with a negative polarity is applied to reduce the phase coherence of the precessing spins (dephasing). Then,

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Echo time (TE)

α

Z-gradient (slice) Y-gradient (phase) X-gradient (frequency) Signal 1

2

3

4

5

Echo

1) Steady state: 2) After excitation 3) Spin dephasing 4) Spin rephasing no magnetization RF pulse (α): through frequency- through frequency in xy-plane all magnetization encoding gradient gradient reversal precessing in xy-plane

5) Rephasing (echo) after TE interval: full recovery of transverse magnetization

Figure 6.26  Gradient echo sequence.

the gradient is reversed (rephasing) to form a gradient Echo. This is shown in Figure 6.26. Due to the non-usage of any RF pulse, GRE can obtain very short TRs, thereby permitting a faster imaging with a very less scan time. This also reduces the motion artifacts. But the shortfall of GRE is that due to a short TR, the time for T1 relaxation is very short. This may cause saturation and decrease the SNR when larger flip angles are used. Also, due to the non-usage of the 180o RF pulse, the static field inhomogeneities are not compensated for, due to which the MR signals decay with T2*. The image contrast seen due to this decay of T2* is called as the T2* contrast, and this T2* contrast in GRE images is affected by TE. In other words, an optimal T1 weighted image is obtained with a very short TE in this case. On the other hand, a longer TE attenuates the T2* contrast. Simultaneously, the T1 effects are reduced by using a long TR. The T2* weighted images are used to detect calcifications in connective tissues. However, some GRE sequences are so fast that a part of the signal remains from cycle to cycle. This signal needs to be flushed out when T1 weighted images are acquired. The deliberate flushing of such residual MR signal is called spoiling and can be done by switching on the slice selecting gradient which will diphase the spins before the delivery of the next RF pulse. Common spoiled GRE

Magnetic Resonance Imaging  209 sequences are Spoiled Gradient Echo (SPGR) and Fast Low Angle Shot (SLASH). PD weighted images can be obtained with a long TR, low flip angle and a short TE. T2* weighted images are obtained with a long TR and a long TE. T1 weighted images are obtained with a short TR and short TE. Spoiled GRE sequences can be obtained in 2D or 3D mode.

6.19 Parallel Imaging Parallel imaging is often preferred to reduce the scan time from the perspective of the hardware as well as the perspective of the ease of the subject. In this regard, parallel imaging aids in a simultaneous acquisition of several reduced datasets with the aid of the surface coils placed side by side. This approach of the usage of multiple receiver coils reduces the acquisition time, but at the same time, is not as similar to conventional fast MR sequences. Instead, the scan time is reduced without speeding up the gradient switching and also without the risk of the heating of the tissues. In parallel imaging, the number of phase encoding steps is reduced by incomplete scanning of the k-space. This results in the acquisition of lesser phase encoding spin echoes, due to which the k-space is not filled densely. This in turn reduces the scan time due to the fact that the image acquisition time depends linearly upon the number of phase encoded echoes acquired. But this results in a smaller FOV in phase encoding direction and results in a wrap-around artifact (i.e., the parts of the imaged volume present beyond the FOV are mismapped in space, to the opposite side of the image). Parallel imaging is equipped to handle the wrap-around artifact. Each element of the array of the coil provides a separate image with a small FOV where a part of the image formation of obscured by the wrap-around artifact. But the superimposed portions are characterized by different weights which vary with spatial sensitivity of the respective coil element. An understanding of these individual sensitivity can aid in separating the superimposed information with mathematical processing during image reconstruction so that the wrap-around artifact is mitigated. These mathematical approaches can also be used to obtain a homogeneous signal intensity despite having different weights. This is shown in Figure 6.27. The most essential hardware requirement for parallel imaging is a suitable array of receiver coils. As per the requirements, the array of coils with up to eight elements can be used. Appropriate geometric arrangement of the coils results in a better SNR. A rigid arrangement (a cage-like formation) during the head scans can help to obtain a constant spatial sensitivity. On the other hand, flexible arrangements can be used during the parallel

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Parallel data aquisition

Individual images

Reconstructed images

• Reduction of phase-encoding steps (factor of 1.0-4.0) • Receiver coil array (at least 2 coil elements)

• Reduced field of view in phase-encoding direction • Different signal weighting resulting from differences in coil sensitivity

• Complete FOV without wraparound artifacts • Homegeneous weighting

Figure 6.27  Parallel imaging and mitigation of wrap-around artifact.

imaging of chest and abdomen. In terms of the receiver, each of the coil elements should be connected to a separate receiver of the MR scanner during parallel imaging. To obtain a reliable image reconstruction, the coding effects of the individual receiver sensitivity needs to be precisely determined. This can be achieved by an additional calibration step before the beginning of the scan. Parallel imaging can reduce the scan time without varying the contrast characteristics, thereby reducing the phase encoding steps. This helps in the imaging applications which require the subject to hold his/her breath. Parallel imaging can also be used to improve the spatial resolution or to obtain more slices with short scan times. Parallel imaging is less noisy as the gradient reversal rate is reduced by shortening the readout train with the same overall scan time.

6.20 MR Artifacts Artifacts in MRI are visual in nature. Many artifacts are seen in MR images which can affect the diagnosis and create confusion with regard to the pathology. These artifacts can be signal processing related, subject related or hardware-related effects. A few important artifacts seen in MR imaging are mentioned below.

Magnetic Resonance Imaging  211

6.21 Motion Artifacts Conventional MR images need more scan time. For instance, one would need a few minutes to obtain a T1 weighted image. In this regard, various movement-related aspects such as breathing, peristalsis and cardiac motion cause artifacts in the images. Such motions degrade the MR image in the form of blurring or discrete ghosts. Chest MRI portrays the ghosting due to cardiac and respiratory motion. There exist various approaches to mitigate such artifacts. Special mathematical approaches such as those of respiratory compensation algorithm are used to reduce the effects of respiratory motion. Also, respiratory gating can be used in which the data is obtained during maximum expiration only. Fast GRE sequences can be used for breath-held volume imaging. Cardiac gated imaging can be used to mitigate cardiac motion triggering the RF excitation pulse to the R wave of the corresponding ECG. Spasmolytic agents can be administered to reduce the motion artifacts seen due to peristalsis. Parallel imaging also reduces motion artifacts.

6.22 Flow Artifacts Flow-related artifacts are seen due to the flowing blood and flowing CSF. These occur in phase encoding gradients due to the fact that the spins moving along a magnetic field gradient experience a phase shift. Due to this shift, an incorrect phase value is assigned to the regions moving during the phase sampling interval. This results in the depiction of the anatomy at a different place, rather than the original location. Flow artifacts are generally seen as ghosts. These effects can be mitigated by the usage of special gradient pulse applied before the signal readout which can in turn compensate for the motion induced dephasing. This is called as the gradient moment nulling (GMN). Alternately, presaturation, i.e., saturation of the blood just before the data acquisition can be done as well. If at all the artifact is seen only in the phase encoding direction, then the frequency encoding and phase encoding axes can be swapped to remove such effects.

6.23 Phase Wrapping Phase encoding errors often result in phase wrapping artifact whenever the dimensions of the object exceed the defined FOV. Such parts are wrapped

212  Medical Imaging around and are spatially mismapped to the opposite side of the image. When a specific FOV is defined, the MR machine assumes that the phase shifts occur from +180o to -180o within the FOV. This creates an issue with the region of interest extending beyond the FOV in phase encoding direction during which the parts outside the FOV are assigned a phase shift of above +180o or below -180o. Objects with these phases are assigned the same spatial encoding and hence appear one on the top of the other, in the MR image. The structures beyond the right margin will be wrapped wound to the left margin of the image and vice versa. This artifact can be reduced by defining a larger FOV so that the entire region of interest is encompassed. This will mitigate the wrap around, but will increase the spatial resolution. Alternately, special algorithms such as fold-over-suppression algorithms can be used to prevent phase wrapping by oversampling in k-space. Surface coils can be arranged such that the plausibly wrap around structures lie outside the sensitive range of the receiver coil. Presaturation can also suppress the signals from regions outside the FOV.

6.24 Chemical Shift Chemical shift is seen due to the variation of the resonant frequency of the protons with their molecular environment. This property can be used to differentiate the lesions with and without fat components. This can also be used to selectively suppress the signals from the fat. However, this phenomenon of chemical shift results in artifacts frequently encountered in MR imaging due to spatial misregistration between fat and water and also due to the cancellation of the signal at the interface between fat and water. The chemical shift artifact due to the spatial misregistration between fat and water is seen when the protons with different precessional frequencies are depicted at different places along the frequency encoding axis because of the spatial mismapping of the signals from water and fat. This is seen from regions where the fat and water are present and adjacent to each other. Such a chemical shift misregistration is seen as a dark band or no signal at the higher spatial frequency and a bright band or high signal at the lower frequency. Such artifacts can be reduced by increasing the receiver bandwidth. But when the receiver bandwidth increases, the SNR decreases. Alternately, appropriate fat suppression techniques can be used to mitigate this artifact. The chemical shift artifact due to the cancellation of the signal at the interface between fat and water are seen in GRE imaging. They appear as black rim or signal void at the boundary between fat and water. This is seen due to the cancellation effects when FRE images are acquired when fat and

Magnetic Resonance Imaging  213 water are out of phase. This can be avoided by using SE sequences and also can be reduced on GRE images by acquiring the MR signal when the water and fat are in phase.

6.25 Magnetic Susceptibility Magnetic susceptibility is an inherent property of all biological tissues and refers to the ability of a given substance to get magnetized with an external magnetic field. This is seen in MR imaging when subjects with metal implants are imaged. These foreign materials result in image distortions at their boundaries. This is called as susceptibility artifact. Less prominent susceptibility artifact is seen at the tissue interfaces or at the interfaces between the bone and air. Local deposition of calcium hydroxyapatite also causes these artifacts. Generally, such susceptibility artifacts can occur with all pulse sequences, but are minimal in SE images as the 180o refocusing pulse rectifies the T2* effects and the SE sequences are not very sensitive to static field inhomogeneities. But higher pronounced susceptibility effects seen in GRE images are exploited for diagnostic purposes such as those in case of identification of hemorrhages or calcifications. Clinically, orthopedic implants result in these artifacts as well. Susceptibility artifacts are addressed by using SE sequences instead of GRE sequences, by swapping the frequency encoding and phase encoding axes, by increasing the receiver bandwidth and by aligning the longitudinal axis of the metal implant with the axis of the main magnetic field.

6.26 Truncation Artifact Truncation artifacts, also called as the ringing artifact, gibbs artifact or spectral leakage artifact, are seen during the usage of fourier transform approach for image reconstruction. They are seen as straight or semicircular parallel lines adjacent to high-contrast interfaces like those of the borders between the muscle and fat. These artifacts can be reduced by increasing the matrix in phase encoding direction.

6.27 Magic Angle The magic angle artifact is seen while imaging the structures with parallel fibers such as those of tendons and ligaments. These regions have low

214  Medical Imaging signal intensity due to their shorter T2. This can be addressed by having the main magnetic field at an angle of 55o to the fibers.

6.28 Eddy Currents Eddy currents are generated when the gradients are turned on and turned off very quickly. These currents may be induced in the subject, at the wires around the subject or in the magnet itself. These appear as a signal drop in the margin of the image. Eddy current artifact can be reduced by optimizing the sequence of the gradient pulses.

6.29 Partial Volume Artifact These artifacts are seen when the spatial resolution is limited. The signal intensities from different tissues located in the same voxel are averaged, which may result in an intermediate signal at the interface between the tissues with high and low intensities. This effect can be reduced by increasing the number of slices in z direction.

6.30 Inhomogeneous Fat Suppression A homogeneous magnetic field results in a uniform fat suppression (saturation) which is achieved by the application of an RF pulse which has the resonance frequency of the fat protons. But in reality, the fat protons precess at different frequencies due to local field inhomogeneities. Hence fat suppression is inhomogeneous in nature because the RF pulse applied for fat suppression cannot match the precessional frequency of all the fat protons. This artifact can be reduced by the usage of STIR sequences.

6.31 Zipper Artifacts This artifact looks like a line of alternately bright and dark pixels across the image in phase encoding or frequency encoding direction. These are seen due to radiofrequency noises which can originate from an external source that reaches the receiver coil. For example, if the door of the scanner room is not fully closed. RF emission from anesthesia monitoring equipment can also cause zipper artifacts, when used inside the scanner rooms.

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6.32 Crisscross Artifact Crisscross artifact is seen due to errors in data processing or reconstruction. This is seen as an oblique stripe across the image. These can be addressed by reconstructing the image again.

6.33 Bioeffects and Safety Static magnetic field of MR scanner have high field strength (about 1.5 T to 4T) which can pose risks to both the subjects as well as the technician operating the machine. Any ferromagnetic objects brought closer to such a high field can pose a huge threat. Although most of the biomedical implants today are not ferromagnetic in nature and are safe for MR scans, many metallic implants can result in image artifacts. However, adequate caution needs to be taken to ensure an MR compatibility in case of subjects with cerebral aneurysms. Cardiac pacemakers are still not safe for MR imaging as they house sensitive electronic components whose functions may get impaired when they get exposed to such high magnetic fields. Similar issues are seen in subjects with neurostimulators and cochlear implants as well. On a generic note, the subject is advised adequately in case of any implant. Problems arise with subjects with large tattoos which may cause burns at times. Such tattoos need to be removed before the scan. Another issue is the exposure to varying magnetic fields generated by the gradient coils which may interfere with cardiac conduction and may result in arrhythmia. Claustrophobia is another issue in MR imaging. Many subjects experience anxiety due to the size and nature of the MR equipment. Such subjects can be prepared or sedated if required. Open bore imaging systems are another alternative for such claustrophobic subjects.

Glossary-Appendix 1. Resonance - Resonance describes the phenomenon of increased amplitude that occurs when the frequency of a periodically applied force is equal or close to a natural frequency of the system on which it acts. 2. Nuclear Magnetic Resonance - Nuclear magnetic resonance is a physical phenomenon in which nuclei in a strong constant magnetic field are perturbed by a weak oscillating

216  Medical Imaging

3.

4. 5.

6.

7.

8.

9.

magnetic field and respond by producing an electromagnetic signal with a frequency characteristic of the magnetic field at the nucleus. Radiofrequency - Radio frequency is the oscillation rate of an alternating electric current or voltage or of a magnetic, electric or electromagnetic field or mechanical system in the frequency range from around 20 kHz to around 300 GHz. Angular momentum - The quantity of rotation of a body, which is the product of its moment of inertia and its angular velocity. Magnetic moment - The magnetic moment is the magnetic strength and orientation of a magnet or other object that produces a magnetic field. Examples of objects that have magnetic moments include: loops of electric current, permanent magnets, elementary particles, various molecules, and many astronomical objects. Electromagnetic Wave - In physics, electromagnetic radiation refers to the waves of the electromagnetic field, propagating through space, carrying electromagnetic radiant energy. It includes radio waves, microwaves, infrared, light, ultraviolet, X-rays, and gamma rays. All of these waves form part of the electromagnetic spectrum. Contrast - Contrast is the difference in luminance or colour that makes an object distinguishable. In visual perception of the real world, contrast is determined by the difference in the colour and brightness of the object and other objects within the same field of view. Noise - Contrast is the difference in luminance or colour that makes an object distinguishable. In visual perception of the real world, contrast is determined by the difference in the colour and brightness of the object and other objects within the same field of view. Gradient - The  gradient  of H at a point is a plane vector pointing in the direction of the steepest slope or grade at that point. The steepness of the slope at that point is given by the magnitude of the gradient vector.

Magnetic Resonance Imaging  217 10. Magnetic Pulse - An electromagnetic pulse, also sometimes called a transient electromagnetic disturbance, is a short burst of electromagnetic energy. Such a pulse’s origin may be a natural occurrence or human-made and can occur as a radiated, electric, or magnetic field or a conducted electric current, depending on the source.

About the Authors

Dr. Sanjay H. S. is a faculty at the Department of Medical Electronics, M  S Ramaiah Institute of Technology. He pursued his bachelor’s degree in Medical Electronics from Visvesvaraya Technological University (2007) and his postgraduate degree in Biomedical Engineering from Manipal University (2009). He obtained his doctoral degree in Electronics Engineering from Jain University with a specialization in Psychophysics (2018). He has been pursuing research in the field of auditory psychophysical applications with regard to industrial exposure as well as for sports rehabilitation and training programs. He is also exploring the positive effects of certain auditory cues, such as those of Hindustani and Carnatic classical ragas and Indian Vedas and slokas in neurological and cardiovascular applications. He has over 10 years of academic experience and has been teaching undergraduate students since 2009. He has contributed in various capacities to over five books under Pearson publishing house as well as for sudha publications. He has also authored over 15 research articles which have been published in journals of repute. He has been awarded for his contributions at different conferences as well. He is a reviewer for more than five international journals. He has delivered invited talks at different forums. He is an active member of various technical societies as well as social service organizations. His research interests include psychoacoustics, Raaga therapy, Behavioral analysis, Machine learning and Biomedical signal & image processing. Dr. Niranjanamurthy M., Assistant Professor(S), Department of Computer Applications, M S Ramaiah Institute of Technology, Bangalore, Karnataka, India. He did his PhD in Computer Science at JJTU, Rajasthan (2016), an MPhil in Computer Science at VMU, Salem (2009), Master of Computer Applications (MCA) at Visvesvaraya Technological University, Belgaum, Karnataka (2007). He earned a bachelor of Computer Applications degree (BCA) from Kuvempu University, Karnataka (2004) with University 5th Rank. He has 12+ years of teaching experience and two years of industry 219

220  About the Authors experience as a Software Engineer. He has published eight books. He has also published 70+ papers in various national/international conferences/ international journals, and filed 22 patents, four of which were granted. He is currently guiding four PhD research scholars in the area of Data Science, ML, and Networking. He is working as a reviewer in 22 international journals. He twice received the Best Research journal reviewer award. He also received the Young Researcher award- Computer Science  – 2018, 2019, 2020. He worked as national/ international PhD examiner. He has conducted various national-level workshops and delivered lectures, and conducted national and international conferences. He is associated with various professional bodies: IEEE Member, Life Membership of International Association of Engineers (IAENG), Membership of Computer Science Teachers Association (CSTA). His areas of interest are Data Science, ML, E-Commerce and M-Commerce related to Industry Internal tool enhancement, Software Testing, Software Engineering, Web Services, Web-Technologies, Cloud Computing, Big data analytics, and Networking.

Index I labelled albumin, 175 I labelled hippuric acid, 175 99m Tc radionuclide generator, 159–160 2D image reconstruction, 94–97 back projection, 94–95 central slice theorem, 95–97 3D rendering, 23 3D volumetric reconstruction techniques, 3 131 131

Absorption of ultrasound waves, 145 Acoustic aspects, at high intensity levels, 147 Acoustic impedance, 133 Acoustic radiation force impulse imaging, usage of, 19 Acoustic waves, attenuation, 125–126 basics of, 121–122 intensity of, 123–124 interference, 124, 125f linear wave equation, 122–123 nonlinearity, 126–127 propagation, Doppler effect in, 130–133 defined, 130 proof, 131–133 statement, 130–131 propagation of waves, in homogeneous media, 122 in non-homogeneous media, 127 reflection and refraction, 127–129 scattering, 129–130 Active shimming, 203

Activity of radionuclide (A), 154, 177 Aliasing, 92 Alpha particles, matter and, 155, 177 Aluminium, as filters, 47 A-mode ultrasound scanning system, 136–138, 139, 140 Amplitude mode (A-mode) scanners, 136–138, 139, 140 Amplitude of echo signal, 138 Anesthesia monitoring equipment, 214 Anger, Hal, 151, 167 Anger camera, 167–170 Angioblast, 4 Angiography, 67 DSA, 70–71 Angular momentum, 180, 216 Anode angle, defined, 43, 82 Antimony, 53 Aperture diaphragms, 48–49, 82 Artifacts, image, beam hardening, 108–109 motion artifact, 109 nonlinear partial volume effect, 109 scattering, 109 stair-step artifact, 109 undersampling, 108 Artifacts in MRI, 210–215 chemical shift, 212–213 crisscross artifact, 215 Eddy current artifact, 214 flow-related, 211 inhomogeneous fat suppression, 214 magic angle artifact, 213–214 magnetic susceptibility, 213

221

222  Index motion, 211 partial volume artifact, 214 phase wrapping, 211–212 truncation artifact, 213 zipper artifacts, 214 Artificial radioisotopes, in radionuclide imaging, 159 Attenuation(s), 82, 118 coefficients, CT number of, 87 factors affecting, 38–39 of different materials, 71–72 computed tomography, 85 correction, 140 PET imaging approach, 174 due to coherent scattering, 39 due to Compton scattering and photoelectric effect, 39–41 of gamma rays, 157 phenomenon, 125–126 X-ray, 85 Auger effect, 35 Auger electrons, 35 Axial resolution, ultrasound image, 146 Axial scan approach, 106 Axial transverse tomography, 86–87 Azimuthal blur, 107 Back projection, 94–95 convolution, 98–101 Back scatter, 129, 130 Barium, 4 Barium sulphate, 66 Bar phantom, 74–75, 176 Base plus fog density, 55 Beam hardening, 41, 108–109 Beam restrictors, 47–48 aperture diaphragms, 48–49 collimators, 49–50 cones and cylinders, 49 Beam width, X-ray, 107 Becquerel, Henri, 151 Becquerel (Bq), defined, 154

Beta particles, matter and, 156 Biological effects, MRI, 215 of radionuclides, 176 X-ray CT, 118 Biological effects of ultrasound, 147–148 acoustic aspects at high intensity levels, 147 bioeffects (thermal and non-thermal effects), 147–148 cavitation, stable, 147 transient, 147 wave distortion, 147 Biological effects of X ray radiations, determinants, 79, 81 cellular sensitivity, 81 exposure area, 81 exposure time, 81 long-term effects, 81 short-term effects, 81 threshold, 79 variation in species and individual sensitivity, 81 Biological half-life, of radionuclide, 158, 177 Black blood effect, 206 Block, F., 179 Blood oxygen dependent (BOLD) signals, 16, 18 Blood volume assessment, 175 Blue powder, 68 Blurring effect, on image of object, 63–64 B-mode scanners, 138–139 Body phantom, 118 Bone scintigraphy, 10f Brain, neurological activity in, 16 Breast(s), assessment of, 68 compression of, 69 tumors, MRI for, 15 Brightness mode (B-mode), 138–139

Index  223 Cadmium telluride (CdTe), 89 Cadmium-zinc-telluride (CZT), 89 Caesium, 53 Caesium iodide, 54 Calcium hydroxyapatite, deposition of, 213 Calcium tungstate, 51–52 Cardiac CT, 106 Cardiac gated imaging, 211 Cardiac pacemakers, 215 Carrier-free radionuclide, 154–155, 177 Cartilage imaging, 193 Cassen, Benedict, 151 Catheters, 70–71 Cavitation, biological effects of ultrasound, 147 Cellular sensitivity, 81 Central slice theorem, 95–97 Cerebral aneurysms, 215 Characteristic curve, 56–57 Characteristic radiations, 42 Charged particle accelerators, 159 Chemical shift artifact, 212–213 Chest, CT image of, 87, 88f MRI, 211 Claustrophobia, 215 Clinical sites, 24 Clinical trials, medical imaging and, 23 Coherent scattering, 32, 38 attenuation due to, 39 Collimation, CT machines, 112 Collimator(s), 49–50, 177 detection of nuclear emission, 164, 165–166 multiple-hole focused, 165, 177 pin-hole, 112, 119 radionuclide imaging, 164, 165–167, 175–176 scintillation camera (gamma camera), 167 single-hole focused, 164, 165, 167, 177 slant hole, 170–171

Color Doppler flow imaging, 143, 144 Compton effect, 32, 33, 38 Compton scattering, attenuation due to, 39–41 Computed axial tomography (CAT), 6 Computed tomography (CT), 6, 7f, 25. see also X-ray computed tomography conventional, 23 CT-based diagnostics, 104–107 cardiac CT, 106 dual energy CT approach, 106–107 multislice CT, 105 single slice CT, 104–105 CT dose index (CTDI), 118 image quality, 107–109 artifacts, 108–109 contrast, 108 noise in CT, 108 resolution, 107–108 imaging, 89–104 back projection, 94–95 central slice theorem, 95–97 2D image reconstruction, 94–97 direct Fourier transform, 97–98 fan beam projections, 101–104 FBP/CBP, 98–101 radon transform, 89–92 sampling, 92–94 machine, hardware aspects, 110–112 collimation, 112 cooling systems, 111 detectors, 112 filtration, 111 gantry, 110, 111 generators, 111 slip rings, 111 X-ray tubes, 111 machines, generations of, 112–117 fifth, electron beam scannerstationary/stationary, 116–117 first, rotate/translate approachpencil beam, 112–113

224  Index fourth, rotate/stationary, 115–116 second, rotate/translate-narrow fan beam, 113–114 sixth, helical, 117 third, rotate/rotate-wide fan beam, 114–115 machines, X-ray detectors in, 88–89 energy integrating detectors, 88 photon counting detectors, 88–89 number, 87, 88f PAT, 22 PET and, 12–13 protocols for imaging technique, 23 SPECT and, 9, 11 Computers, of MR machines, 204 Cone beam approach, for reconstruction with multiple cameras, 172 Cones and cylinders, 49 Constructive interference, 124 Continuous wave Doppler system, 142, 146 Contrast, film, 59, 60 image, 216 CT, 108 efficiency function, 176 MR image, 188 radionuclide imaging, 176 ultrasound imaging, 146 X-ray image, 78–79 Contrast agents, allergic to, 67 attenuation coefficients of, 72 concentration of, 71 non-ionic, 67 usage of, 4 Contrast medium, 66, 67, 68, 188 Conventional tomography, 73–75, 83 defined, 72 image attributes, 74 spatial resolution, 74–75 working principle of, 73

Conventional X-ray radiography, 62–63 Convolution back projection (CBP), 98–101 Convolution filter, 108 Convolution kernel, 100, 119 Cooling mechanisms, 111 Copper, as filters, 47 Crisscross artifact, 215 Cryogens, defined, 202 Cupping, 109 Curie, Marie, 151 Curie, Pierre, 151 Curie (Ci), defined, 154 Curve, characteristic, 56–57 Cyclotron(s), 13, 14f in PET imaging, 159 units, 174 Data acquisition, pulsed ultrasound signals and, 136 Data acquisition and reconstruction, CT imaging, 89–104 2D image reconstruction, 94–97 back projection, 94–95 central slice theorem, 95–97 direct Fourier transform, 97–98 fan beam projections, 101–104 FBP/CBP, 98–101 radon transform, 89–92 sampling, 92–94 Data acquisition system (DAS), 88 Decay constant, 154 Destructive interference, 124 Detection, of X-rays, 54–60 characteristic curve, 56–57 double-emulsion film, 59f, 60 film, 55 film gamma, 57 film latitude, 58f, 59 optical density, 55, 56f speed, 57, 58, 59 nuclear emission, 160–166

Index  225 collimator, 164, 165–166 ion collection detectors, 161–162 scintillation detector, 162–164 solid state detectors, 164, 165f radionuclide, 166–174 LST approach, 170–171 PET, 172, 173–174 rectilinear scanning machines, 166–167 scintillation camera (gamma camera), 167–170 SPECT, 171–172 Detector(s), channels, 107 CT machines, 112 ion collection, 161–162 multidetector approach, 171 multiple, 105 probes, diagnostic approaches using, 174–175 blood volume assessment, 175 renal function test, 175 thyroid function assessment, 175 radiation, 60–61 ionization chamber, 61 in radionuclide imaging, 157–158 photographic or digital, 3 scintillation, 60–61 rotation of, 107 sampling, 93f scintillation, 60–61, 82, 88–89, 118, 162–164 solid state, 164, 165f X-ray, 113 X-ray, in CT machines, 88–89 energy integrating detectors, 88 photon counting detectors, 88–89 Diagnostic approaches using radiation detector probes, 174–175 blood volume assessment, 175 renal function test, 175 thyroid function assessment, 175 Diagnostic images, 23

Diagnostic imaging, X-ray-based approaches, 62–66 conventional X-ray radiography, 62–63 field size, 64–65 film magnification, 65–66 penumbra, 63–64 Diagnostic imaging modalities, images by, 23 types of, 2–22 elastography, 19, 20f, 21f fMRI, 16–18 FNIR, 18–19 MPI, 22 MRI, 14–16 nuclear medicine, 9–14 photoacoustic imaging, 20, 21f, 22 radiography, 2–4 tomography, 4, 6, 7f ultrasound imaging, 6, 8, 9f Diagnostic radiology, defined, 2, 26 Diagnostics, CT-based, 104–107 cardiac CT, 106 dual energy CT approach, 106–107 multislice CT, 105 single slice CT, 104–105 Diaphragms, aperture, 48–49, 82 Differential uptake, radionuclide, 158 Diffraction, defined, 124 Digital detectors, 3 Digital Imaging and Communication in Medicine (DICOM) Standard, 23 Digital subtraction angiography (DSA), 70–71 Direct Fourier transform, 97–98 Distortion, in tissues, 19 Doppler effect in propagation of acoustic wave, 130–133 defined, 130 proof, 131–133 statement, 130–131

226  Index Doppler imaging approaches, in ultrasound imaging, 141–144 color Doppler flow imaging, 143, 144 continuous wave Doppler system, 142 pulse wave Doppler system, 142, 143 Double-emulsion film, 59f, 60 DSA (digital subtraction angiography), 70–71 Dual energy CT approach, 106–107 Dual energy subtraction approach, 71–72 Dynodes, 61, 83, 163 Echogenic aspect of tissues, 144, 145, 146 Echogenic reflection, 146 Echo signal, amplitude of, 138 Echo time (TE), 189–191, 200–201, 205, 208, 209 Eddy current artifact, 214 Edge spread function (ESF), 76, 77f Elastic scattering, 41 Elastography, 19, 20f, 21f, 26 Electrical matching, 136 Electric and Musical Industries Ltd., 112 Electromagnetic radiations, 27–28 Electromagnetic wave, 183, 216 crests of, 29 sinusoidal, 28f, 29f Electron beam intensity of CRT, 138 Electron beam scanner-stationary/ stationary, 116–117 Electronic collimation in PET, 174 Electronic processing unit, of gamma camera, 169f, 170 Elevation resolution, ultrasound image, 146 Emission, property of radionuclides, 157–158 Emulsion, double-emulsion film, 59f, 60

light sensitive, 55 in mammograms, 68 Energy integrating detectors, 88 Energy window, 163 Envelope detection, 140 Ernst Angle, 192 ESF (edge spread function), 76, 77f Exposure area, X-ray scans and, 81 Exposure time, X-ray scans and, 81 F-18 (fluoro-de-oxy-glucose or FDG), 12, 13 Fajans, Kasimir, 151 Fan beam(s), approach, for reconstruction with multiple cameras, 172 narrow, 113–114 projections, 101–104 wide, 114–115 Faraday cage, defined, 204 Far field approach, 124 Fast field echo (FFE) sequence, 207–208 Fast low angle shot (SLASH), 208–209 Fat suppressed imaging, 206 Fat suppression, 207 inhomogeneous, 214 techniques, 212 FBP (filtered back projection), 98–101 FDG (fluoro-de-oxy-glucose), 12, 13 FFE (fast field echo) sequence, 207–208 Field of view (FOV), MR machine and, 200, 209, 212 Field size, X-ray beam, 64–65 Field uniformity, scintillation cameras, 170 Filament current, 46–47 Film gamma, 57 Film latitude, 58f, 59 Film(s), X-ray, 55 contrast, 59, 60 defined, 3 double-emulsion, 59f, 60

Index  227 H-D curve of, 56–57 magnification, 65–66 speed, 57, 58, 59 Filtered back projection (FBP), 98–101 Filtering, RF signals, 140 Filters, 47–51 aperture diaphragms, 48–49 beam restrictors, 47–48 collimators, 49–50 cones and cylinders, 49 radiographic grids, 50–51 Filtration, CT machines, 111 FLAIR (fluid attenuated recovery) sequences, 207 Flip angle, 192, 200–201 Flow-related artifacts, 211 Fluid attenuated recovery (FLAIR) sequences, 207 Fluorescence, defined, 51 Fluorine, 13, 171 Fluoro-de-oxy-glucose (FDG), 12, 13 Fluoroscopy, 3, 4, 5f, 6f, 26, 66, 67f FNIR (functional near infrared imaging), 18–19, 26 Focal spot, 107 blurriness and, 63–64 Fold-over-suppression algorithms, 212 Fourier transform, 2-dimensional, 95, 96, 99 central slice theorem and, 95–97 direct, 97–98 inverse, 99 of line spread function, 77 one-dimensional, 95, 97 projection of X-ray beam, 92, 93f spatial, 76 Frame grabber, 23 Free protons, 192, 193 Frequency compounding, 146 Frequency encoding, 197–198, 213 Frequency information, 198 Fulcrum, 73 Functional magnetic resonance imaging (fMRI), 16–18, 179

Functional near infrared imaging (FNIR), 18–19, 26 Fundamental resonance frequency, defined, 133 Gadoliniumoxysulfide phosphor, 52 Gallium 67Ga, 11 Gamma camera (scintillation camera), 9, 11, 151, 167–170 Gamma particles, matter and, 156–157 Gamma ray photon, 163, 164 Gantry, 110, 111 Geiger-Muller (GM) counters functions, 162 Generators, CT machines, 111 X-ray, 42–47 component of, 42 filament current, 46–47 line focus principle, 43–45 target material, 46 tube current, 46 tube ratings, 45–46 tube voltage (V), 46 Generic image intensifier, 54f Germanium-based detector, 164 Ghosting, 211 Gibbs artifact, 213 Glucose, cancerous cells and, 12 Godfrey Hounsfield, 112 Gradient echo (GRE) sequence, 207–209, 213 Gradient moment nulling (GMN), 211 Gradient(s), 216 coils, 194–196 frequency encoding, 197 magnetic field, 203–204 phase encoding, 197, 198, 211 Gray scale imaging, 136–140 amplitude mode (A-mode), 136–138 brightness mode (B-mode), 138–139 data acquisition, 136 motion mode (M-mode), 139–140

228  Index GRE (gradient echo) sequence, 207–209, 213 Grid ratio (gr), defined, 50 Grids, radiographic, 50–51 Half-life of radionuclide, 154, 177 biological, 158 physical, 157 Half value layer (HVL), 37 Harmonics, 126, 147, 148 H-D curve of film, 56–57 Head phantom, 118 Heel effect in X-ray tube, 44f Helical CT, 117 Helical scan approach, 106, 119 Hemodynamic response, defined, 16 Hippocampal atrophy, 24 Hippuric acid, 175 Homogeneous media, propagation of waves in, 122 Hounsfield units (HU), 87, 118 Huygen’s principle, 126f, 127 Hyperthyroid, 175 Hypogenic reflection, 146 Hypothyroid, 175 Image attributes, X-ray, 74 Image contrast, CT, 108 MR image, 188, 216 radionuclide imaging, 176 ultrasound imaging, 146 X-ray, 78–79 Image intensifiers, 53–54 Image noise, MR image, 199–201, 216 radionuclide imaging, 176 X-ray, 77, 78 Image quality, X-ray CT, 107–109 artifacts, 108–109 beam hardening, 108–109 motion artifact, 109 nonlinear partial volume effect, 109 scattering, 109

stair-step artifact, 109 undersampling, 108 contrast, 108 noise in CT, 108 resolution, 107–108 Image reconstruction, 2D, 94–97 back projection, 94–95 central slice theorem, 95–97 attenuation correction, 140 envelope detection, 140 filtering, 140 log compressions, 140 scan conversion, 140 Image subtraction technique, 69–72 DSA, 70–71 dual energy subtraction approach, 71–72 K-edge subtraction technique, 72 Imaging biomarkers, usage of, 23–24 Imaging centre, 24 Impedance, acoustic, 133 Individual sensitivity, variation in species and, 81 Inertia of medium, 121, 148 Inhomogeneities, magnetic field, 203 static, 205–206 Inhomogeneous fat suppression, 214 Intensifying screens, 51–53 Intensity, loudness and, 123–124 of X-ray beam, 30–31 Interaction(s), of X-rays, 31 nuclear particles and matter, 155–157 alpha particles, 155 beta particles, 156 gamma particles, 156–157 X-ray and tissues, 36–38 Interference phenomenon, 124, 125f Interpolation process, 108 Intrinsic resolution of gamma camera, 168

Index  229 Inversion recovery (IR) sequence, 206–207 Inversion time (TI), 206, 207 Iodine, 72 in thyroid, 175 Iodine 123I, 11 Ion collection detectors, 161–162 Ionization, 82 chamber, 61, 162 Ionizing radiation, defined, 30 IR (inversion recovery) sequence, 206–207 Isomeric decay, 153 Isotopes, defined, 153, 177 Jacobian determinant, 96, 119 K-edge subtraction technique, 72 Keyes, John, 151 K-space, 198–199 Lanthanumoxysulfide phosphor, 52 Larmor frequency, 182–183, 184f, 185f, 193, 194 Lateral resolution, ultrasound image, 146 Lead zirconate titanate (PZT), 133 Linear attenuation coefficient, 37, 38, 87, 89, 109, 157, 177 Linear tomography, 73–74, 86 Linear wave equation, 122–123 Line focus principle, 43–45 Line spread function (LSF), 75–76, 77 Liver cirrhosis, 137 Liver studies, MRI for, 15 Log compressions, 140 Longitudinal magnetization (Mz), 186, 187, 188, 191 Longitudinal relaxation, 185–186 Longitudinal section tomography (LST) approach, 170–171 Longitudinal waves, representation of, 121, 122f Loudness and intensity, 123–124

LSF (line spread function), 75–76, 77 Macromolecular protons, magnetization of, 193 Magic angle artifact, 213–214 Magnetic field strength, 200 Magnetic moment, 180, 181, 216 Magnetic particle imaging (MPI), 22, 26 Magnetic resonance-based scanning methods, 69 Magnetic resonance imaging (MRI), 14–16, 25, 85, 215–216 angular momentum (M), 180 artifacts in, 210–215 chemical shift, 212–213 crisscross artifact, 215 Eddy current artifact, 214 flow-related, 211 inhomogeneous fat suppression, 214 magic angle artifact, 213–214 magnetic susceptibility, 213 motion, 211 partial volume artifact, 214 phase wrapping, 211–212 truncation artifact, 213 zipper artifacts, 214 assessment of oncological and neurological therapeutic effects, 24 basics of, 179–182 bioeffects and safety, 215 conventional, 23 echo time (TE) and T2 weighting, 189–191 flip angle/tip angle, 192 fMRI, 16–18 frequency encoding, 197–198 image contrast, 188 image noise, 199–201 k-space, 198–199 Larmor frequency, 182–183, 184f, 185f

230  Index magnetic field strength, 200 magnetic moment (B), 180, 181 MR scanning machine, 201–204 components of, 201 computer system, 204 gradient system, 203–204 magnets, 202 permanent magnet, 202 quenching, 202–203 radiofrequency system, 204 resistive magnets, 202 shielding, 203 shimming, 203 superconducting magnets, 202 MR signals, 183, 186, 187, 188, 189 MTC, 192–193 overview, 179 parallel imaging, 209–210 phase encoding, 196–197 presaturation, 192 protocols for imaging technique, 23 pulse sequences, 204–209 black blood effect, 206 FLAIR, 207 GRE, 207–209 IR sequence, 206–207 SE, 205–206 STIR, 207 relaxation, 185–187 T1 (longitudinal relaxation), 185–186 T2 (transverse relaxation), 186–187 repetition time (TR) and T1 weighting, 188–189 saturation at short repetition times, 191 slice selection, 193–196 spatial encoding, 196–198 Magnetic susceptibility, 213 Magnetization transfer imaging (MTC), 192–193 Magnets, MRI machines permanent, 202

quenching, 202–203 resistive, 202 shielding, 203 shimming, 203 superconducting, 202 Mammography, 68 Matter, interaction between X-ray and, 31 Mechanical matching, 135 Medical imaging, 3D rendering, 23 advantage of, 2 defined, 1, 26 diagnostic images, 23 equipment, 1 in pharmaceutical applications, 23–24 modalities, types of, 2–22 (see also Diagnostic imaging modalities) overview, 1–2 techniques, 2 M-mode scanner, 139–140 Mobile X-ray machine, 4f Modulation transfer function (MTF), 77, 78f Molecular medicine, 9–14 Molybdenum (Mo) anode, 68 Monochromatic X-ray beams, 28, 41, 72, 118 Motion artifacts, CT scan, 109 in MRI, 211 Motion mode (M-mode), 139–140 MTC (magnetization transfer imaging), 192–193 Multidetector approach, 171 Multiple-hole focused collimator, 165, 177 Multislice CT, 105 Myocardial infarctions, 137 NaI(TI), 162–163 Narrow fan beams, 113–114 Near field approach, 124

Index  231 Near infrared spectroscopy approach, 18–19 Net magnetization vector (NMV), 183 Neuroperfusions, 22, 26 Niobium-titanium (Nb-Ti) alloy, 202 Noise, image in CT, 108 in X-ray images, 77, 78 MR image, 199–201, 216 radionuclide imaging, 176 Noisy clanging, defined, 204 Non-homogeneous media, propagation of waves in, 127 Noninvasive medical imaging technology, 18–19 Non-ionic contrast agents, 67 Nonlinearity, 126–127 Nonlinear partial volume effect, 109 Nuclear emission, generation of, 159–166 99m Tc radionuclide generator, 159–160 detection, 160–166 collimator, 164, 165–166 ion collection detectors, 161–162 scintillation detector, 162–164 solid state detectors, 164, 165f nuclear sources, 159 Nuclear magnetic resonance (NMR) imaging. see Magnetic resonance imaging (MRI) Nuclear medicine, 9–14, 26 Nuclear particles, 152–153 matter and, interactions between, 155–157 alpha particles, 155 beta particles, 156 gamma particles, 156–157 Nuclear reactors, 13 Nuclear sources, 159 Nyquist criterion, 94, 104, 118

Ophthalmic applications (eye tumors), 137 Optical density, 55, 56f Outflow effect, 206 Oxygen 18, 13 Pair production, 35, 156 Parallel imaging, 209–210, 211 Parent-daughter radioisotope, 159–160 Partial volume artifact, 214 Particle nature, X-ray, 30 Passive shimming, 203 PD (proton density) weighted images, 190–191 Pencil beam approach, 112–113 Penumbra (P), 48–49, 63–64 Peristalsis, 211 Permanent magnets, MRI machines, 202 PET. see Positron emission tomography (PET) Phantoms, types, 118 Phase coherence, 186–187 Phase encoding, 196–197, 209, 210, 211, 213 Phase information, 198 Phase wrapping artifact, 211–212 Photoacoustic computed tomography (PAT), 22 Photoacoustic imaging, 20, 21f, 22, 26 Photoacoustic microscopy (PAM), 22 Photocathode, 53–54, 61, 83, 163 Photodisintegration, 36, 156, 157 Photoelectric effect, 34–36 attenuation due to, 39–41 pair production, 35 photodisintegration, 36 Photoelectron, defined, 35 Photographic density, 55, 56f Photographic detectors, 3 Photomultiplier tube, 60 Photomultiplier tubes (PMTs), 163, 168–170 Photon counting detectors, 88–89

232  Index Photons, 30 Photons, X-ray, 66, 68 attenuation of, 79 coherent scattering with, 32 collision of, 33 detection of, 54, 55, 77 energy of, 30, 31, 32, 35, 39, 40, 41 incident, 32 in pair production, 35 ionizing chamber, 61 light photons, 51, 52, 53, 54, 55, 57, 60–61 materials and, interaction, 36, 38 particle (matter) and, interaction, 32, 34 photodisintegration, 36 photoelectric effect, 40 photoelectric effect with, 34, 35 production, 44, 45 quantity of, 30 scattered, 33, 39, 41, 50f visible light photons, 51, 52, 53 Physical half-life of radionuclide, 157 Picture archiving & communication systems (PACS), 23 Piezoelectric crystal, 133, 134–135, 142 Pin-hole collimator, 112, 119 Pixel-based back projection, 95 PMTs (photomultiplier tubes), 163, 168–170 Point scatterer, 129, 130 Point spread function (PSF), 75–77 ESF, 76, 77f LSF, 75–76, 77 STF, 76, 77, 78f Polyvinylidene fluoride (PVDF), 133 Positron decay, 153 Positron emission tomography (PET), 6, 12–14, 24, 25, 85 advantages of, 174 attenuation correction, 174 cyclotrons in, 159 development of, 151–152

principle of, 153–154 radionuclide imaging, 172, 173–174 Preamplifier for pulse amplification, 168, 169 Precession, defined, 181 in hydrogen protons, 181, 182f Predictor collimation, 112 Prepulse, defined, 192 Presaturation, 192, 211, 212 PRF (pulse repetition frequency), 142, 143 Probes, radiation detector, 174–175 blood volume assessment, 175 renal function test, 175 thyroid function assessment, 175 Projection, defined, 89 radiography, 3, 4 Proportional counters, defined, 162 Proton density (PD) images, 188 weighted images, 190–191 Proton-rich nucleus, 153 PSF (point spread function), 75–77 ESF, 76, 77f LSF, 75–76, 77 STF, 76, 77, 78f Pulse-echo systems, 137 Pulse height analyzer (PHA), 163 Pulse height window, 163 Pulse repetition frequency (PRF), 142, 143 Pulse sequences, 204–209, 217 FLAIR, 207 GRE, 207–209 IR sequence, 206–207 SE, 205–206 black blood effect, 206 STIR, 207 Pulse wave Doppler system, 142, 143, 146 Purcell, E., 179 Pure specular reflections, defined, 129

Index  233 Quanta, 30 Quantitative assessment of image noise, 77–78 Quantitative characterization of tissues, 144 Quantitative mapping, 141 Quantitative measure of spatial resolution, 76 Quantum mottle, 77 Quartz, 134 Quenching, 202–203 RAD (radiation absorbed dose), 31 Radial points, 98, 119 Radiation absorbed dose (RAD), 31 Radiation detector probes, diagnostic approaches using, 174–175 blood volume assessment, 175 renal function test, 175 thyroid function assessment, 175 Radiation detectors, 60–61 ionization chamber, 61 in radionuclide imaging, 157–158 scintillation, 60–61 Radiation(s), characteristic, 42 therapy, protocols for imaging technique, 23 white, 41–42 X-ray, biological effects of, 79, 81 cellular sensitivity, 81 exposure area, 81 exposure time, 81 long-term effects, 81 short-term effects, 81 threshold, 79 variation in species and individual sensitivity, 81 Radioactive decay, 153–154, 177 Radioactive pharmaceuticals, 171, 173 Radioactivity, insight into, 152–158 interactions between nuclear particles and matter, 155–157 alpha particles, 155

beta particles, 156 gamma particles, 156–157 nuclear particles, 152–153 properties of radionuclides, 157–158 biological half-life, 158 differential uptake, 158 emission, 157–158 physical half-life, 157 preparation approaches, 158 specific activity, 158 toxicity, 158 radioactive decay, 153–154 specific activity, 154–155 Radiofrequency (RF), 216 coils, 199–200 pulse, 183 signal, 14, 15, 140, 149 system, MRI machine, 204 Radiographic grids, 50–51 Radiographic imaging defined, 1 principles, examples of, 1 Radiography, 2–4, 26 conventional X-ray, 62–63 protocols for imaging technique, 23 Radio isotopes, defined, 153 in SPECT, 9, 11 production, 13 properties of, 9 Radiology, defined, 1 Radionuclide generator, 159–160, 177 Radionuclide imaging, 152 biological effects of, 176 brief history, 151–152 characteristics, image contrast, 176 image noise, 176 spatial resolution, 175–176 defined, 153 detection, 166–174 LST approach, 170–171 PET, 172, 173–174

234  Index rectilinear scanning machines, 166–167 scintillation camera (gamma camera), 167–170 SPECT, 171–172 diagnostic approaches using radiation detector probes, 174–175 blood volume assessment, 175 renal function test, 175 thyroid function assessment, 175 insight into radioactivity, 152–158 alpha particles, 155 beta particles, 156 biological half-life, 158 differential uptake, 158 emission, 157–158 gamma particles, 156–157 interactions between nuclear particles and matter, 155–157 nuclear particles, 152–153 physical half-life, 157 preparation approaches, 158 properties, 157–158 radioactive decay, 153–154 specific activity, 154–155, 158 toxicity, 158 nuclear emission, generation of, 159–166 99m Tc radionuclide generator, 159–160 collimator, 164, 165–166 detection of, 160–166 ion collection detectors, 161–162 nuclear sources, 159 scintillation detector, 162–164 solid state detectors, 164, 165f Radiopharmaceuticals, advances in, 152 Radiotracers, 12–13, 26 Radon, Johann, 85 Radon transform, 89–92, 95, 118 Ram-lak filter, 101 Ramp filter, 99–101

Rare earth screens, 52 Ray, defined, 89 Ray integral, defined, 89 Realistic imaging protocol, 24 Real-time imaging functionality of ultrasound, 8 Rebinning, 102, 119 Receiver, sensitive, 204 Receiver bandwidth, 200 Receiver operating curve (ROC), 79, 80f Reconstruction kernel/convolution filter, 108 Recorder module, 166 Rectilinear scanning machines, 166–167, 170 Reflection(s), of waves, 127–129 scattered, 129 Refraction, of waves, 127–129 Region of interest (ROI), 86, 112, 113, 137, 140 3D view of, 23 attenuation of, 74 cross sectional images of, 85 during X-ray scans, 81 for distortions, 19 features of, 11, 13 image of, 14 MR signal, measurement, 199 multiple scans of, 104 pathology of, 145 predefined line of strike across, 142 radioactivity from, 174 reflected echoes from, 143 spatial information from, 136 tissues of, 144–146 two-dimensional image of, 138 ultrasound imaging, 6, 8 X-ray images of, 6, 66 Relaxation, 185–187 T1 (longitudinal relaxation), 185–186 T2 (transverse relaxation), 186–187

Index  235 Renal function test, 175 Repetition time (TR), GRE and, 208, 209 short, MR signal with, 192 saturation at, 191 SNR and, 200–201 T1 weighting and, 188–189 Resistive magnets, 202 Resolution, of CT image, 107–108 intrinsic, of gamma camera, 168 Resonance, defined, 133, 215 Resonance condition, defined, 183 Respiratory compensation algorithm, 211 RF (radiofrequency), 216 coils, 199–200 pulse, 183 signal, 14, 15, 140, 149 system, MRI machine, 204 Ringing artifact, 213 Roentgen (R), 31 Roentgen, Wilhelm, 27 ROI. see Region of interest (ROI) Rotate/rotate-wide fan beam, 114–115 Rotate-translate mechanism, 112–114 Rotation of tube/detector, 107 Rutherford, Earnest, 151 Safety-based aspects, X-ray CT, 118 Sampling, detector, 92–94 Saturation at short repetition times, 191 Saturation voltage, defined, 46 Scan conversion, 140 Scanning machine, MR, 201–204 components of, 201 computer system, 204 gradient system, 203–204 magnets, permanent, 202 resistive, 202 superconducting, 202

quenching, 202–203 radiofrequency system, 204 shielding, 203 shimming, 203 Scan parameters, 200–201 Scattering, 109, 129–130, 145–146 Schlieren system, 141 Scintigraphy (gamma scan), 9, 10f, 26 Scintillating crystal, 88, 118, 168 Scintillation camera (gamma camera), 151, 167–170 collimator, 167 PMTs, 168–170 scintillation crystal, 168 Scintillation detection mechanism, 166 Scintillation detectors, 60–61, 82, 88–89, 118, 162–164 Screens, intensifying, 51–53 Selenium coated plate, 68 Sequences, in MR imaging, 204–209 FLAIR, 207 GRE, 207–209 IR sequence, 206–207 SE, 205–206 black blood effect, 206 STIR, 207 SE (spin echo) sequences, 205–206 black blood effect, 206 Shepp-Logan phantom, 101, 119 Shielding, magnetic, 203 RF, 204 Shimming in MRI, 203 Short repetition times MR signal with, 192 saturation at, 191 Short TI inversion recovery (STIR) sequences, 207 Signal-to-noise ratio (SNR), of MR image, 199, 200–201, 208 Silicon-based detectors, 164 Silver bromide, 55 Silver halide, 55

236  Index Silver iodide, 55 Single-hole focused collimator, 164, 165, 167, 177 Single photon emission computed tomography (SPECT), 9, 11 advantages of, 174 development of, 151 radionuclide imaging, 171–172 Single slice CT, 104–105 Single slice imaging, 172 Sinogram, 91f, 92 Slant-hole collimator, LST with, 170–171 SLASH (fast low angle shot), 208–209 Slice selection, 193–196 Slice thickness, 200 Slip rings, CT machines, 111 Snell’s law, 128 SNR (signal-to-noise ratio), of MR image, 199, 200–201, 208 Soddy, Frederick, 151 Sodium iodide, 60, 67 Solid-state crystal detectors, 112 Solid state detectors, 164, 165f Sonogram, 9f, 118 Sound waves, reflection coefficients of, 8 Source collimators, 112 Space charge, defined, 43 Sparses, 98, 119 Spasmolytic agents, 211 Spatial compounding, 146 Spatial encoding, 196–198 Spatial misregistration, 212 Spatial resolution, 74–75 of CT image, 107–108 radionuclide imaging, 166–167, 170, 175–176 ultrasound image, 146 Specific activity, in radionuclide imaging, 154–155, 158, 177 Speckles, 146

SPECT (single photon emission computed tomography), 9, 11 advantages of, 174 development of, 151 radionuclide imaging, 171–172 Spectral leakage artifact, 213 Speed of X-ray film, 57, 58, 59 SPGR (spoiled gradient echo), 208–209 Spin echo (SE) sequences, 205–206 black blood effect, 206 Spin-lattice relaxation, 185–186 Spin-spin interaction, 185, 187, 205, 206 Spoiled gradient echo (SPGR), 208–209 Spoiling, defined, 208 Spontaneous discharge region, 162 Stable cavitation, biological effects of ultrasound, 147 Stable isotopes, 159 Stair-step artifact, 109, 119 Static magnetic field inhomogeneities, 205–206, 208 Step-and-shoot method, 106, 119 STF (system transfer function), 76, 77, 78f STIR (short TI inversion recovery) sequences, 207 Superconducting magnets, 202 Susceptibility artifact, 213 Synchrotron radiation sources, 72 Synods, 163 System transfer function (STF), 76, 77, 78f Target material, X-ray generator, 46 Tattoos, 215 TE (echo time), 189–191, 200–201, 205, 208, 209 Technetium isotope, in radionuclide imaging, 153 Technetium 99mTC, 11

Index  237 Thallium 201TI, 11 Thermograms, 69 Threshold value of X-ray intensity, 79 Thyroid function assessment, 175 Tip angle, 192 Tissue characterization, 144–146 absorption, 145 scattering, 145–146 velocity, 145 Tissues, interaction between X-ray and, 36–38 Titled plane reconstruction, 105 Tomography, 4, 6, 7f, 26. see also X-ray computed tomography axial transverse, 86–87 conventional, 72, 73–75, 83 CT. see computed tomography (CT) image attributes, 74 linear, 73–74, 86 LST approach, 170–171 spatial resolution, 74–75 TST, 171 Toxicity, radionuclide, 158 TR (repetition time), GRE and, 208, 209 short, MR signal with, 192 saturation at, 191 SNR and, 200–201 T1 weighting and, 188–189 Transducer, ultrasonic, 134–135 Transient cavitation, biological effects of ultrasound, 147 Trans-impedance amplifier, 88, 118 Transverse magnetization decay of, 186–187, 190 defined, 183, 185 T1 (longitudinal relaxation), 185–186 Transverse relaxation, 186–187 Transverse section tomography (TST), 171 T1 relaxation, 185–186, 208

T2 relaxation, 186–187 T2 time, 188 T1 time of tissue, 188 T1 weighted images, 206, 208, 209, 211 repetition time (TR) and, 188–189 T2 weighted images, 188, 206, 208, 209 echo time (TE) and, 189–191 Truncation artifact, 213 Tube current, 46 Tube ratings, X-ray, 45–46 Tube voltage (V), 46 Tumor(s), assessment, 66, 67, 171, 172 degree of, PET, 12 reduction of, 24 region of, 12 Tungsten, 111 anode, 43 target, 43 Ulcer, diagnosis of, 4, 66 Ultrasonic emission, 22 Ultrasonic texture, 146 Ultrasonic transducer, 134–135 Ultrasound imaging, 6, 8, 9f, 25, 26 3D ultrasound, 23 acoustic waves, basics of, 121–122 attenuation, 125–126 biological effects, 147–148 acoustic aspects at high intensity levels, 147 bioeffects (thermal and nonthermal effects), 147–148 cavitation, 147 stable cavitation, 147 transient cavitation, 147 wave distortion, 147 characteristics, image contrast, 146 spatial resolution, 146 ultrasonic texture, 146 detectors, 22

238  Index Doppler effect in propagation of acoustic wave, 130–133 defined, 130 proof, 131–133 statement, 130–131 Doppler imaging approaches, 141–144 color Doppler flow imaging, 143, 144 continuous wave Doppler system, 142 pulse wave Doppler system, 142, 143 electrical matching, 136 generation and detection, 133 gray scale imaging, 136–140 amplitude mode (A-mode), 136–138 brightness mode (B-mode), 138–139 data acquisition, 136 motion mode (M-mode), 139–140 image reconstruction, attenuation correction, 140 envelope detection, 140 filtering, 140 log compressions, 140 scan conversion, 140 interference, 124, 125f linear wave equation, 122–123 loudness and intensity, 123–124 mechanical matching, 135 nonlinearity, 126–127 overview, 121 PACS in, 23 photoacoustic imaging system, 20, 21f, 22 propagation of waves in homogeneous media, 122 propagation of waves in nonhomogeneous media, 127 protocols for imaging technique, 23

reflection and refraction, 127–129 scattering, 129–130 schlieren system, 141 tissue characterization, 144–146 absorption, 145 scattering, 145–146 velocity, 145 ultrasonic transducer, 134–135 ultrasound-based mammographic scans, 69 Undersampling, 108 Uranium 235, 13 Variation in species and individual sensitivity, 81 Vascular constrictions, 67 Vascular disruptions, assessment of, 15 Velocity of ultrasound waves, 145 Visible light-based photographic approaches, 2 Visualization, X-ray, 51–54 image intensifiers, 53–54 intensifying screens, 51–53 Voxel, defined, 198, 200 Wave distortion, biological effects of ultrasound, 147 Wavelength, of acoustic wave, 123, 124, 130, 131, 133 Wave nature, X-rays, 28–33 coherent scattering, 32 Compton effect, 32, 33 intensity of X-ray beam, 30–31 interaction of X-rays, 31 particle nature, 30 RAD, 31 Roentgen (R), 31 Wave propagation, in homogeneous media, 122 in non-homogeneous media, 127 Wedge filters, 47 Well counters, 164 White radiation, 41–42

Index  239 Wide fan beams, 114–115 Wiener power spectrum, 77, 78 Wrap-around artifact, 209, 210 Xenon, 61 gas detector, 112 Xeroradiography, 68–69 X-ray beam width, 107 X-ray computed tomography, biological effects and safety-based aspects, 118 CT-based diagnostics, 104–107 cardiac CT, 106 dual energy CT approach, 106–107 multislice CT, 105 single slice CT, 104–105 CT imaging, 89–104 2D image reconstruction, 94–97 back projection, 94–95 central slice theorem, 95–97 direct Fourier transform, 97–98 fan beam projections, 101–104 FBP/CBP, 98–101 radon transform, 89–92 sampling, 92–94 CT machine, hardware aspects, 110–112 collimation, 112 cooling systems, 111 detectors, 112 filtration, 111 gantry, 110, 111 generators, 111 slip rings, 111 X-ray tubes, 111 CT machines, generations of, 112–117 fifth, electron beam scannerstationary/ stationary, 116–117 first, rotate/translate approachpencil beam, 112–113 fourth, rotate/stationary, 115–116

second, rotate/translate-narrow fan beam, 113–114 sixth, helical, 117 third, rotate/rotate-wide fan beam, 114–115 CT number, 87, 88f detectors in CT machines, 88–89 energy integrating detectors, 88 photon counting detectors, 88–89 image quality, 107–109 artifacts, 108–109 contrast, 108 noise in CT, 108 resolution, 107–108 overview, 85–87 X-ray imaging, 4, 5f, 6, 25, 26 X-ray(s), angiography, 67 attenuation, coefficients, factors affecting, 38–39 due to coherent scattering, 39 due to Compton scattering and photoelectric effect, 39–41 characteristic radiations, 42 conventional tomography, 73–75 image attributes, 74 spatial resolution, 74–75 detection of, 3, 54–60 characteristic curve, 56–57 double-emulsion film, 59f, 60 film gamma, 57 film latitude, 58f, 59 films, 55 optical density, 55, 56f speed, 57, 58, 59 diagnostic approaches, 62–66 conventional X-ray radiography, 62–63 field size, 64–65 film magnification, 65–66 penumbra, 63–64

240  Index electromagnetic radiations, 27–28 filters, 47–51 aperture diaphragms, 48–49 beam restrictors, 47–48 collimators, 49–50 cones and cylinders, 49 radiographic grids, 50–51 fluoroscopy, 66, 67f generation of, 2, 41 generators, 42–47 component of, 42 filament current, 46–47 line focus principle, 43–45 target material, 46 tube current, 46 tube ratings, 45–46 tube voltage (V), 46 image contrast, 78–79 image noise, 77, 78 image subtraction technique, 69–72 DSA, 70–71 dual energy subtraction approach, 71–72 K-edge subtraction technique, 72 interaction between X-ray and tissues, 36–38 lower intensity of, 4 mammography, 68 mobile X-ray machine, 4f overview, 27 photoelectric effect, 34–36 pair production, 35 photodisintegration, 36 properties, 2 PSF, 75–77 ESF, 76, 77f LSF, 75–76, 77 STF, 76, 77, 78f

radiation detectors, 60–61 ionization chamber, 61 scintillation, 60–61 radiations, biological effects of, 79, 81 cellular sensitivity, 81 determinants, 79, 81 exposure area, 81 exposure time, 81 long-term effects, 81 short-term effects, 81 threshold, 79 variation in species and individual sensitivity, 81 ROC, 79, 80f visualization, 51–54 image intensifiers, 53–54 intensifying screens, 51–53 wave nature, 28–33 coherent scattering, 32 Compton effect, 32, 33 intensity of X-ray beam, 30–31 interactions, 31 particle nature, 30 RAD, 31 Roentgen (R), 31 white radiation, 41–42 xeroradiography, 68–69 X-ray tubes, CT machines, 111 Yttrium oxysulfide phosphor, 52 Z-filtering, 105 Zinc calcium sulphide, 54 Zipper artifacts, 214

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