Advances in hemodynamics research 9781634832144, 1634832140

Table of contents :
ADVANCES IN HEMODYNAMICS RESEARCH......Page 3
ADVANCES IN HEMODYNAMICS RESEARCH......Page 5
Library of Congress Cataloging-in-Publication Data......Page 6
CONTENTS......Page 7
Preface......Page 9
Part I: Basic Science of Hemodynamic Research......Page 11
Abstract......Page 13
1.1. Developments in Hemodynamic Research......Page 14
1.2.1. Heart Muscle Work and Pressure-Volume Evaluation in One Cardiac Cycle......Page 18
1.2.2. Peripheral Vasculature and Its Characteristics in Hemodynamic Research......Page 20
1.2.3. Wave Propagation and Its Reflection......Page 23
1.3. Basic Theorem Forming Blood Flow Dynamics......Page 27
1.4.2. Computational Modeling......Page 29
1.4.3. Flow Visualization with MRI (Magnetic Resonance Imaging)......Page 33
1.4.4. Flow Visualization with Echocardiography......Page 35
1.4.5. Pressure Estimation Method with Echocardiography......Page 38
1.5.1. Swirling Flow Indices: Vorticity, Circulation and Helicity......Page 39
1.5.2. Wall Shear Stress (WSS) and Its Related Parameters......Page 42
1.5.3. Flow Energy Loss (EL)......Page 45
1.6. What Hemodynamic Research Is Aiming toward in Future......Page 48
1.A.1. Pipe Flow and Vascular Characteristics......Page 49
1.A.2. Streamline Cross-Linking Number and Helicity......Page 51
1.A.3. Definition of Flow Energy Loss......Page 52
References......Page 54
2.1. Hedmodynamic Assessment Using Echocardiography......Page 61
2.2.1. Doppler Echocardiography......Page 62
2.2.2. Bernoulli Equation......Page 63
2.3.2. The Assessment of LV Systolic Function: LV Ejection Fraction......Page 64
2.3.3. The Assessment of LV Systolic Function: Global Strain......Page 65
2.3.4. The Assessment of LV Diastolic Function: Relaxation......Page 66
2.3.5. The Assessment of LV Diastolic Function: Stiffness......Page 68
2.3.6. The Estimation of LV Filling Pressure......Page 70
2.3.7. Ventricular-Arterial Coupling......Page 71
2.4.2. Color Doppler Based Methods......Page 72
2.4.3. Color Doppler Based Methods: Cross-Beam Doppler......Page 73
2.4.4. Color Doppler Based Methods: Vector Flow Mapping......Page 74
2.4.5. Color Doppler Based Methods: Blood Flow Imaging......Page 76
2.4.6. B-Mode Based Method......Page 78
2.5.2. Dilated Cardiomyopathy......Page 79
2.5.3. Hypertrophic Cardiomyopathy......Page 80
References......Page 81
Abstract......Page 89
3.1.1. Basic Principle of the Magnetic Resonance (MR) Signal......Page 90
3.1.2. MR Measurements of the Flow......Page 91
3.2.1. 2D Phase Contrast (PC) MRI (2D PC)......Page 94
3.2.2. Phase Resolved 2D Phase Contrast MRI (2D Cine PC)......Page 95
3.2.3. 3D Phase Contrast MRI......Page 96
3.2.5. Cartesian and Non-Cartesian Data Sampling for Phase Resolved 3D PC MRI......Page 97
3.3.1. Post-Processing for Flow Analysis......Page 98
3.3.3. 3D Vector Field......Page 99
3.3.5. WSS (Wall Shear Stress) and OSI (Oscillatory Shear Stress)......Page 100
3.4.2. Clinical Relevance of Flow Analysis......Page 101
References......Page 106
Abstract......Page 109
4.1. Concept of a Continuum Mechanics......Page 110
4.2.1.Compressibility......Page 111
4.2.2. Viscosity......Page 112
4.3.1. Reynolds Number......Page 114
4.3.2. Womersley Number......Page 116
4.4.1. Discretization......Page 118
4.4.2. Formulation......Page 123
4.4.3. Collocate and Staggered Grids......Page 124
4.4.4. Formulation of the Navier-Stokes Equation by the Finite Volume Method (FVM)......Page 126
4.4.5. Coupling the Navier-Stokes Equation with the Equation of Continuity......Page 130
4.4.6. Meshes......Page 133
4.4.7. Boundary Conditions......Page 134
4.4.8. Turbulent Models......Page 137
4.4.9. Fluid-Structure Interaction Analysis......Page 138
4.5. A Warkflow of Hemodynamics Simulations......Page 140
4.6. Challenges in Hemodynamics Simulations......Page 143
References......Page 144
Abstract......Page 147
2. The Cardiac Cycle......Page 148
3.1. Pressure......Page 149
3.3. Instantaneous Pressure and Volume Calculation......Page 151
4.1. Factors That Affect Myocardial Shorting......Page 152
4.2. Pressure-Volume Loop Analysis......Page 153
4.4. Afterload......Page 155
4.5. Contractility......Page 156
5.1. LV Pump Performance......Page 157
5.2. Systolic Performance......Page 158
5.3.1. Isovolumetric Relaxation Indices......Page 159
5.3.3. LV Diastolic Filling......Page 160
6. Integrated Cardiovascular Performance: The Response to Exercise......Page 162
7.1. Definition of Heart Failure......Page 163
7.2. Mechanisms of Abnormal Diastolic Properties in Heart Failure with a Reduced EF......Page 164
7.3. Abnormal Interaction of the LV and the Arterial System in Heart Failure with a Preserved EF......Page 165
7.4. Contribution of Diastolic Abnormalities to Exercise Intolerance in Heart Failure......Page 167
References......Page 170
Part II: Clinical Application of Hemodynamic Research......Page 173
Abstract......Page 175
1.1. Fetal Circulation......Page 176
1.2. Hemodynamics in Neonates......Page 179
2.1. Ventricle with Pressure Overload......Page 180
2.2. Ventricle with Volume Overload......Page 183
3.1. Anatomical and Physiological Characteristics of Right Ventricle......Page 186
3.2. Consideration in Tetralogy of Fallot......Page 187
4.1. Fontan Procedure......Page 188
4.2. Aortic Arch......Page 189
4.3. Main Ventricle and Vessels......Page 190
4.4. Fontan Anastomosis......Page 192
References......Page 193
ABSTRACT......Page 201
2.1. Definitions......Page 202
2.2. Clinical Background of IVPD and Development of IVPD......Page 203
2.3. The Mechanisms Underlying IVPD......Page 204
2.4. Measuring IVPD Using Echocardiography......Page 206
3.1. Relationship between IVPD and Systolic and Diastolic Function......Page 208
3.2. Simultaneous Analysis of Spatial and Temporal Information......Page 209
3.3. Analysis of Inertial and Convective IVPD......Page 210
3.4. IVPD during Exercise and Dobutamine Infusion......Page 211
3.5. IVPD in Patients with Dilated Cardiomyopathy......Page 212
3.8. Impact of Aging on Diastolic Function......Page 213
3.9. IVPD in Right Ventricle......Page 214
3.10. IVPD in Left Ventricle with Different Size......Page 215
REFERENCES......Page 216
Abstract......Page 223
1.1. Coronary Vessel Anatomy......Page 224
1.2. Coronary Vessel Tissue......Page 226
1.4. Coronary Vessel Movement......Page 227
2.1. Overview of the Geometry Measurements of Coronary Arterial Diseases......Page 229
2.3. Image Acquisition in Coronary Angiography (CAG)......Page 231
3.1. Overview of the Measurements of Hemodynamics in Coronary Arterial Diseases......Page 232
3.2. Fractional Flow Reserve (FFR) Measurement......Page 233
3.3. Index of Microcirculatory Resistance (IMR) Measurements......Page 235
4.1. Pathological Process in Coronary Artery Atherosclerosis......Page 236
4.2. Mechanical Factors Related to the Progression in Coronary Atherosclerosis......Page 238
4.3. Definition of the Vulnerable Plaque......Page 240
5.1. Motivation of the Numerical Coronary Flow Simulation......Page 241
5.2. Model Creation in Coronary Arterial System......Page 242
5.3. Boundary Condition Settings for Coronary Flow Simulation......Page 244
6.1. Myocardial Oxygen Demand and Supply......Page 245
6.3. Single Photon Emission CT......Page 247
6.5. Myocardial Contrast Echocardiography......Page 248
6.6. CMR......Page 251
6.7. CT Perfusion Imaging......Page 252
References......Page 253
Abstract......Page 259
1. Heart Transplantation with Donation after Circulatory Determination of Death (DCDD)......Page 260
2. Warm Ischemia - The Major Obstacle for Heart Transplantation with DCDD......Page 261
3. Principal Mechanisms Underlying Cardiac Ischemia-Reperfusion Injury......Page 262
5. Our Strategy – DCDD Graft Evaluation with Hemodynamic Parameters at the Time of Procurement......Page 263
Perspectives......Page 268
References......Page 269
Abstract......Page 273
2.1. Overview of Tools for Hemodynamics Evaluation......Page 274
2.3. Hemodynamic Research Using Echocardiography......Page 277
2.5. Blood Flow Simulation Using Numerical Models......Page 278
2.6. Computerized Virtual Surgery Based on Computational Fluid Dynamics......Page 280
3.1. Hemodynamic Evaluation in Surgery for Congenital Heart Diseases......Page 282
3.2. Flow Evaluation in Coronary Artery Bypass Grafting (CABG)......Page 286
3.3. Prediction of the Prognosis of Aortic Disease......Page 288
3.4. Applications in Valve Surgery......Page 293
Future Perspectives and Conclusion......Page 295
References......Page 296
Index......Page 301

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CARDIOLOGY RESEARCH AND CLINICAL DEVELOPMENTS

ADVANCES IN HEMODYNAMICS RESEARCH

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CARDIOLOGY RESEARCH AND CLINICAL DEVELOPMENTS

ADVANCES IN HEMODYNAMICS RESEARCH

KEIICHI ITATANI EDITOR

New York

Copyright © 2015 by Nova Science Publishers, Inc.

All rights reserved. No part of this book may be reproduced, stored in a retrieval system or transmitted in any form or by any means: electronic, electrostatic, magnetic, tape, mechanical photocopying, recording or otherwise without the written permission of the Publisher. We have partnered with Copyright Clearance Center to make it easy for you to obtain permissions to reuse content from this publication. Simply navigate to this publication‘s page on Nova‘s website and locate the ―Get Permission‖ button below the title description. This button is linked directly to the title‘s permission page on copyright.com. Alternatively, you can visit copyright.com and search by title, ISBN, or ISSN. For further questions about using the service on copyright.com, please contact: Copyright Clearance Center Phone: +1-(978) 750-8400 Fax: +1-(978) 750-4470 E-mail: [email protected]. NOTICE TO THE READER The Publisher has taken reasonable care in the preparation of this book, but makes no expressed or implied warranty of any kind and assumes no responsibility for any errors or omissions. No liability is assumed for incidental or consequential damages in connection with or arising out of information contained in this book. The Publisher shall not be liable for any special, consequential, or exemplary damages resulting, in whole or in part, from the readers‘ use of, or reliance upon, this material. Any parts of this book based on government reports are so indicated and copyright is claimed for those parts to the extent applicable to compilations of such works. Independent verification should be sought for any data, advice or recommendations contained in this book. In addition, no responsibility is assumed by the publisher for any injury and/or damage to persons or property arising from any methods, products, instructions, ideas or otherwise contained in this publication. This publication is designed to provide accurate and authoritative information with regard to the subject matter covered herein. It is sold with the clear understanding that the Publisher is not engaged in rendering legal or any other professional services. If legal or any other expert assistance is required, the services of a competent person should be sought. FROM A DECLARATION OF PARTICIPANTS JOINTLY ADOPTED BY A COMMITTEE OF THE AMERICAN BAR ASSOCIATION AND A COMMITTEE OF PUBLISHERS. Additional color graphics may be available in the e-book version of this book.

Library of Congress Cataloging-in-Publication Data ISBN: (eBook)

Library of Congress Control Number: 2015942935

Published by Nova Science Publishers, Inc. † New York

CONTENTS Preface

vii

Part I: Basic Science of Hemodynamic Research

1

Chapter 1

Historical and Current Role of Hemodynamic Research Keiichi Itatani and Katsu Takenaka

3

Chapter 2

Hemodynamic Assessment and Flow Visualization in Echocardiography Hiroaki Semba and Tokuhisa Uejima

51

Chapter 3

Flow Visualization in Magnetic Resonance Imaging (MRI) Yasuo Takehara and Masataka Sugiyama

79

Chapter 4

Computational Modeling of Blood Flow Masanori Nakamura

99

Chapter 5

Hemodynamics and Ventricular Dynamics Evaluated with Catheter Hidekatsu Fukuta and Nobuyuki Ohte

137

Part II: Clinical Application of Hemodynamic Research

163

Chapter 6

Congenital Heart Disease and Circulatory Physiology Takashi Honda, Kagami Miyaji and Masahiro Ishii

165

Chapter 7

Ventricular Sucking Forces and Diastolic Function: Intraventricular Pressure Gradient in Ventricle during Early Diastole Gives Us New Insights into Diastolic Function Ken Takahashi and Takahiro Ohara

Chapter 8

Chapter 9

Hemodynamics in Coronary Arterial Disease and Myocardial Perfusion Tadashi Yamamoto, Sachi Koyama, Keiichi Itatani and Satoshi Yamada Reperfusion Hemodynamics As an Early Predictor of Cardiac Function in a DCDD Setting Sarah L. Longnus, Natalia Mendez Carmona and Hendrik T. Tevaearai Stahel

191

213

249

vi Chapter 10

Index

Contents Application to Cardiovascular Surgery Shohei Miyazaki, Keiichi Itatani, Sachi Koyama, Kouki Nakashima, Tetsuya Horai, Norihiko Oka, Tadashi Kitamura and Kagami Miyaji

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291

PREFACE Hemodynamics is the study of the dynamics of the circulatory system. Hemodynamics has been essentials in the clinical practice pertaining to cardiovascular diseases from ancient days. Although it is essential, because it is based on dynamics and physics, the understanding of hemodynamics is hard work for all those concerned with cardiovascular diseases. In addition, with the rapid progress of recent imaging and computer technology, hemodynamics research undergone an evolution that provides beautiful colorful blood flow visualization. This kind of innovation contributes novel insights into the approach to the pathophysiology of cardiovascular diseases. This textbook includes the comprehensive knowledge regarding hemodynamic research from basic physiology to recent clinical problems. This textbook has two parts: first includes the basics of hemodynamics research and the second presents its clinical applications as follows. Part I: Chapter 1: Chapter 2: Chapter 3: Chapter 4: Chapter 5: Part II: Chapter 6: Chapter 7:

Basic Science of Hemodynamic Research Historical and Current Role of Hemodynamic Research Hemodynamic assessment and flow Visualization in Echocardiography Flow Visualization with Magnetic Resonance Imaging Computational Modeling of the Cardiovascular System Hemodynamics and Ventricular Dynamics Evaluated with Catheter Clinical Application of Hemodynamic Research Congenital Heart Disease and Circulatory Physiology Ventricular Sucking Forces and Diastolic Function: Intraventricular pressure gradient in ventricle during early diastole gives us new insights into diastolic function Chapter 8: Hemodynamics in Coronary Arterial Disease and Myocardial Perfusion Chapter 9: Reperfusion hemodynamics as an early predictor of cardiac function in a DCDD setting Chapter 10: Application to Cardiovascular Surgery I believe this textbook covers all the current topics and all the important historical topics related to hemodynamics. In this edition of the textbook, I appreciate so much the efforts of the members of the ―Research Committee on Blood Flow and Cardiovascular System‖ http://ketsuryukai.com 『血流会』(ketsuryukai) in Japan. Each chapter was written by professional authors regarding respective topics.

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Although this book deals with the least “advances”, careful attentions was paid to make it appeal to a wide range of professionals including clinicians, engineers, physicians, and researchers. Each chapter is independent of the others, and this textbook was written both to be read through and to be used as a reference for any special topics. I hope this textbook will provide new perspectives to all those interested in the research regarding hemodynamics.

Keiichi Itatani, MD, PhD Project Associate Professor Department of Cardiovascular Surgery Kyoto Prefectural University of Medicine 465 Kajiicho, Kawaramachi-Hirokoji, Kamigyo-ku, Kyoto, Japan, 602-8566 [email protected] [email protected]

PART I: BASIC SCIENCE OF HEMODYNAMIC RESEARCH

In: Advances in Hemodynamics Research Editor: Keiichi Itatani

ISBN: 978-1-63483-187-1 © 2015 Nova Science Publishers, Inc.

Chapter 1

HISTORICAL AND CURRENT ROLE OF HEMODYNAMIC RESEARCH Keiichi Itatani1,* and Katsu Takenaka2 1

Departments of Hemodynamic Analysis and Cardiovascular Surgery, Kitasato University School of Medicine, Tokyo, Japan 2 Department of Cardiology, Nihon University, Chiyoda, Tokyo, Japan

ABSTRACT Hemodynamics is the study of the mechanics of the blood flow and the circulatory system, and it has become indispensable in the clinical management of patients with cardiovascular disease. It can be classified as a physiology of the blood flow and cardiac function, and it has an inherently close relationship with the physics of flow: fluid dynamics. Although the interests of hemodynamic research have aspects of rheological and fluid dynamic approaches, the clinical measurements have been historically restricted to the pressure in the cardiovascular lumen by catheterization. Otherwise, changes in the geometrical configuration of the heart and vessel structure by echocardiography are another frequently utilized hemodynamics evaluation tool. On the other hand, the principle of fluid dynamics is described by equations for flow velocity and pressure distribution in arbitrary time; thus, the development of hemodynamic research historically distinct from knowledge accumulated through the study of fluid dynamics. As a result, the outcome of the hemodynamic research was simply descriptive and implicative of the pathological process of the disease, and did not directly venture further into the pathophysiological mechanisms. However, recent developments in computer engineering and clinical imaging techniques have enabled blood flow visualization, leading to a revolution in the field of hemodynamic research. Recent flow visualization methods have illustrated the vortex flow inside the heart chamber and vessel lumen, which has been considered by researchers since ancient times. Because these approaches based on flow velocity fields have high affinity with fluid dynamic equipment, they provide several novel indices that *

Corresponding author: E-mail: [email protected].

4

Keiichi Itatani and Katsu Takenaka are applicable to the pathophysiology of the cardiovascular diseases because they are profoundly based on the theorems that govern the phenomenon. Because pressure and flow distribution are not independent parameters in the physics of fluid, these recent flow visualization imaging should finally aim toward revealing hemodynamics in relation to the absolute pressure distribution. Several novel indices derived from the flow visualization modalities have emerged, but most of them is mechanical forces induced by the blood flow. These mechanical forces especially flow energy loss should be evaluated in the comparison with the work produced by the circulatory pump: the heart, absolute pressure evaluation will be inevitable. Recent novel technologies in the hemodynamic research results will be and should be linked with each other to obtain the profound insight into the pathophysiology of the cardiovascular diseases. This chapter explains the process of hemodynamic research development by introducing several recent topics, and further explains the relationship between the theory of fluid dynamics and the assessment of cardiovascular disease.

Keywords: hemodynamics, circulatory physiology, fluid dynamics, pressure, flow velocity, flow visualization, hemodynamic indices

1.1. DEVELOPMENTS IN HEMODYNAMIC RESEARCH Hemodynamics is the dynamic in the cardiovascular system. The cardiovascular system is a closed circulatory system through which blood flows to deliver oxygen to all tissues of the body. Blood flow within this system is supported mainly by the central pump: the heart. ((Figure 1.1) Other organs that affect or support the circulatory system include the lungs (breathing results in pulmonary flow and venous return fluctuation), and musculoskeletal system (blood pooled in the venous system is pumped by surrounding muscles). Hemodynamics is therefore critical for the maintenance of blood pressure and blood flow within the heart and vessel lumen. In addition to the central pump, the peripheral vasculature has a hemodynamic effect. Because blood is a viscous liquid, the dynamics of blood are closely related to the physics of fluids: fluid dynamics. Therefore, basic concepts in hemodynamics are largely based on the theorem of fluid dynamics. Hemodynamics is often challenging for clinicians because it is based on mathematical and physical principle. However, hemodynamics is not a purely academic discipline such as pure mathematics or basic laboratory based-experimentation, but rather a practical tool in daily clinical practice in cardiovascular medicine, and has been a powerful and useful tool used by physicians since ancient times for the systematical description of the cardiovascular diseases using several macroscopic parameters, including systemic blood pressure, cardiac output, arbitrary vessel blood flow rate, and peripheral vessel resistances. These parameters are essential in clinical practice and are widely used in settings ranging from outpatient clinics to intensive care units. Historically, discussions regarding hemodynamic research predominantly focused on blood pressure measurements using catheter examination. In addition, echocardiography was also used in hemodynamics evaluations. For example, noninvasive blood pressure (NIBP) measurement at the calf has been used widely in clinical practice ((Figure 1.2A). The device was invented by Samuel Siegfried Karl Ritter von Basch in 1881. Scipione Riva-Rocci

Historical and Current Role of Hemodynamic Research

5

introduced an easier version in 1896. In 1901, Harvey Cushing modified the device for medical use (Booth J. 1977). Direct pressure measurement by arterial cannulation was tried in much elder era, was performed in 1733 by Stephan Hales, who inserted a tube into the carotid artery of a horse ((Figure 1.3). Direct arterial pressure measurements have been widely used in intensive care and perioperative patient management ((Figure 1.2B). They are useful parameters for evaluating the hemodynamic state of patients with cardiovascular disease. Central venous pressure (CVP) measurement by catheterization is a method enabling evaluation of blood volume within the cardiovascular system, and Swan-Ganz catheters ((Figure 1.2C) enable the measurement of pulmonary artery pressure, pulmonary capillary wedge pressure, and cardiac output. These methods have increased the detail of hemodynamics parameters particularly in intensive care.

Figure 1.1. Explanation of a circulatory system. A: an image from Wikipedia with key word ―Circulatory system‖. http://en.wikipedia.org/wiki/Circulatory_system. This describes the location of the heart and large vessels. B: an image from ―revision world‖http://revisionworld.com/a2-level-level-revision/biology/physiology-transport/humancirculatory-system This image describes the function of a circulatory system.

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Figure 1.2. Pressure measurement equipment. A; Manchette calf for NIBP measurement. B: arterial cannulation for direct pressure measurement from ―Medline Plus‖. http://www.nlm.nih.gov/medlineplus/ency/imagepages/19871.htm C: Swan-Ganz catheter and its insertion. Images from ―The critical care nurse‖. http://ccrnnurse.blogspot.jp/2012/05/why-use-swanganz-catheter.html.

Figure 1.3. Stephan Hale‘s experiment of blood pressure measurement.

Historical and Current Role of Hemodynamic Research

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The fact that the main parameter in evaluating hemodynamics has been the absolute pressure of various sites is quite characteristic and unique when we consider that theoretical basis of the hemodynamics should be conform to the fluid dynamics, because fluid dynamics generally describes and focuses on the flow stream constructed from velocity distribution, and rarely considers absolute pressure values. However, flow stream observation itself is much elder than pressure measurement and has been one of the main interests since ancient days. Leonardo da Vinci (1452-1519) illustrated the vortex inside the Valsalva sinus in addition to the heart anatomy and vortex flow in a pipe ((Figure 1.4), but actually measured flow stream has not been available until MRI (magnetic resonance imaging) phase velocity mapping emerged recently. Before that, regarding the flow, the available tools are cardiac output estimation based on the echocardiography, and flow velocity measurement based on Doppler ultrasonography ((Figure 1.5) B-mode echocardiography cross-sectional imaging has been used for decades, providing information regarding the geometrical configuration of the heart chambers. Left ventricular (LV) dimension and volume measurement estimation have been powerful tools in evaluating congestive heart failure patient. The ejection fraction (EF) is a global parameter describing the pump function of the heart ((Figure 1.5A). Doppler echocardiography can be used to detect the unidirectional flow velocity at specific portion of the heart and vessel lumen. Although these are simple 2D imaging techniques, they provide essential information regarding the hemodynamic state of patients ((Figure 1.5B).

Figure 1.4. Pictures of Leonardo da Vinci. Leonardo da Vinci illustrated vortex flow in the sinus of Valsalva.

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Keiichi Itatani and Katsu Takenaka

Figure 1.5. B-mode and Doppler echocardiography. A: Shema of the echocardiography scan https://www.healthtap.com/topics/echo B: B-mode image of the LV geometry configuration and its change in long-axis view. C: Pulse wave Doppler flow velocity measurements of the transmitral flow.

The ultimate goal of hemodynamic research is not the complete description of blood fluid dynamics, but optimizing the efficiency of oxygen delivery to all organs. Attentions should be paid on the process in the clinical settings and on the biological response with change in hemodynamic parameters. This chapter describes the use of hemodynamics in solving clinical problems and the development of hemodynamic research to reveal physiological mechanisms and predict the clinical course of patients by discussing several previous studies reported in the hemodynamics literatures. Despite this chapter discussing the development of hemodynamic research, all previous important studies could not be described in this book.

1.2. DEVELOPMENTS IN HEMODYNAMIC RESEARCH RELATED TO PRESSURE MEASUREMENT 1.2.1. Heart Muscle Work and Pressure-Volume Evaluation in One Cardiac Cycle Since the beginning of hemodynamic research, there has been widespread interest in ventricular muscle function and pressure change. We later describe details of heart muscle dynamics based on catheter measurements (Chapter 5). Ventricular contractility and its mechanism of action are based on the classical and well-known concept of the ventricular pressure-volume (PV) loop. The PV loop allows simultaneous illustration of both pressure and LV volume. (Figure 1.6 illustrates the PV loop of the LV. During isovolumic systole, pressure increases while volume remains constant. The peak pressure change during isovolumic systole, max dP/dt is a parameter that describes the contractility of the LV. After ejection and decrease in LV volume, the aortic valve closes and the isovolumic diastolic phase begins before the mitral valve opens. Although LV volume does not change during isovolumic diastole, the mean LV flow does not remain constant. With the decrease in LV pressure, negative pressure is generated between basal regions and the apex, and LV flow can be detected. Diastolic function is estimated by the speed of the decreasing pressure, max – dp/dt or the time constant tau that describes the time constant when the pressure decrease is assumed to be an exponential curve with time. ON reduction in preload, the loop shifts

Historical and Current Role of Hemodynamic Research

9

leftward and downward, the loop size reduces, and the end-systolic point would describe a line toward LV dead space V0. Ees represents the gradient of the end-systolic pressure volume relationship and also the end-systolic elastance, measure myocardial contractility. Ea is the arterial elastance and is measured by the gradient of the line connecting the end-systolic and end-diastolic points. In relation to the PV loop and LV work, we provide an explanation of the work and energy generated by the LV. The area within the PV loop represents LV wall muscle work, and is estimated to be approximately 1J (=1000 mJ) in the average adult human LV in one cardiac cycle. When the heart rate is around 60 beats per minute, the cardiac cycle length lasts 1.0 sec, and LV work becomes 1.0 W (=1000 mW). When the required nutrition of an adult is assumed to be1800 kcal/day (7536240 J = 1800 kcal×4186.8), and the heart is assumed to consume 10% of the total energy intake, the heart consumes energy of (1.1) This energy would be the total energy consumed by the heart. It includes required for the contraction of all 4 chambers, electrical activity, and metabolism of the heart muscle cells. Thus, we can conclude that 11-12% of consumed energy for LV ejection power is wasted.

Figure 1.6. Pressure-Volume (PV) loop of the left ventricle. Ees is the slope of the end-systolic pressure volume relationship and represents the end-systolic elastance, which provides an index of myocardial contractility. Ea is the arterial elastance and is measured by the slope of the line that connects the endsystolic point and end-diastolic point. V0 is a chamber volume with zero pressure (dead space).

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Figure 1.7. Peripheral vasculatures and their analog to the electrical circuit components.

Table 1.1.

Aorta Arterial capillary Pulmonary venous capillary Pulmonary artery Pulmonary arterial capillary Vena cava Systemic capillary

Resistance (mmHg/ sec/L) 198.8 3511.2 11 28.4 41.69 82.7 322.3

Compliance (ml/mmHg) 0.0612 0.00535 0.888 0.274 0.0408 4.079 0.31

Inertance (mmHg sec2/ml) 18 1.13 4.12 4.73 0.29

1.2.2. Peripheral Vasculature and Its Characteristics in Hemodynamic Research In addition to the function of the central pump: the heart, the functions of peripheral vessels have been revealed by circulatory physiology. It is well known that central and peripheral vessels have the following passive properties: resistance, compliance, and inertance. Table 1.1 presents properties of each types of vessel in the circulatory system. These properties are often described by analogy with the electrical circuit, with each of these

Historical and Current Role of Hemodynamic Research

11

properties corresponding to resistance R, capacitance C, and inductance L, respectively (Figure 1.7). Vessel resistance R is defined by the decrease in pressure (pressure drop) caused by blood flow through relatively narrow vessel diameters with a degree of viscosity, as follows. (1.2) Pressure drop (ΔP) should be measured between the inlet and outlet of the vessel tube. Pproximal and Pdistal represents the absolute value of the pressure at the proximal and distal measurement sites. Peripheral vessels with small diameters have higher R than central vessels with large diameters. Arterial capillary have a higher R than venous capillaries, and systemic arterial capillaries have a higher R than pulmonary arterial capillaries. Vessel compliance C refers to the volume change with increased pressure. It is defined as follows. (1.3) where ΔP and ΔVolume mean pressure and volume change inside the vessel, respectively. Because the flow is generated by the vessel volume change with time, the relationship between the pressure change and flow Q through the vessel can be described with the following equation. (1.4) Compliance C is the volume reserve function of the vessel, and the venous system has a higher C than the arterial system. This property results from vessel wall elastic motion. Inertance is another effect caused by vessel wall motion. In the circulatory system, dynamic flow rate changes during a single cardiac cycle. Pressure changes when flow increases or decreases within vessels; however, the vessel wall simultaneously has an inertial force that prevents rapid pressure change in response to the flow change. This effect causes a negative pressure gradient within the vessel with constant L. (1.5) where ΔP represents the potential pressure change or pressure correction within the vessel. Inertial force L is higher in the arterial system than in the venous system and higher in central vessels than in peripheral vessels. These vessel properties combine as in an electrical circuit and can be used to simulate the entire circulatory system. This model is termed as ―lumped parameter model‖, because many vessel property parameters for each vessel type are used in model construction. Figure 1.8 demonstrates an example of the ―lumped parameter model‖ of the systemic and pulmonary circulation of the Fontan procedure. These properties are often used in combination with computer flow simulation models, where peripheral vessel properties may be assumed. In

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Appendix 1.A.1, the reason why resistance and inertance occur is explained using pipe flow model.

Figure 1.8. Electric circuit analog of the Fontan circulation reported by Corcini et al. 2014. P: pressure, Q: flow, R resistance, C: compliances, L: inertances, SA: single atrium, SV: single ventricle, PA: pulmonary artery, PV: pulmonary vein, UBA: upper body artery, USV: upper body vein.

Historical and Current Role of Hemodynamic Research

13

1.2.3. Wave Propagation and Its Reflection Despite vessel properties have similarities with electrical circuit components, the actual circulatory system has several bifurcations and is highly complex, i.e. it is not structured as a straightforward pipe that entire circulatory system has different characteristics from that of electrical circuit. When the pulse wave propagation is considered in the context of a circulatory system, the forward pulse wave collides with vessels at each bifurcation point. After the collision, a reflection wave is generated and propagates backwards. In general, the pulse wave is reflected at bifurcation points. A measured pulse wave can be decomposed into the forward and reflection wave. Using pressure P and flow Q measurement in a vessel, the forward Pf and reflection Pr pressure waves are described as follows.

(1.6) where Z0 is the characteristic impedance of the vessel. Characteristic impedance is impedance characteristically specific to the vessel, and is often expressed with the following definition. (1.7) c is a wave speed of the pulse, A is the cross-sectional area of the vessel. Because the characteristic impedance is an impedance without reflection, ∫.

/

∫.

/

√

(1.8)

From the definition of Pf and Pr described above, the following relationship can be calculated. (1.9) A flow wave can also be decomposed into forward and backward waves. ⁄ ⁄

(1.10)

The concept of the forward and backward pressure wave is illustrated in Figure 1.9. With forward flow Q, the pressure P inside the vessel increases in accordance with the characteristic impedance.

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Keiichi Itatani and Katsu Takenaka

Wave propagation is described using the parameter termed Wave Intensity (WI). WI represents the transmitted energy of the pulse wave. Originally it was defined with measured pressure P and velocity u. (1.11) Positive WI (WI > 0) represents a forward wave, and negative WI (WI < 0) represents backward wave. Here, a forward wave indicates that the wave propagates with flow in a direction away from the pump, whereas a backward wave indicates that the wave propagates with flow in a direction toward the pump (Figure 1.10). WI is a particularly interesting parameter because it provides information regarding the direction of the wave propagation, even though it can be calculated using one measurement point. When combined with pressure increase

or decrease

, indicating compression and expansion waves, wave

patterns can be classified into 4 patterns (Figure 1.10). Wave intensity can be decomposed into positive and negative components. . .

/ /

(1.12)

Figure 1.9. Forward and reflection pressure wave. Black solid and dashed lines represent measured pressure and aortic flow, respectively. Blue and red solid line represent forward and reflection pressure wave, respectively.

Historical and Current Role of Hemodynamic Research

15

where P+, P- represent forward and backward (reflection) pressure wave, respectively like in Equation (1.6), and u+, u- represents forward and backward (reflection) velocity wave corresponding to their flow (1.10), respectively. Thus, the sum is termed ―Net WI‖. (1.13) Originally. WI was studied to determine the flow wave in arterial systems. The first peak detected during early systole is a forward positive wave, and is result of contraction of the LV muscle (Figure 1.11). The second peak detected during late systole is a forward expansion wave and is considered to be due to the deceleration force caused by the ventricular relaxation starting in late systole. Presently, these WI analyses can be applied to various situations including artery pulse wave analysis in atherosclerosis or pulmonary arterial pulse wave analysis in pulmonary hypertension with clinical application (Quail et al. 2015.). One of the most prominent results of the WI analysis is flow drive detection in coronary arteries (Davies et al. 2006.). Because WI can detect the wave propagation direction, it can clarify the nature of forces occurring in a system. Davies et al. demonstrated coronary WI is generated by forward flow through the aortic valve, and by compression and expansion of the capillary within the LV muscle during contraction and relaxation of the LV.

Figure 1.10. Classification of wave propagation based on Wave Intensity (WI). Forward wave indicates that flow directs away from the pump, whereas backward wave indicates that flow directs toward the pump. Compression and expansion wave indicates pressure increasing or decreasing wave, respectively.

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Keiichi Itatani and Katsu Takenaka

Figure 1.11. Wave intensity (WI) in normal arterial system. A: flow and velocity in one cardiac cycle. B: WI in one cardiac cycle. WI has two peaks: compression peak and expansion peak. (Jones et al. 1993).

Figure 1.12. Flow recognition and visualization. A and C: Vortex flow in an ocean. B and D: Flow inside the vascular lumen with bifurcation. A and B: Lagrangian representation, C and D: Eulerian representation.

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Historical and Current Role of Hemodynamic Research

1.3. BASIC THEOREM FORMING BLOOD FLOW DYNAMICS Richter et al. 2006 proposed ―Cardiology Is Flow‖, and they noted the words of Heraclitus (Greek philosopher) ―Everything flows and nothing abides, everything gives way and nothing stays fixed‖. In their editorial, the predicted mechanisms of blood flow causing the cardiovascular disease were illustrated. Since then, the flow visualization method has been used in numerous clinical situations. When considering how (Figure 1.12), flow can only be understood when the distribution of velocity and pressure is completely known. There are two ways in describing flow. One is based on Lagrangian representation (Figure 1.12A, B), in which flow is described with the moving particle, and the other is Eulerian representation (Figure 1.12C, D), in which flow is described with the fixed coordinate system. Velocity has both quantity and direction and it should be described as a vector ⃗

(

)

(1.14)

where x, y, z present direction of Cartesian coordinates. In the 3D space within the heart and vasculature, each vector component has spatial distribution that varies at each point with time; thus the velocity vector can be described by spatial and temporal parameters for (x, y, z) and t. ⃗⃗⃗⃗⃗⃗⃗⃗⃗⃗⃗⃗⃗⃗⃗⃗⃗⃗⃗⃗⃗⃗ ( )

.

(

)

(

)

(

)/

(1.15)

Conversely, pressure P is a scalar parameter dependent on space and time. (

)

(1.16)

Because blood is a liquid, it is incompressible fluid. The fluid dynamics of an incompressible fluid is determined by 4 parameters, composed of one scalar P and three velocity vector components (ux, uy, uz) at each point in space and at arbitrary time. The mass and momentum preservation equation for an incompressible fluid, called the Navier-Stokes equation is described in Eulerian representation becomes as follows. ⃗ ⃗

(⃗

(1.17) )⃗

⃗

(1.18)

where ρ represents density, and μ represents viscosity. In the literature, the ρ of blood is commonly reported to be 1.06 kg/m3, and μ between 0.003 - 0.005 Pa・s when assuming blood is a Newtonian fluid. Here, ∂ is a partial differential operator, which differentiates with respect to a defined parameter in the denominator, while all other parameters are fixed. For example, differential with respect to x, whereas y, z, and t, are fixed. Nabla differential operator.

refers to the

is a vector partial

18

Keiichi Itatani and Katsu Takenaka . Further, Laplasian

/

(1.19)

is defined as follows. (1.20)

Equation (1.17) is commonly termed the continuity equation, representing the mass flow preservation law, whereas the Navier-Stokes equation (1.18) represents the flow momentum preservation law. Equations (1.4) and (1.5) can be written with partial differential as follows. (1.21) .

/

.

/

.

/

–

.

/

(1.22)

.

/

(1.23)

.

/

(1.24)

Thus, this equation composed of 4 describes for 4 unknown parameters. They have oneorder partial differential in time, and second order partial differential in space, and have nonlinear components. The left hand side of the equation (1.18) defines the temporal change in velocity: acceleration multiplied by unit mass giving the force generated by blood per unit volume. In the right hand side of the equation, the first term, (the convection term), describes convectional or rotational force, the second term describes flow drive under a pressure gradient, and the third term describes the frictional force resulting from blood viscosity. The Navier-Stokes equation includes only the pressure gradient, not the absolute pressure value, and relies on an arbitrary uniform constant pressure value as a reference pressure. Again we emphasize that the historical development of hemodynamics started with blood pressure measurement is unusual when considering that the theorem of physics should enable a complete description of organ system physiology or at least, that of a model that is compatible with theory of physics. The momentum preservation Navier-Stokes equation (1.18), (1.22-24) is based on the Eulerian expression. Lagrangian representation which describes the flowing particle (Figure 1.12A, B) can be expressed as follows. ⃗

The derivative

⃗

(1.25)

is called material derivative or material time derivative, and the

derivative is based on the moving particle. The forces given to the moving particles are only pressure gradient and viscous friction forces. Thus, the derivative should be expressed in Eulerian partial differentials.

19

Historical and Current Role of Hemodynamic Research

(1.26) Thus, the convective term appears after transposing latter terms to the left side of the Navier-Stokes equation (1.18), (1.22-24). Another characteristic feature of hemodynamics is the complicated boundary condition applied to the circulatory system. Boundary condition is a technical terms in differential equations referring to values set within the boundary surfaces of given domain. If we consider the fluid dynamics of the circulatory system, boundary conditions should be compatible with the pressure and velocity conditions of each boundary surface of the heart and vascular lumen. Generally in problems of fluid physics, either the pressure or velocity should have the absolute value (Diriclet) condition, and the other value have to constant gradient (Neumann) condition. In a closed circulation, the wall boundary should be given as the fixed wall shape or their movements as velocity condition. Thus, historically, hemodynamic research has dealt with geometrical configurations and change in structure of the heart and vessel wall; however, these analysis have focused only on boundary conditions when considering hemodynamics as fluid dynamics of the circulatory system.

1.4. DEVELOPMENTS IN HEMODYNAMIC RESEARCH RELATED TO FLOW VISUALIZATION 1.4.1. Flow Visualization Methods Blood flow visualization is a method for the detection of blood flow in the cardiovascular lumen. The flow visualization method provides the blood flow velocity vector distribution. These techniques are novel techniques and some of them are based on complete measurement, while others are based on calculation of the Navier-Stokes equations (1.17), (1.18), (1.21)-(1.24). Because they assess visualized flow including vortex flow patterns, they are predominantly based on imaging modalities. The methods can be classified into the following two types. 1. Flow visualization based on computational modeling (Chapter 4). 2. Flow visualization based on medical imaging (Chapter 2 and 3). The following chapters describe further details. In this chapter, we introduce hemodynamic indices that have been applied to practice and been the focus of previously reported research articles.

1.4.2. Computational Modeling Computational Fluid Dynamics (CFD) is a method that uses numerical computation to solve and analyze fluid flows. Recent improvements in computer performance have made CFD a powerful evaluation tool for numerous industries because it reduces time and cost compared with experimental approaches related to fluid flow, and the CFD modeling method has recently begun to be applied. The original application of CFD simulation in

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cardiovascular medicine was in the Fontan procedure, a congenital open heart surgery for single ventricular physiology. CFD has been used to inform selection of surgical procedures. Recently, CFD has been used as a noninvasive method of predicting ischemic severity in coronary arterial disease, and later in Chapter 8, hemodynamic research regarding coronary arterial flow and perfusion will be introduced and discussed. The process of CFD modeling using clinical imaging data such as CT (computed tomography) slices is illustrated in Figure 1.13.

Figure 1.13. CFD (computational fluid dynamics) flow visualization process. A case of the aortic arch of a child. After the extraction of a vascular structure from medical image such as CT or MRI slice data, boundary conditions are set to realize the physiological flow. The extracted 3D geometry is subdivided with computational mesh to determine the pressure and velocity distribution at each point. Incompressible Navier-Stokes equation is calculated using computers. Flow is visualized with the calculated results.

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21

CFD computes the Navier-Stokes equations (1.17), (1.18), (1.21)-(1.24) and provides spatial and temporal fields of velocity (1.14) and pressure (1.16) in the analysis domain. The analysis domain is subdivided into a computational mesh, and velocity vectors (1.14) and pressure (1.16) on each node is provided by calculating the mass and momentum preservation in each of the subdivided small elements. In the CFD calculation process, the Navier-Stokes equations are solved iteratively until errors in the mass and momentum preservation termed ‗residual‘ becomes sufficiently small (convergence criteria). The balance between space and time resolution is generally controlled by CourantFriedrichs-Levy condition based on a parameter known as the Courant number. (1.27) where Δx is the spatial resolution (mesh size), Δt is a time step size of the transient calculation, u represents the representative velocity, and Cmax is a constant. A Courant number of < 1.0 is recommended, In CFD analysis boundary conditions should be applied to inlets, outlets and wall surfaces. Boundary conditions majorly define the features of flow: inlet boundary conditions should be compatible to the cardiac output, wall motion should be comparable with that observed in actual physiology. Because CFD is a flow simulation, not an actual measurement, there are several advantages and disadvantages. With the progress in computational equipment and the sophistication in data analysis processes, recent studies have dealt with a large number of patient-specific models, and enabled establishment of statistically significant evidences. However, CFD can be used to create simplified models and arrive at generalized conclusions. We introduced the concept of ―Idealized geometry‖ based on averaged patient data to investigate generalized knowledge related to therapeutic strategies. This approach can aid in determining optimal surgical procedure with use of few models with limited calculation cost. Itatani et al. 2009 used this approach to determine the optimal conduit size and pulmonary arterial size when using the extracardiac Fontan procedure. Idealized 3D geometry models based on angiograms were generated for several patients (Figure 1.14). Another advantage of CFD is ―computerized virtual surgery‖, in combination with 3D computer graphics. Virtual surgery enables prediction of post-operative blood flow which improves optimization of operative methods based on individual hemodynamics. For example attempted ―virtual coronary arterial bypass‖ using CT data from several patients before the actual surgery, to determine the optimal bypass graft design. Although CFD has the advantage of low invasiveness and virtual simulation, CFD results are largely dependent on calculation assumptions and parameter settings. These algorithms and parameters, including boundary conditions, do not always realize the actual physiological blood flow. Thus, elaborate modeling strategies for the realization of physiological flow is essential particularly in boundary conditions. Many recent studies have adopted the lumped parameter model which uses a combination of circuit components resistance, condenser and impedance to model peripheral arteries as outlet boundary conditions. However, the setting of these ―lumped‖ parameters is a cumbersome procedure, and as the number of modeled parameters increases, the accuracy is likely to reduce.

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Figure 1.14. CFD studies of a Fontan extracardiac conduit reported by Itatani et al. 2009.

Figure 1.15. MRI flow analysis process. After the extraction of cardiovascular lumen, the binarized geometrical mask is superposed with PC MRI data, and blood flow velocity vector is visualized. Because MRI has acculturated slices, 3D blood flow with pulsatile fluctuation is reconstructed.

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23

1.4.3. Flow Visualization with MRI (Magnetic Resonance Imaging) Modalities used in flow visualization based on medical imaging are predominantly MRI (magnetic resonance imaging) and echocardiography. Flow visualization based on measurements have the advantages of using actual flow information; however, the accuracy of measurements is not precisely known. Temporal and spatial resolutions are particularly insufficient when using current imaging modalities. These methods are unable provide explicit pressure information.

Figure 1.16. Examples of 4D flow analysis in aortic diseases. A: spiral flow inside the ascending aortic aneurysm reported by Markl et al. 2011. B: Visualization of the false lumen flow of the chronic aortic dissection patients are reported by Clough et al. 2012.

MRI flow measurements are based on PC (phase contrast) MRI. PC MRI is a mode of MRI that provides the flow velocity distribution of the direction in which the magnetic gradient fields are generated. PC MRI has 4 image series: magnitude and 3 phase image series (Figure 1.15). The magnitude image provides geometrical information; however, the contrast is insufficient. Phase image series has one through-plane flow and 2 in-plane flow (vertical

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Keiichi Itatani and Katsu Takenaka

and horizontal flow) images. PC MRI does not require contrast medium. Using PC MRI, the blood flow field can be visualized as velocity vectors, a process termed phase velocity mapping. In PC MRI, magnitude images depict the vessel geometry and phase images depict the blood flow velocity distribution. Recent development of MRI machines has enabled multi-slice phase velocity mapping. The accumulation of multiple slices by PC MRI, to determine a time-resolved three-dimensional blood flow field is term ―Four Dimensional flow MRI (4D Flow MRI)‖.

Figure 1.17. Echo PIV images of a human LV reported by Hong et al. 2008. During ejection (A to C), the direction of the contrast-vector flow was from LV apex to LV outflow tract. After the aortic valve closure, in the early isovolumic relaxation (IVR) period, the direction of flow reversed from LV base to apex. During mid-late IVR period (E and F), the nonvertical columnar flow was seen directed from base to apex (early ejection: 16 ms after aortic valve opening (A); mid-ejection: 118 ms after aortic valve opening (B); late ejection: 245 ms after aortic valve opening (C); IVR: 32 ms, 80 ms, and 112 ms after aortic valve closure (D to F).

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25

4D Flow MRI is based on in vivo actual measurement, and requires no assumptions in reconstructing flow. However, because 4D Flow MRI is a comparatively new flow visualization modality, and post-processing and data acquisition methods for simple postprocessing have not yet been completely demonstrated, several case reports with impressive images have recently emerged, but large cohort observation studies have yet to be conducted. Figure 1.16 illustrates the application of 4D flow analysis to blood flow analysis in aortic disease. Analysis of blood flow in chronic aortic dissection may help predict the prognosis of false lumen from the blood flow feature. In applications other than aortic disease, Eriksson et al. 2013 performed pathline analysis in the LV of a DCM patient, and in a normal control, and described that in the DCM case, a higher percentage of the blood flowing from the left atrium stayed within the LV even after one cardiac contraction cycle, compared with the normal control. However, current 4D flow MRI has several limitations including poor spatial and temporal resolutions, insufficient imaging contrast, low signal to noise ratio, need to control breathing, and dependency on complicated post-processing (Figure 1.15). Regarding the resolution of the 4D flow MRI, the spatial resolution is 1.0 - 3.5 mm, unsuitable for calculating hemodynamic parameters defined by spatial differentials that are described later. The frame rate is approximately 10-30. This value is rather coarse and insufficient for the capture of the peak systolic flow in the aorta or peak diastolic filling of the LV. When the fine temporal resolutions in CFD are considered, Courant-Friedrichs-Levy conditions (1.33), the relative coarseness of MRI temporal resolution becomes apparent.

1.4.4. Flow Visualization with Echocardiography When compared with MRI, echocardiography is a portable tool, and has higher spatial and temporal resolution. Flow visualization with echocardiography is currently based on 2D imaging. Currently, echocardiography flow visualization is largely classified into two groups: B-mode image based methods and color Doppler based methods. Echo-PIV (particle imaging velocimetry), first reported experimentally by Kim et al. 2004 and utilized clinically by Hong et al. 2008, is a representative B-mode image based method, that traces a speckle pattern of small particles filling the chamber using intravenous contrast medium. It is an application of optical PIV (Particle Imaging Velocimetry), a well-known principle allowing the velocity and direction of fluid streams to be determined by tracing small particles. In Echo-PIV, intravenous contrast medium is used to trace small particles in the LV (Figure 1.17). It is commercialized by Siemens Medical Solutions. Clinical application studies of Echo-PIV have been reported including in post mitral valve surgery, and post myocardial infarction. Technically improvements are also reported to visualize 3D vortex flow by combining multiplane measurements. The accuracy of the Echo-PIV system has been validated with moving phantoms. Prinz C et al. 2012, demonstrated velocity estimation with Echo-PIV is accurate up to a velocity around 40 cm/s, not always a sufficiently high value when intraventricular flow velocity field measurement is necessary. Another B-mode based visualization method is Bflow (Figure 1.18) commercialized by GE Healthcare. The B-flow technique uses digitally encoded sonographic technology to suppress tissue clutter and can improve sensitivity for the direct visualization of blood reflectors in gray scale. Because this method is based on high frame rate B-mode images, it has been widely applied even to the small-size vessel flow, including that in fetal congenital heart disease, and hepatic vessels, and abdominal visceral

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Keiichi Itatani and Katsu Takenaka

flow. However, this method does not provide the flow velocity field, or provide hemodynamic parameters derived from flow velocity fields. The oldest flow visualization using echocardiography is the Color Doppler based flow visualization method first reported by Ohtsuki et al. 2006. Their principle is based on the division of flow into basal flow and vortex, defined by the integral of the stream function calculated using color Doppler data toward the azimuthal direction. Their methods was initially termed ―Echodynamography‖, and later a commercial package software was released from Hitachi-Aloka Medical, where the velocity vector estimation method was named ―Vector Flow Mapping (VFM)‖. This method was numerically validated with reasonable accuracy (Uejima et al. 2010); however, a theoretical problem was detected. First the stream function was integrated without boundary condition, and did not satisfy non-slip wall conditions. Second, division of basal and vortex flow was non-unique. Garcia et al. 2011. reported a novel color Doppler based flow visualization method based on the integral of the continuity equation, whose boundary conditions were given by wall motion tracking. Their method overcame theoretical weak points of VFM. Itatani et al. 2013. modified Garcia‘s vector estimation method in weight function of the two solutions of the azimuthal velocity obtained by the bilateral wall boundaries. Their method was developed to calculate hemodynamic parameters based on the differential of velocity fields, and Hitachi-Aloka medical updated VFM by adopting their algorism (Figure 1.19). Clinical applications of VFM have begun to be reported. Honda et al. 2014 presented a case of intra-cardiac repair of Tetralogy of Fallot, which has the post-stenotic dilatation with pulmonary valve stenosis due to fused commissures. In this case, following commissurotomy to relieve pulmonary stenosis, flow EL in the right ventricular outflow tract (RVOT) and main pulmonary prominently was reduced. Because this system enables estimation of hemodynamic parameters related to flow energy, a few researchers have used this method to investigate the pathophysiology of diastolic dysfunction. Nogami et al. 2014 revealed the role of the diastolic flow kinetic energy index in diastolic sucking functions. Currently, VFM has several limitations. First, because they are based on the 2D continuity equation, the measurement plane should detect main dominant flow. Not through plane flow, but its spatial differential that disturbs 2D assumption of the continuity equation, thus highly distorted 3 dimensional flow is not suitable in VFM analysis. The second limitation is the echo window. Because it requires bilateral wall boundaries, echo-window should cover the whole heart structure. The biggest limitation of the color Doppler dependent VFM is the Nykist limit. Current VFM manually collects the aliasing flow, but highly aliased color flow mapping cannot be corrected. Current VFM cannot always deal with diseased jet flow in a heart valve case. Another reported flow visualization method using the color Doppler method is Doppler vortography, a unique method of vortex detection based on the red and blue color Doppler mapping pattern. Mehregan et al. 2014 validated this method with in-vitro PIV and compared vorticity derived from vortography with that derived from VFM. Because their method does not rely on information regarding boundary tracking, it‘s the clinical application may be challenging in dilated large LV where the wall edge may be difficult to detect in a single echo window.

Historical and Current Role of Hemodynamic Research

27

Figure 1.18. B-flow image of carotid artery flow. http://www3.gehealthcare.com.

Figure 1.19. Normal LV flow visualized with the VFM (vector flow mapping) in the apical long axis view. VFM can visualize blood flow with hemodynamic parameter including vorticity, flow energy loss. During systole a clockwise flow in the basal portion of the LV facilitate the smooth outflow flow energy dissipation inside the vortex is small. During diastole, two opposite directed vortices are formed beneath the anterior and posterior leaflets of the mitral valve. The vortex beneath the posterior leaflet gradually decreases in size and finally disappears, whereas the vortex beneath the anterior mitral leaflet propagates to the apex and gradually increases in size, and flow energy loss gradually decreases, preserving energy for the preparation of the efficient ejection.

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Keiichi Itatani and Katsu Takenaka

Figure 1.20. Intraventricular pressure difference or gradient (IVPD or IVPG) based on the color Mmode image. A: color M-mode image with corrected aliasing. B: surface mapping of pressure during diastole.

1.4.5. Pressure Estimation Method with Echocardiography Greenberg et al. 2001 reported a novel concept of ―Intraventriuclar Pressure Difference (IVPD)‖ or ―Intraventricular Pressure Gradient (IVPG)‖ by solving the Euler equation based on M-mode color Doppler imaging during the diastolic filling phase (Figure 1.20). The Euler equation is a modification of the Naiver-Stokes equation without the viscous dissipation term. ⃗

(⃗

)⃗ –

(1.28)

In their assumption, the M-mode should coincide with the centerline of the diastolic filling flow; thus, the flow direction is one-dimensional, and the equation (1.28) can be changed into one dimension from the basal to the apical portion of the LV. (

)

(

)

(

)

(1.29)

Historical and Current Role of Hemodynamic Research

29

Because color M-mode describes the flow velocity distribution with depth (x) and time (t), its partial differential with space (x) and time (t) can be easily calculated with the original color M-mode image. Thus, the pressure difference can be obtained (1.30) As much as the assumption that the flow streamline coincides with the M-mode beam line is applicable, the pressure distribution can be estimated using this method. This method represents a simple and powerful method for the estimation of pressure change and distribution, because the color M-mode has sufficiently high temporal resolution. IVPD has recently attracted attention, because it is closely related to the diastolic sacking force and may provide information regarding the cause of diastolic heart failure (Rovner et al. 2005). Chapter 7 will describe the relationship between IVPD generated by the diastolic sucking force and diastolic heart functions.

1.5. ESSENTIAL INDICES FOR HEMODYNAMIC RESEARCH 1.5.1. Swirling Flow Indices: Vorticity, Circulation and Helicity In the vortex flow evaluation, swirling flow direction and strength should be visualized and estimated. One of the traditional and famous parameters is ―vorticity‖ ω. (⃗ )

⃗

⃗

(1.31)

In 3D Euclidian coordinates, Vorticity ω components are described as follows. ⃗

.

In a 2D flow, in which uz = 0,

/

(1.32)

, ω becomes a scalar (Z component).

, and

(1.33) In a 2D vortex, a clockwise vortex has negative vorticity, whereas a counterclockwise vortex has positive vorticity (Figure 1.21A). Vorticity is a parameter used to evaluate local swirling flow strength microscopically; however, the vorticity does not directly provide information regarding macroscopic vortex flow. Circulation is a parameter used to define the rotational speed of a closed loop C. ∮ ⃗

(1.34)

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Keiichi Itatani and Katsu Takenaka

Figure 1.21. Hemodynamic indices in a combined pipe. Symmetrical vortices are formed in a larger pipe. A: streamline and vorticity. Counterclockwise and clockwise vortices are formed in a larger pipe in the left and right portion, respectively B: High wall shear stress (WSS) are detected around the center of the vortices. Almost zero WSS is found at the top of the vortex, where vertical flow to the wall dose not shear neither upwardly or downwardly. C: Flow energy loss is high inside the vortices, but small in the laminar flow.

If Green‘s theorem is applied to a region D bounded with closed loop C, Circulation becomes ∬

(⃗ ) ⃗

∬ ⃗

⃗

(1.35)

where dA indicates area incremental. Thus, circulation is the surface integral of the vorticity inside a region D. Vortex flow structures in the human LV are believed to facilitate smooth diastolic filling (Martínez-Legazpi et al. 2014) or smooth ejection toward outflow (Itatani K. 2014); thus, swirling flow characteristics are believed to be important underlying mechanisms of ventricular failure. Total swirling strength of a 3D region Ω is defined as Enstrophy. ∫ |⃗ |

(1.36)

Enstrophy is a useful parameter used to provide information regarding the structure of the turbulence, and is often discussed in relation to kinetic energy. ∫ |⃗ |

(1.37)

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Historical and Current Role of Hemodynamic Research

Figure 1.22. Image of the helical flow and helicity. A: Low helicity flow with well-aligned swirling streamlines. B: High helicity disturbed flow.

Another parameter to evaluate complicated helical flow structure is Helicity H. ∫ ⃗

⃗

(1.38)

Helicty (Figure 1.22) refers to the tangle or torsion of the flow stream, whereas enstrophy refers to accumulated swirling strength. As with flow energy, helicity is also a conservative quantity that dissipates with viscous dissipation. Figure 1.22 illustrates examples of high and low helicity flow. A well-aligned swirling vortex ring has low helicity, whereas a turbulent helical flow with a complicated tangle streamline has a high absolute helicity value. We describe the theoretical background of helicity briefly in Appendix 1.A.2, and explain that helicity indicates the cross-linking number of the streamlines. Application of these indices relating to vortex or swirling flow in the evaluation of hemodynamics of the aortic flow following aortic valve or aortic root surgery was reported by von Knobelsdorff-Brenkenhoff et al.2014 (Figure 1.23). As a curved pipe, aortic flow has secondary vortex flow inside the arch, resulting in swirling helical flow. This study evaluated vorticity and helicity of the aortic flow based on 4D flow MRI.

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Figure 1.23. Visualization of the blood flow in the ascending aortic using streamlines during peak systole presented by von Knobelsdorff-Brenkenhoff et al. 2014: A: Healthy volunteer with cohesive systolic streamlines with mild helical (a) and no vortical (b) flow. B: Two exemplary cases with AVR, who exhibited helical (a) and vortical (b) flow each graded as severe. a) A mechanical prosthesis (St. Jude Medical 21); b) a stented bioprostheses (Medtronic Freestyle 25). The helical flow is shown in a transverse cut plane, whereas the vortex is shown in a sagittal cut plane.

Figure 1.24. Basic concept of WSS (or ESS). Near wall flow profile vertical to the wall surface is necessary to determine WSS.

1.5.2. Wall Shear Stress (WSS) and Its Related Parameters Wall shear stress (WSS) or endothelial shear stress (ESS), is a shear force applied to the endothelial tissues of the cardiovascular lumen. The basic concept of WSS is illustrated in Figure 1.24, and WSS is determined by the velocity profile near the wall. A high degree of WSS on a plaque promotes plaque rupture, whereas a low degree of WSS is believed to

Historical and Current Role of Hemodynamic Research

33

accelerate plaque progression due to lipid accumulation. Physically, WSS is shear stress on the vessel wall. Shear stress is a tensor and in a Newtonian fluid, is expressed as follows with strain deformation tensor. (

)

(1.39)

Thus, WSS can be expressed in vector form with surface normal vector ⃗ . ⃗⃗⃗⃗⃗⃗⃗⃗⃗

⃗

(1.40)

Figure 1.25. VFM flow analysis of a normal and severe AR (aortic regurgitation) patient. A: color Doppler image during mid-diastole. Regurgitation jet is observed in the severe AR patient. B: Diastolic flow with flow EL with viscous dissipation. In the severe AR patient, regurgitation jet dissipated flow energy, and secondary turbulent flow in the apical portion also causes flow EL. C: EL plot inside the LV in one cardiac cycle.

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Keiichi Itatani and Katsu Takenaka

Figure 1.26. Blood flow and flow EL with viscous dissipation of a dilated cardiomyopathy case presented by Nabeta et al. 2015. Before the medication, LV inflow showed a large vortex during diastole. Inside the well-organized vortex, flow dissipated small EL, but around the vortex, EL was prominently high (A–D). After the medication, the size of vortex during diastole decreased, and located in the basal portion, and the vortex facilitated the smooth outflow. Energy loss in this improved LV was significantly low especially in the mid and apical portion (E–H). Total EL during one cardiac cycle reduced from 0.403 to 0.322 W/m (I and J).

A high degree of WSS is reported to cause plaque rupture in acute myocardial infarction patients (Fukumoto et al. 2008), whereas a low degree of WSS causes plaque progression (Chatzizisis et al. 2008). The fluctuation of WSS is also important. Oscillatory shear index (OSI) is a parameter of the WSS direction fluctuation in one cardiac cycle and defined as follows. (

|∫ ⃗⃗⃗⃗⃗⃗⃗⃗⃗ ∫ |⃗⃗⃗⃗⃗⃗⃗⃗⃗ |

|

)

(1.41)

A high OSI indicates highly fluctuating WSS, whereas a low OSI indicates unidirectional WSS. From basic cell culture experiments (Hwang et al. 2003), oscillatory shear was shown to increase reactive oxygen production in endothelial cells compared with laminar shear. High OSI causes high reactive oxygen production in endothelial cells, resulting in fibrous tissue regeneration following endothelial injury. Other parameters related to WSS, include the TWSSG (temporal wall shear stress gradient) ⃗⃗⃗⃗⃗⃗⃗⃗⃗

and SWSSG (Spatial wall shear stress gradient)

(1.42)

Historical and Current Role of Hemodynamic Research

35

Figure 1.27. Total pressure change with a flow separation in a stenosis site (Sugawara et al.). Behind the stenosis site, velocity increases whereas the static pressure dropped. Total pressure loses as the flow separated.

√

(1.43)

where m and n are the direction of normal and tangent direction of the endothelial surface, are also well-known parameters. WSS and related parameters are markers that can be used to predict endothelial degeneration and plaque progression and/or rupture.

1.5.3. Flow Energy Loss (EL) Although hemodynamics should be based on the fluid dynamics of the circulatory system, flow and pressure measurements have several limitations particularly when measured using clinical diagnostic devices. The historical development of hemodynamic research had a substantial amount of ground to cover before describing the main focus of the fluid dynamics: blood flow velocity fields. One of the applications of the completely revealed flow dynamics is the evaluation of stenosis site with flow energy loss (EL). This term indicates that adequate pressure and flow velocity is necessary for adequate oxygen supply to peripheral tissues. The flow EL of stenosed vessels is defined as follows. ∑

.

|⃗ |

/

∑

.

|⃗ |

/

(1.44)

36

Keiichi Itatani and Katsu Takenaka This energy loss is based on the total pressure defined as follows (Figure 1.27). |⃗ |

Figure 1.28. Normal heart chambers and a single ventricle patient.

(1.45)

37

Historical and Current Role of Hemodynamic Research

The first term refers to kinetic pressure, and the second term refers to static pressure. The sum of the kinetic and static pressure is termed the total pressure, and represents the total energetic potential of the blood flow. Generally, kinetic pressure increases with flow acceleration, static pressure decreases and the total pressure remains constant even at the site of stenosis; however, with flow deceleration distal to the stenosis, kinetic pressure markedly decreases, and static pressure recovers to some extent. This phenomenon is termed ―pressure recovery‖ and total pressure decreases according to the amount of energy lost by the inefficient jet flow or vortex flow distal to the site of stenosis. The difference in pressure loss multiplied by flow Q is defined as the flow EL. Distal to the stenosis, vortex flow termed ―flow detachment‖ occurs with EL in the flow detachment. This type of EL is difficult to measure in clinical practice, because it requires simultaneous measurement of pressure and velocity distributions in inlets and outlets. However, several previous studies of heart valve disease have demonstrated that EL strongly associated with overall survival and cardiac death. For example, Garcia et al. 2000 established a novel index for the assessment of aortic stenosis based on EL measured by echocardiography, defined as follows. ( Coefficient 4 can be derived from

) .

/

(1.46)

by the unit conversion from SI units to mmHg

values commonly used in clinical practice. 4(velocity)2 termed the Euler equation in clinical practice and represents the pressure gradient (drop) at the stenosis site. Term (1.46) is the modification of this form of ―pressure gradient‖ based on the total pressure decrease. Aortic cross sectional area can be calculated from the aortic diameter, and the effective valve orifice area can be determined by direct measurement of the orifice area using B mode short-axis sections of the aortic valve in echocardiography. Bahlmann et al. 2013 demonstrated aortic stenosis with higher EL indices defined as a corrected valve orifice area based on (1.46) had lower survival after observation for several years in patients with aortic stenosis. Flow EL has been used to evaluate vessel anastomosis site in addition to the stenosis site. One of the oldest example is the Fontan procedure in congenital heart disease, where superior and inferior vena cava are anastomosed directly or with an artificial graft to the pulmonary artery to without the functional right ventricle (Figure 1.28). Because congenital heart disease involves complex anatomical anomalies, early research in this field of hemodynamics results in the development of computational modeling of the cardiovascular system. Later in Chapter 6, hemodynamic research specifically related to congenital heart disease will be discussed. Flow collision at anastomosis sites has been investigated for procedure optimization, and several numerical models have been designed and reported. Computational models evaluated the total pressure loss, or flow EL. Honda et al. 2013 performed direct measurement of the total pressure and EL in Fontan patients based on simultaneous catheter measurements of pressure and flow velocity, and demonstrated that high flow EL associated with decreased diastolic function of the single systemic ventricle in these patients. This report provides the first evidence of the clinical utility of flow EL estimation. Flow EL with viscous dissipation is illustrated in Figure 1.21C. The definition of EL with viscous dissipation is defined as follows

38

Keiichi Itatani and Katsu Takenaka ∫

(

)

(1.47)

This term can be calculated using flow velocity vector component distribution. Thus flow EL with viscous dissipation is available in flow visualization method, compared with the flow EL based on total pressure (1.45), which requires simultaneous measurement of pressure and flow velocity in all inlets and outlets. Appendix 1.A.3 explains the theoretical details. Itatani K. 2014 explained that flow EL with viscous dissipation is a marker of cardiac workload. For example, in Figure 1.29, patients with a normal LV and severe aortic regurgitation (AR) are compared. During diastole, secondary turbulent flow in the apical portion in addition to the regurgitation jet causes high flow energy dissipation, resulting in a large flow EL. Stugaard M et al. 2015 demonstrated EL increase in AR with animal experiment. Nabeta et al. 2015. examined the flow EL in a case of dilated cardiomyopathy based on PC MRI, and demonstrated that flow EL is large around large vortices in a dilated heart chamber, and that EL reduced the following effective medication therapy (Figure 1.26). Flow EL is a novel parameter allowing estimation of cardiac workload (Figure 1.29) proposed by Itatani K 2014. In a normal heart ventricle, the ventricle use a large amount of energy to efficiently eject blood, resulting in small EL. If physiological inefficient flow occurs due to a cardiovascular disease, such as myocardial disease or heart valve disease, cardiac workload increases, and ventricular function compensates for short time. However, when the workload becomes too large for the heart to tolerate, the ventricle falls into a heart failure state, where flow EL is small because the ventricle cannot generate the large energy efficiently. Traditional diagnostic parameters including ejection fraction or cardiac output are used to estimate the generated energy by the heart ventricle; however, there is a clinical need for a parameter that can quantify the loss itself not to miss the optimal timing of therapeutic interventions in cardiovascular diseases. Hayashi et al. 2015 presented a reference value of EL in LV from neonate to adults, and proved that it depends on the heart rate, age, and transmittal flow velocity.

1.6. WHAT HEMODYNAMIC RESEARCH IS AIMING TOWARD IN FUTURE Although the ―central player‖ in the fluid dynamics is the blood flow velocity distribution, the absolute pressure value has an essential and dominant function in clinical practice involving hemodynamics. Flow visualization may reveal underlying the pathophysiology of diseases, because the concept greatly differs from the traditional approach of hemodynamics, the flow visualization method needs several steps before it becomes a useful tool for revealing hemodynamics in clinical practice. One of the most important processes is the calculation of indices that predict the risk of disastrous situations. WSS and its related parameters predict risk of plaque progression or rupture risk in atherosclerotic diseases. Flow EL would be a parameter to estimate cardiac workload. In a sense, the indices obtained by flow visualization tools have utility as clinical markers based on imaging in a manner similar to blood test markers such as tumor markers, and predict the risk of catastrophic events in cardiovascular diseases.

Historical and Current Role of Hemodynamic Research

39

Figure 1.29. Clinical meaning of the energy loss estimation reported by Itatani K 2014.

Flow EL with viscous dissipation is a suitable formula for current flow visualization tools because it does not implicitly require pressure. However, the fact that no index that directly measures the cardiac work itself remains an issue. Defining cardiac work to evaluate the flow EL, pressure data and its change during one cardiac cycle are necessary, and hemodynamic research will revisit the issue of pressure estimation.

1.A. APPENDIX 1.A.1. Pipe Flow and Vascular Characteristics The theoretical background of the concept of resistance (1.20) and inertance (1.23) can be explained by Hagen-Poiseuille flow (Figure 1.A.1). In a laminar flow through a cylindrical pipe as in Figure 1.A.1, the centerline direction of the Navier-Stokes equation becomes (1.A.1) because the flow has no convective property and the convective term in equation (1.5) becomes 0. If steady flow equation (1.A.1) is assumed and rewritten with polar coordinate, equation (1.A.1) becomes .

/

.

/

(1.A.2)

40

Keiichi Itatani and Katsu Takenaka

if the polar coordinate expression of the Laplasian is used (1.A.3) and if uniform flow in the θ direction is assumed. Then, equation (1.A.2) can be integrated as follows ( )

(

)

(

)

(1.A.4)

with the following boundary conditions. (1.A.5) ( )

(1.A.6)

Thus, Hagen-Poiseuille flow has parabolic profile. Flow rate through the vessel becomes ∫ ∫

( )

∫ (

) (1.A.7)

In this situation, resistance R can be expressed as follows. (1.A.8) In non-steady flow, inertance can be derived from equation (1.A.1), by adding the transient term in equation (1.A.2) .

/

(1.A.9)

The first term is due to the resistance and the second term represents the pressure modulation with inertance. If pressure change is assumed to be the sum of the resistance and inertance components .

/

(1.A.10)

The equation leaves the inertance relation (1.A.11) This equation can be combined with the definition of flow

41

Historical and Current Role of Hemodynamic Research ∫

∫

(1.A.12)

Thus, in combination with the definition (1.A.11), inertance L in a transient pipe flow becomes (1.A.13)

1.A.2. Streamline Cross-Linking Number and Helicity Cross-linking number of two streamlines (Figure 1.A.2) can be expressed as ⃗

∬

⃗ |

(1.A.14)

⃗|

and coincides with the covering number of a unit sphere by the unit vector |

⃗

.

⃗|

The flow flux can be described by modifying the term (1.A.14) by multiplying flow volume velocity at each point of each streamline, ⃗

∬

⃗ |

(1.A.15)

⃗|

Thus, it is deformed into the following form. ∬

⃗

⃗ |

( ) ∫ ⃗⃗⃗⃗⃗⃗⃗⃗⃗

⃗|

( ) ∫ ⃗⃗⃗⃗⃗⃗⃗⃗⃗

⃗ |

⃗|

(1.A.16)

If we apply the Bio-Savart law in vortex flow, the vortex flow potential becomes (⃗ )

( ) ∫ ⃗⃗⃗⃗⃗⃗⃗⃗⃗

Figure 1.A.1. Hagen-Poiseuille flow in a cylindrical pipe.

⃗ |

⃗|

(1.A.17)

42

Keiichi Itatani and Katsu Takenaka Thus, the cross-linking number of the flux become (⃗ ) ⃗

∫

(1.A.18)

Although it is not a direct form but a potential form of helicity, the cross-linking number of streamlines is described with the potential of helicity H.

1.A.3. Definition of Flow Energy Loss In fluid flow, the energetic potential of the flow can be defined as follows. |⃗ |

|⃗ |

(1.A.19)

where e represents the internal energy, and T and S represent the temperature and entropy of the system, respectively. In this equation, we have represented the entropy of a unit volume as TS/V for convenience. When considering the circulatory system as incompressible and adiabatic, or if thermodynamic changes due to flow dynamics of the blood circulatory system are assumed to be negligible, the right hand term of the equation (1.A.19) can be simplified. |⃗ |

(1.A.20)

Flow energy is defined as the total pressure multiplied by the flow Q through the vessel structure. .

|⃗ |

/

Figure 1.A.2. Mathematical definition of the cross-link of two streamlines.

(1.A.21)

Historical and Current Role of Hemodynamic Research

43

Changes of the energy can be described as follows .

|⃗ |

/

|⃗ | /

.

(1.A.22)

The right hand side of the equation (1.A.19) is derived from the first and the second law of the thermodynamics. In an incompressible and adiabatic system, this should be simply .

|⃗ | /

(1.A.23)

The time derivative of the energy expresses energetic change .∫

|⃗ | /

(1.A.24)

where the integral is the volume integral of the concerned region. If we substitute the time derivative of the energy to the Navier-Stokes equation (1.17), (1.18), (1.21)-(1.24) (

|⃗ | )

(⃗

⃗ (⃗

).

|⃗ |

)⃗

⃗ (

/

)

(1.A.25)

where the tensor σi,j is shear stress tensor (1.44). Since the blood is incompressible, continuity equation (1.17) can be applied to (1.A.25), and we can write the first term on the right as a divergence. |⃗ | /

.

.

|⃗ |

/

(1.A.26)

If we integrate (1.A.26) over the whole volume concerned such as the vessel anastomosis site, and exchange the space integral and the time derivative with Gauss theorem and the equation of continuity (1.17), then .∫ ∫.

|⃗ |

/⃗

⃗

⃗) ⃗

∫(

|⃗ | ∑ ∫

/ (

)

(1.A.27)

where ⃗ is the vector normal to the surface (outward from the domain) and A refers to the section of the surface area and its integral is the surface integral. If we give the physiological boundary condition assuming blood vessels, ⃗

(1.A.28)

44

Keiichi Itatani and Katsu Takenaka ⃗

⃗

(1.A.29) (1.A.30)

then, ∫(

⃗) ⃗

(1.A.31)

Thus integrated energetic changes become as follows |⃗ | /

∫. ∫.

|⃗ |

/⃗

∑ ∫

⃗

(

)

(1.A.32)

If we assume the existence and uniqueness of the solution of the Navier-Stokes equation and assume pulsatile fluid flow repeats the same fluid field in every cardiac cycle, we can derive the equation below by integrating equation (1.A.32) for one cardiac cycle. ∫

∫

|⃗ |

0∫

|⃗ |

1

|⃗ |

0∫

1

(1.A.33)

)

(1.A.34)

From the equations (1.A.32) and (1.A.33) ∫

∫.

|⃗ |

/⃗

⃗

∫

∫

(

The left hand side of equation (1.A.34) is the EL calculated by the concept of the total pressure (1.A.20) and the right hand side of equation (1.A.34) refers to energy dissipation caused by confliction of the viscous fluid (Figure 1.23C).

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Marsden, AL; Vignon-Clementel, IE; Chan, FP; Feinstein, JA; Taylor, CA. Effects of exercise and respiration on hemodynamic efficiency in CFD simulations of the total cavopulmonary connection. Ann Biomed Engi., 2007, 35-2, 250-263. Martínez-Legazpi, P; Bermejo, J; Benito, Y; Yotti, R; Pérez Del Villar, C; GonzálezMansilla, A; Barrio, A; Villacorta, E; Sánchez, PL; Fernández-Avilés, F; del Álamo, JC. Contribution of the diastolic vortex ring to left ventricular filling. J Am Coll Cardiol., 2014, 64(16), 1711-21. Masters, JC; Ketner, M; Bleiweis, MS; Yoganathan, A; Lucas, CL. The effect of incorporating vessel compliance in a computational model of blood flow in a total cavopulmonary connection with caval centerline offset. J Biomech Engi, 2004, 126, 709-13. Mehregan, F; Tournoux, F; Muth, S; Pibarot, P; Rieu, R; Cloutier, G; Garcia, D. Doppler vortography: a color Doppler approach to quantification of intraventricular blood flow vortices. Ultrasound Med Biol., 2014, 40(1), 210-21. Migliavacca, F; de Leval, RM; Dubini, G; Pietrabissa, R; Fumero, R. Computational fluid dynamic simulation of cavopulmonary connections with an extracardiac lateral conduit. Med Engi Phys, 1999, 21, 187-193. Nabeta, T; Itatani, K; Miyaji, K; Ako, J. Vortex flow energy loss reflects therapeutic effect in dilated cardiomyopathy. Eur Heart J., 2014 Sep 28. pii: ehu394. [Epub ahead of print] Nogami, Y; Ishizu, T; Atsumi, A; Yamamoto, M; Kawamura, R; Seo, Y; Aonuma, K. Abnormal early diastolic intraventricular flow 'kinetic energy index' assessed by vector flow mapping in patients with elevated filling pressure. Eur Heart J Cardiovasc Imaging., 2013, 14(3), 253-60. Nogami, Y; Ishizu, T; Atsumi, A; Yamamoto, M; Nakamura, A; Machino-Ohtsuka, T; Kawamura, R; Seo, Y; Aonuma, K. Diastolic suction in heart failure: impact of left ventricular geometry, untwist, and flow mechanics. Life Sci., 2014, 102(2), 111-7. Nyrnes, SA; Løvstakken, L; Torp, H; Haugen, BO. Blood Flow Imaging—A New AngleIndependent Ultrasound Modality for the Visualization of Flow in Atrial Septal Defects in Children Echocardiography, 2007, 24(9), 975-81. Ohtsuki, S; Tanaka, M. The flow velocity distribution from the Doppler information on a plane in three-dimensional flow. J Visualization, 2006, 9, 69-82. Pekkan, K; de Zelcourt, D; Ge, L; Sotiropoulos, F; Frankes, D; Fogel, MA; Yoganathan, AP. Physics-driven CFD modeling of complex anatomical cardiovascular flows–a TCPC case study. Ann Biomed Eng., 2005, 33, 284-300. Pekkan, K; Kitajima, HD; de Zelicourt, D; Forbess, JM; Parks, WJ; Fogel, M a; Sharma, S; Kanter, KR; Frakes, D; Yoganathan, AP. Total cavopulmonary connection flow with functional left pulmonary artery stenosis: angioplasty and fenestration in vitro. Circulation., 2005, 112, 3264–71. Prinz, C; Faludi, R; Walker, A; Amzulescu, M; Gao, H; Uejima, T; Fraser, AG; Voigt, JU. Can echocardiographic particle image velocimetry correctly detect motion patterns as they occur in blood inside heart chambers? A validation study using moving phantoms. Cardiovasc Ultrasound., 2012, 10, 24. Quail, MA; Knight, DS; Steeden, JA; Taelman, L; Moledina, S; Taylor, AM; Segers, P; Coghlan, JG; Muthurangu, V. Non-Invasive Pulmonary Artery Wave Intensity Analysis in Pulmonary Hypertension. Am J Physiol Heart Circ Physiol., 2015 Feb 6, ajpheart.00480.2014. doi: 10.1152/ajpheart.00480.2014. [Epub ahead of print]

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Richter, Y; Edelman, ER. Cardiology is flow. Circulation., 2006, 113(23), 2679-82. Rovner, A; Greenberg, NL; Thomas, JD; Garcia, MJ. Relationship of diastolic intraventricular pressure gradients and aerobic capacity in patients with diastolic heart failure. Am J Physiol Heart Circ Physiol., 2005, 289(5), H2081-8. Ryu, K; Healy, TM; Ensley, AE; Sharma, S; Lucas, C; Yoganathan, AP. Importance of Accurate Geometory in the Study of the Total Cavopulmonary Connections: Computational Simulations and In Vitro Experiments Ann Biomed Engi, 2001, 29, 844453. Sengupta, PP; Pedrizetti, G; Narula, J. Multiplanar visualization of blood flow using echocardiographic particle imaging velocimetry. JACC Cardiovasc Imaging., 2012, 5(5), 566-9. Steine, K; Stugaard, M; Smiseth, O. Mechanisms of diastolic intraventricular regional pressure differences and flow in the inflow and outflow tracts. J Am Coll Cardiol., 2002, 40, 983-990. Stugaard, M; Koriyama, H; Katsuki, K; Masuda, K; Asanuma, T; Takeda, Y; Sakata, Y; Itatani, K; Nakatani, S. Energy loss in the left ventricle obtained by vector flow mapping as a new quantitative measure of severity of aortic regurgitation: a combined experimental and clinical study. Eur Heart J Cardiovasc Imaging., 2015 Mar 9. pii: jev035. [Epub ahead of print] Sugawara, M; Kajiya, F; Kitabatake, A; Matsuo, H. Blood flow in the heart and large vessels. Springer-Verlag Tokyo, 1989. Uejima, T; Koike, A; Sawada, H; Aizawa, T; Ohtsuki, S; Tanaka, M; Furukawa, T; Fraser, AG. A new echocardiography method for identifying vortex flow in the left ventricle: numerical study. Ultrasound Med Biol, 2010, 36(5), 772-88. Van Haesdock, JM; Mertens, L; Sizaire, R; Montas, G; Purnode, B; Daenen, W. Comparison by computerized numeric modeling of energy losses in different Fontan connections. Circulation, 1995, 92(Suppl II), II-322-II-326 von Knobelsdorff-Brenkenhoff, F; Trauzeddel, RF; Barker, AJ; Gruettner, H; Markl, M; Schulz-Menger, J. Blood flow characteristics in the ascending aorta after aortic valve replacement--a pilot study using 4D-flow MRI. Int J Cardiol. 2014, 170(3), 426-33. Wachsberg RH: B-flow; a non-Doppler technology for flow mapping: Early experience in the abdomen. Ultrasound., 2003, 19, 114–122. Wang, C; Pekkan, K; de Zelicourt, D; Horner, M; Parihar, A; Kulkarni, A; Yoganathan, AP. Progress in the CFD modeling of flow instabilities in anatomical total cavopulmonary connections. Ann Biomed Eng., 2007, 35-11, 1840-1856. Weskott, HP. B-flow—a new method for detecting blood flow. Ultraschall Med., 2000, 21, 59. Whitehead, KK; Pekkan, K; Kitajima, HD; Paridon, SM; Yoganathan, AP; Fogel, MA. Nonlinear power loss during exercise in single-ventricle patients after the Fontan: insights from computational fluid dynamics. Circulation., 2007, 116(11 Suppl), I165I171.

In: Advances in Hemodynamics Research Editor: Keiichi Itatani

ISBN: 978-1-63483-187-1 © 2015 Nova Science Publishers, Inc.

Chapter 2

HEMODYNAMIC ASSESSMENT AND FLOW VISUALIZATION IN ECHOCARDIOGRAPHY Hiroaki Semba and Tokuhisa Uejima* The Cardiovascular Institute, Japan

ABSTRACT Doppler echocardiography, although it is inherently a one-dimensional measurement, can provide the proper assessment of cardiovascular hemodynamics that agrees favorably with invasive direct measurements. Accordingly, the quantitative evaluation of volumetric flow, chamber pressure and vascular resistance with Doppler are now being incorporated as a major part of comprehensive echocardiographic examinations. Blood flow patterns inside the heart are closely related to the cardiac structure and function. Despite a huge challenge in the accurate display of blood streams, several ultrasoundbased approaches have been emerged for obtaining two-dimensional flow vectors and extracting flow-specific information. In this chapter, we summarize the current utility of Doppler echocardiography for the hemodynamic assessment and review the potentials of the cutting-edge methods for blood flow visualization.

Keywords: flow visualization, doppler echocardiography

2.1. HEDMODYNAMIC ASSESSMENT USING ECHOCARDIOGRAPHY Echocardiography is a powerful diagnostic tool for cardiac structure and function. It is now widely used in clinical practice as a noninvasive alternative to cardiac catheterization. This section begins with reviewing the basic principles of echocardiography, followed by discussing the recent applications of echocardiography for assessing the cardiac function.

*

Corresponding author: E-mail: t.uejima@nifty com.

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2.2. HEMODYNAMIC ASSESSMENT: PRINCIPLES OF ECHOCARDIOGRAPHY 2.2.1. Doppler Echocardiography While M-mode and two-dimensional echocardiography create ultrasonic images of the heart, Doppler echocardiography provides information on the movement of bloods and myocardial tissue. The Doppler principle is based on the ultrasound characteristics that the frequency of a wave increases as the source of the wave moves toward an observer, while the frequency of a wave decreases as the source moves away from the observer. The change in the frequency of ultrasound waves depends on the velocity of the moving targets. Doppler echocardiography exploits this principle of ―frequency shift‖ to determine velocities of the bloods or tissues to be studied. The Doppler shift is the change in the frequency between the transmitted ultrasound waves and the reflected ultrasound waves (Figure 2.1). The relation between the Doppler shift and velocity is expressed in this equation: (2.1) where F0 is the transmitted frequency, Fr is the reflected frequency, θ is the angle between the ultrasound beam and blood flow, V is the velocity of red blood cells and c is the speed of ultrasound in human body. Blood flow velocities can be obtained by solving this equation as: (2.2.)

Figure 2.1. Diagram of the Doppler shift and Bernoulli equation.

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The number ―2‖ in the above equation results from the fact that there are actually two Doppler shifts: one when the ultrasound wave sent from the transducer strikes the red blood cells, and the other when the wave reflected from the red blood cells is sent back to the transducer. And crucially, Doppler echocardiography is extremely angle-dependent. Ideally, the angle between the ultrasound beam line and the direction of blood flows should be less than 20° which results in a minimal underestimation of true flow velocity.

2.2.2. Bernoulli Equation The pressure in fluid is lowered in regions where the flow velocity is increased. This phenomenon is termed ―Bernoulli effect‖. It is based on the principle of energy conservation and can be expressed as the Bernoulli equation: (2.3) (

)

(2.4)

where P1 and P2 are the pressures at the proximal and distal locations, V1 and V2 are the velocity at the proximal and distal locations and ρ is the blood density (1.06 × 103 kg/m3) (Figure 2.1). ρgh2 and ρgh1 are similar because the two sites are close. V1 is usually low and can be ignored. Thus, the equation can be simplified as: 0

1

,

-

(2.5)

This simplified Bernoulli equation relates velocities and pressure in the flows; therefore can be applied to calculate the pressure gradient across the valves or intra-cardiac defects. It has been validated in human against direct pressure measurement with catheters.

Figure 2.2. The measurement of longitudinal strain using speckle tracking. Speckle tracking plots the strain curves on each segment of the LV myocardium as well as global curves across the whole LV.

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2.2.3. Speckle Tracking Echocardiography The strain measurements with speckle tracking is one of the recent innovative developments, providing the assessment of multidimensional mechanics of the left ventricular (LV) myocardium, including long and short axis direction and rotation. Each region of the myocardium has a unique pattern of speckles. The speckles follow the motion of the myocardium; the position of the speckles will shift from one frame to the next, as the myocardium moves. Thus, when a region (kernel) is defined in one frame, a searching algorithm will be able to recognize the area with the most similar speckle pattern in the next frame, within a predefined searching area. The spatial shift of the kernel of interest will give the displacement of the myocardium that can be translated into strain (Figure 2.2). This method has been validated against magnetic tagged resonance imaging; long axis strain measured with speckle tracking echocardiography was slightly underestimated, but correlated significantly with corresponding measurement with magnetic resonance (r = 0.87) (Amundsen et al. 2008). Notomi et al. 2005 also verified the accuracy of speckle tracking echocardiography for LV torsion measurement in comparison with tagged magnetic resonance imaging and tissue Doppler imaging; LV torsion estimated by speckle tracking well correlated with both those by tagged magnetic resonance (r = 0.93) and by the tissue Doppler (r = 0.76).

2.3. HEMODYNAMIC ASSESSMENT: THE ASSESSMENT OF LV FUNCTION 2.3.1. The Assessment of LV Systolic Function All forms of heart diseases can be associated with abnormalities of systolic function at some point in their natural history. Therefore, the assessment of LV systolic function plays a crucial role in diagnosis, medical management and prognostic prediction in cardiovascular diseases.

2.3.2. The Assessment of LV Systolic Function: LV Ejection Fraction LV ejection fraction (LVEF) is an index of LV systolic function that has been established and accepted, therefore, is the most commonly used in clinical practice. It can also implicate prognosis in heart failure. Two-dimensional echocardiography with the biplane method of disks (modified Simpson‘s rule) is currently recommended to use when measuring LVEF. However, the measurement with this method requires clear visualization of endocardial borders and can be affected by inappropriate scan images of the LV. Alternatively, threedimensional echocardiography can be more reliable, but needs further validations to see if it is accurate and robust enough to be used in the clinical setting.

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Figure 2.3. Bull‘s eye plot of strain values during the cytotoxic chemotherapy. These images demonstrate a ―bull‘s eye‖ plot of strain values for each of the myocardial segments. In a cancer patient, GLS was reduced, although LVEF was preserved, immediately after the chemotherapy; LVEF became reduced later on during follow-up. GLS is an early marker of myocardial dysfunction and can be used for therapeutic monitoring. (From Thavendiranathan P et al. J Am Coll Cardiol. 2014; 63: 2751-68, with permission).

LVEF is not intrinsically sensitive to detect early myocardial damages, because of the compensatory mechanisms involved in the LV chamber. The direct assessment of the deformation of the LV myocardium with speckle tracking echocardiography is more informative. The values of the deformation assessment in detecting subclinical diseases and identifying the risk for the adverse outcomes are discussed below.

2.3.3. The Assessment of LV Systolic Function: Global Strain LV contraction is a coordinated complex action involving longitudinal shortening, circumferential contraction and radial thickening. Strain imaging with speckle tracking allows the measurement of multidimensional myocardial mechanics and has been reported to be useful for the early detection of myocardial diseases and prognostic prediction of heart failure. There has been a large body of evidence demonstrating that global longitudinal strain (GLS) can serve as a sensitive marker of myocardial diseases. Wang et al. demonstrated that it was reduced in heart failure with preserved ejection fraction (HFPEF), whereas circumferential deformation was relatively preserved. In this type of heart failure, the endocardial layer, where myocardial fibers are aligned longitudinally, is primarily damaged from the early stage (Wang et al. 2008). GLS was able to differentiate HFPEF from normal using a cut-off value of -16% at a sensitivity of 95% and specificity of 95%. GLS shows the capability to diagnose cardiomyopathy. Butz et al. reported that GLS was helpful for differentiation of pathological from physiological LV hypertrophy (Butz et al. 2011). GLS was significantly reduced in patients with hypertrophic cardiomyopathy when compared with athletes‘ hearts and normal controls (-8.1±3.8% vs. -15.2±3.6% vs. -16.0±2.8%). A cut-off value of GLS < -10% for the diagnosis of HCM resulted in a sensitivity of 80% and a specificity of 95%.

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Previous studies have demonstrated that GLS can detect subclinical myocardial involvement in patients at risk for the development of heart failure. Nakai et al. showed that diabetic patients had a reduced GLS even with an apparently normal LV function, compared to healthy subjects (-17.6±2.6% vs. -20.8±1.8%); it could be useful for the risk stratification in asymptomatic diabetic population. Some anticancer drugs are potentially cardio-toxic so that patients receiving them need to be carefully monitored (Nakaiet al. 2009). Thavendiranathan et al. 2014 reported that the administration of anthracycline, a typical cardio-toxic anticancer drug, caused 10-20% reduction in GLS, even without a reduction in LVEF; an early fall in GLS by 10-15% during the therapy was able to prognosticate clinically relevant outcomes such as subsequent LVEF reduction or the development of symptomatic heart failure (Figure 2.3). GLS could potentially be used for monitoring the myocardial toxicity during the treatment. GLS can also predict the prognosis in various cardiovascular diseases. In heart failure with reduced ejection fraction (HFREF), GLS is more sensitive than LVEF to identify HFREF patients with major adverse cardiac events. Nahum et al. identified a cutoff value of GLS > -9% to indicate an increase in cardiovascular events with a sensitivity and specificity of 83% and 54%, respectively (Nahum et al. 2010). Bertini et al. 2012 confirmed that GLS was independently related to all-cause mortality (per 5% increase in GLS, hazard ratio = 1.69) and combined end points including all-cause mortality and heart failure hospitalization (per 5% increase in GLS, hazard ratio=1.64) in chronic ischemic cardiomyopathy. They identified the cutoff value at -11.5%. On the other hand, in HFPEF, GLS fails to predict adverse outcomes. Several studies have shown that HFPEF exhibits reduced LV functional reserve. Wang et al. indicated that this reduced functional reserve, as demonstrated by low GLS response to exercise, was significantly related to all-cause mortality and HF hospitalization in those patients (Wang et al. 2015). Low GLS during exercise with a cutoff value of 17.9% was able to discriminate the adverse events with a sensitivity of 84% and a specificity of 61%. GLS is also useful for predicting the outcomes after the surgical intervention in valvular heart diseases. Lancellotti et al. 2008 demonstrated that LV in asymptomatic degenerative mitral regurgitation exhibited a limited contractile reserve during exercise, compared to normal LVs; the exercise-induced increase in GLS of < 1.9% yielded a sensitivity of 92.3% and a specificity of 70.6% for predicting postoperative reduction in LVEF.

2.3.3.1. The assessment of LV diastolic function LV filling during diastole is a complex process governed primarily by the suction forces that LV elastic recoil / relaxation generate and by LV stiffness. This section discusses the echocardiographic assessment of the diastolic function in two components: relaxation and stiffness.

2.3.4. The Assessment of LV Diastolic Function: Relaxation Because slowed LV relaxation is one of the earliest manifestations of LV myocardial diseases, the assessment of LV relaxation is a crucial component of comprehensive evaluation of LV function. It is conventionally assessed by measuring time decay in LV pressure during the isovolumic relaxation. The time constant of the pressure decay (tau) is calculated by

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fitting the pressure curve, obtained with a high-fidelity pressure catheter, to an exponential function (Weiss et al. 1976). Although this method is appropriate for clinical researches, it is not widely used in clinical practice because of the cumbersomeness. Echocardiographic assessment of LV relaxation is traditionally based on the Doppler pattern of transmitral flow. Because it reflects the pressure gradient between the left atrium (LA) and LV, transmitral E velocity is not only related to LV relaxation, but also influenced by LA pressure. Therefore, the use of the transmitral flow patterns remains limited. Tissue Doppler imaging records systolic and diastolic velocities of the myocardium. The velocity of the mitral annular motion during early diastole (e‘), reflected by the longitudinal LV lengthening, can be measured with tissue Doppler and has been established and accepted as an accurate and robust measure of LV relaxation; it has been shown to correlate well with the direct measurement of tau, independently of LVEF (Figure 2.4) (Ommen et al. 2000). e‘ has been also shown to be unaffected to physiological loading and to be able to help differentiate a pseudo-normal from a normal transmitral flow pattern (Sohn et al. 1997). The measurement of e‘ is quite useful for clinical diagnoses. To establish a diagnosis of HFPEF, the presence of the abnormalities in diastolic function is required. Reduced e‘ is now included in the diagnostic criteria for this type of disease. Vinereanu et al. 2001 pointed out the significance of e‘ to distinguish between pathologic and physiologic LV hypertrophy; e‘ was reduced in hypertrophic cardiomyopathy and hypertensive heart disease, while it was preserved in athlete‘s heart (Vinereanu et al. 2001). e‘ can also be used to distinguish between constrictive pericarditis and restrictive cardiomyopathy; in constrictive cardiomyopathy, e‘ is augmented and E/e‘ is found to be inversely correlated with pulmonary capillary wedge pressure (PCWP) as PCWP = 36.1-1.2 × (E/e‘) (Ha et al. 2001).

Figure 2.4. Scatter plot of peak early diastolic mitral annular velocity versus time constant of relaxation. e‘ is linearly related with tau, with a better correlation in patients with reduced EF (open circle) than that in patients with preserved EF (filled circle). (From Ommen SR et al. Circulation. 2000; 102: 178894, with permission).

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Early observational studies have demonstrated that e‘ decreases with aging. Okura et al. 2009 pushed forward and revealed that the age-related impairment in LV relaxation were gender specific. In the elderly population, e‘ decreased more significantly in women than in men. These results may link to the fact that the elderly women are more common and have worse cardiovascular outcomes in patients with diastolic heart failure. The measurement of e‘ also provides prognostic implications. Wang et al. 2005 found out that e‘ adds a significant incremental value in predicting adverse cardiovascular outcomes over clinical data and standard echocardiographic parameters. The increase in e‘ by 1 cm/s was associated with 30% reduction in risk for cardiac death.

2.3.5. The Assessment of LV Diastolic Function: Stiffness LV stiffness is passive characteristics of the LV chamber that determines the LV filling during mid to late diastole. Increased stiffness is attributed to the stiffness of myocardial cells, the interstitial matrix and LV geometry. LV stiffness is characterized by the slope of LV pressure-volume relation during diastole. The relation is not linear, but rather curvilinear; therefore, diastolic pressure-volume relation is analyzed with an exponential fitting to obtain the chamber stiffness constant (LV stiffness constant) (Forrester et al. 1972). This analysis is not easy to carry out, because it requires high-fidelity pressure measurements and simultaneous volume assessment with high temporal resolution. Although noninvasive assessment of LV stiffness is much more difficult, there have been several challenges of estimating LV stiffness constant (KLV), using echocardiography. The initial series of attempts were made with use of the measurement of transmitral flow velocities and a mathematical modelling. Little et al. created a simplified model of the LA and LV chambers with the mitral valve in between as a harmonic oscillator and proposed a formula for predicting KLV (Little et al. 1995). This model indicated that the deceleration time (DT) of transmitral E wave should be proportional to the inverse square root of KLV. They have validated this formula in animal models of heart failure. Garcia et al. 2001 further verified in patients with cardiac diseases that KLV was able to predict from DT as KLV = (0.07 / DT) 2 with (measured KLV) = 1.01 × (estimated KLV) − 0.02; the prediction error was minimal, although the formula involved simplifications (Figure 2.5). Analogous approach using a mathematical modeling has been established by Lisauskas et al. 2001. They created a kinematic approximation modeling of the filling process, called the parameterized diastolic filling formalism, which accounts for both the transmitral E and A waves (Figure 2.6). It provides the unique parameters describing the characteristics of the LV chamber, namely, relaxation / viscoelastic (k) and passive / stiffness (c) parameters (Shmuylovish et al. 2006). They have validated this modeling against the direct measurement of LV stiffness in human; during early diastole, k = 220.9 × (ΔP/ΔV) + 113; during late diastole, k = 1640 × (ΔP/ΔV) − 8.40, where ΔP/ΔV is the slope of LV pressure-volume relation during diastole, that is, the LV chamber stiffness (Hall et al. 1994). They have also conducted clinical validation studies observing the effect of lifestyle modulations on the cardiac function, using this parameterized diastolic filling formalism; in patients with HFPEF, sodium restriction lowered blood pressure and improved the relaxation / viscoelastic and passive / stiffness of the LV chamber (Hummel et al. 2013); long-term caloric restriction has

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also cardiac-specific effects that ameliorate aging-associated changes in diastolic function (Meyer et al. 2006). Another attempt was made with measuring mitral A-wave transit time. LA contraction generates a pressure-velocity wave that enters the LV. The wave moves through the inflow tract and reflects off the apex toward the aortic valve. The time taken for the pressure-velocity wave to propagate through the ventricle, referred to as A-wave transit time, can be measured using pulsed-wave Doppler. Pai et al. 1994 reported that this time interval relates well to late diastolic stiffness and LVEDP measured with high-fidelity pressure catheters. The limitations to this approach include its dependence on Doppler sampling site and LV geometry.

Figure 2.5. The prediction of LV stiffness by deceleration time. There was a significantly correlation between observed stiffness constant (KLV) and quantitative prediction of KLV, using the equation: KLV_predicted = (0.07 / DT)2. (From Garcia MJ et al. Am J Physiol Heart Circ Physiol. 2001; 280: H554-61, with permission).

Figure 2.6. Parameterized diastolic filling formalism. This figure illustrates sequence of steps in the calculation of characteristics of the LV filling using a parameterized diastolic filling formalism: (A) A digital transmitral Doppler image is acquired, (B) diastolic interval of interest is selected, (C) maximum velocity envelope is identified, and (D) the envelope is smoothed with a fitting method. This method gives relaxation/viscoelastic (c) and stiffness (k) parameters. (From Lisauskas JB et al. J Appl Physiol 2001; 91: 154-62, with permission).

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Estimating LV stiffness also provides prognostic significance. Akkan et al. 2008 have reported that increased LV stiffness, as evidenced by a shortened deceleration time, during hospitalization is an ominous prognostic sign, independent of LV systolic function, in a heterogeneous population of symptomatic heart failure.

2.3.6. The Estimation of LV Filling Pressure The determination of LV filling pressure is important in patient management in heart failure. In clinical setting, echocardiography is the most widely used to estimate filling pressures noninvasively. LV filling pressure can be appreciated by the combined assessment of transmitral flow profile and mitral annular velocities. Transmitral E wave velocity is directly influenced by the LA pressure and inversely altered by the change in the time constant of relaxation. On the other hand, the early diastolic velocity of the mitral annulus (e‘) measured with tissue Doppler behaves as a preload-independent index of LV relaxation. Transmitral E wave velocity corrected for the influence of relaxation, i.e. E/e‘, is supposed to yield an estimate of LV filling pressure. Nagueh et al. 1997verified a linear relationship between E/e‘ and PCWP as PCWP = 1.9 + 1.24 × (E/e‘); Ommen confirmed that a cut-off value of E/e‘ ratio >10 had a predictive accuracy of 71%; E/e‘ ratio of > 15 is highly correlated with PCWP of > 20 mmHg (64% positive predictive value), while an E/e‘ ratio of < 8 corresponds to a normal PCWP (97% negative predictive value) (Figure 2.7) (Ommen et al. 2000). Current guidelines have included this E/e‘ as one of the key parameters for estimating LV filling pressure. However, some recent researches called attention that E/e‘ may not be reliable in predicting LV filling pressures in some cardiac conditions. Geske et al. elucidated that LV filling pressure cannot be derived accurately with E/e‘ ratio for patients with symptomatic HCM ((LA pressure) = 13.8 + 0.28 × (E/e‘), r = 0.28, p = 0.07); positive predictive values of E/e‘>15 was 44% for LA pressure > 20mm Hg, 73% for LA pressure > 15mmHg (Geske et al. 2007). Mullens showed that E/e‘ may not be reliable in predicting LV filling pressures in decompensated patients with advanced systolic heart failure in whom the LV is extensively remodeled, often with dyssynchronous wall motion; sensitivity and specificity for E/e‘ > 15 to identify a PCWP > 18mmHg were 66% and 50% (Mullens et al. 2009). In order to use E/e‘ in the therapeutic monitoring, E/e‘ needs to show accurate tracking of the changes in LV filling pressure or LA pressure within individuals as the filling pressure varies. Ritzema et al. demonstrated that single and serial measurements of E/e‘ correlated with simultaneous LA pressure; E/e‘ ≥ 15 accurately detected the elevated LA pressure (Ritzema et al. 2011). These findings support the serial use of E/e‘ to assess filling pressure in these patients. On the other hand, Bhella et al. revealed that in healthy individuals or in patients with HFPEF, the relationship between E/e‘ and PCWP is highly variable, with a linear regression slope within an individual subject ranging from negative to positive, suggesting that E/e‘ is not reliable to use for monitoring in these patients (Bhella et al. 2011). E/e‘ provides prognostic implications in various cardiac conditions. Several recent studies have shown that E/e‘ is highly predictive of adverse clinical events after acute myocardial infarction and in hypertensive heart disease, severe secondary mitral regurgitation, end-stage renal disease, atrial fibrillation, and cardiomyopathy (Troughton et al. 2005, Wang et al. 2003, Yamamoto et al. 2003).

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Figure 2.7. The LV diastolic pressure by septal E/E′. LV diastolic pressure increases along with the increase in E/e‘. Open and filled circles denote patients with EF 50%, respectively. (From Ommen SR et al. Circulation. 2000; 102: 1788-94, with permission).

2.3.7. Ventricular-Arterial Coupling LV end-systolic elastance (Ees) is a major determinant of cardiac systolic function. The direct assessment of Ees requires simultaneous measurement of LV pressure and volume. Chen et al. has recently proposed a noninvasive approach for estimating Ees without loading interventions (Chen et al. 2001). It employs systolic and diastolic arm-cuff pressures (Ps and Pd), stroke volume measured with Doppler (SV) and a normalized ventricular elastance at arterial end-diastole estimated from a group-averaged value adjusted for individual contractile/loading effects (ENd); Ees can be estimated as Ees = [Pd - (ENd × Ps × 0.9)] / (ENd × SV). Chen et al. have validated this equation; (measured Ees) = 0.86 × (estimated Ees) + 0.40, r = 0.91) Effective arterial elastance (Ea) is also an important counterpart and can be approximated as Ea = 0.9 × Ps / SV; Kelly et al. have demonstrated the accuracy of this approximation ((measured Ea) = 1.0 × (estimated Ea) + 0.11, r = 0.97) (Kelly et al. 1992). These approaches would enhance large-scale clinical researches on the ventriculararterial coupling in heart failure. Ky et al. have disclosed that the ventricular-arterial coupling was associated with symptoms and outcomes in HFREF (Ky et al. 2013); Ees/Ea, an indicator of the ventricular-arterial coupling, increased as heart failure symptoms, as graded by NYHA functional classification, worsened (median value; class I, 1.55; class II, 1.80; class III, 2.10; class IV, 2.46). Ea/Ees was also associated with adverse clinical outcomes in unadjusted (hazard ratio = 2.6) and fully adjusted (hazard ratio = 2.1) models, with a greater than 2-fold increased risk of adverse outcomes in patients in the highest quartile compared with the lowest; Ees alone was not associated either with symptoms or outcomes. On the other hand, in HFREF, Lam et al. 2007 revealed that both Ees and Ea increased, but the ratio stayed the

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same with that in normal and hypertensive subjects. It indicates that arterial stiffening is accompanied by LV stiffening, but the both are coupled. Burke et al. 2014 demonstrated that Ea/Ees was not associated with adverse outcomes (in the unadjusted model: hazard ratio = 1.09; in the adjusted model: hazard ratio = 1.06).

2.4. FLOW VISUALIZATION USING ECHOCARDIOGRAPHY 2.4.1. Methodologies There have been many technological developments in imaging blood streams, using ultrasound. Because of the high spatio-temporal resolution and easy applicability, these imaging techniques are expected to be incorporated into clinical researches as well as clinical routines. Recent advancements in this field are reviewed here.

2.4.2. Color Doppler Based Methods Color Doppler ultrasound produces flow maps superimposed onto corresponding B-mode images. It utilizes multi-gated pulsed wave Doppler and measures a mean velocity at a given point in an area of interest (Omoto et al. 1984). In clinical practice, however, it has been used not for measuring flow velocities, but for capturing abnormal flow patterns and turbulences, mainly in valvular heart diseases. Because it measures only axial velocities along the line of each ultrasound beam, it is not possible to measure the direction of flows, therefore, to demonstrate blood streams inside the cardiovascular system. Several attempts have been made to create more accurate flow images, using color Doppler.

Figure 2.8. The working principle of crossed-beam Doppler. The transducer has three apertures. The apertures on the both side receive ultrasound waves which the central aperture transmits and measure a velocity along each beam line. The vector is obtained by summing the two velocity components.

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2.4.3. Color Doppler Based Methods: Cross-Beam Doppler The first method proposed is crossed-beam Doppler or vector Doppler (Dunmire et al. 2000). This technique is a simple extension of one dimensional Doppler. Combining two Doppler measurements taken from different directions by triangulation makes two dimensional flow vectors (Figure 2.8). Crossed-beam Doppler typically uses a linear array transducer with 3 sub-apertures. The central aperture acts as a transmitter and two lateral apertures act as receivers. Its application is limited to vascular examination, because the width of the transducer limits the depth at which velocities can be measured. Crossed-beam Doppler has been proven to work in simple phantoms, although there is residual angle dependence in the measurement (Kripfagans et al. 2006, Ricci et al. 2009, Steel et al. 2004). Some underestimations are evident when flows are directed horizontally on the ultrasound images. In more complex phantom, it has been shown to capture the gross feature of flow phenomena, but also to produce some spurious vectors that make the flow images distorted (Swillens et al. 2010). This method has not yet been implemented for clinical use. The reasons for this include a lack of robustness and accuracy for complex pathological flows.

Figure 2.9. The basic principle of vector flow mapping. This method takes flow velocity datasets measured with color Doppler and wall motion datasets measured with speckle tracking as an input and maps flow vectors as well as energetics by applying the two-dimensional continuity equation (HitachiAloka version).

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2.4.4. Color Doppler Based Methods: Vector Flow Mapping An alternative method is called vector flow mapping (VFM). This method combines radial velocities measured with color Doppler with azimuthal velocities (directed at a right angle relative to the radial velocities) estimated based on the concept of mass conservation. The initial attempt to estimate the azimuthal velocities was with decomposing flows being studied into vortical flow and non-vortical flow components (Ohtsuki et al. 2006). The azimuthal velocities in each component were estimated using stream function and the resulting vectors were summed up into the final result of flow vectors. Although this method includes the decomposition process, it has been validated through numerical simulation and it is often able to delineate the main features of intra-cardiac flows (Uejima et al. 2010). More recently, another approach without any decomposition process has been proposed (Figure 2.9) (Garcia et al. 2010, Itatani et al. 2013). The new method estimates the azimuthal velocities from pixel to pixel in such a way that the flow field must satisfy the continuity equation (mass conservation). The myocardial velocities measured with speckle tracking are taken into account as boundary condition. This approach as well as the initial attempt involves a planar assumption, i.e., ignores through-plane flows in the third dimension, and because of that, the estimation errors in the azimuthal velocities, which accumulate during the pixel-by-pixel calculations, need to be corrected by a simple linear or weighted function at the end of the calculations. Although this approach relies on the planar assumption, it has been proven to work in the experimental validation against optical particle image velocimetry; the error was around 15-20% for the whole velocity vectors, but the large-scale patterns of flow streams were accurately captured. In the comparisons with phase contrast magnetic resonance imaging, the error was also found to be also around 15-20% for healthy subjects and patients with a dilated LV (Garcia et al. 2010). Currently, VFM is being developed independently by two groups across the world, each of whom provides their unique quantification tool for intra-cardiac flows. Itatani et al. 2013 in collaboration with Hitach-Aloka are commercially distributing the software not only for depicting blood flow directions and streamlines and measuring the size and intensity of vortices, but for quantifying energy that is dissipated by viscous friction. The energy dissipation increases when flows become unstable and turbulent. Previous studies have indicated that physiological intra-cardiac flows form optimal vortices and avoid excessive energy dissipation, whereas maladaptation is associated with disrupted and unorganized intracardiac flows, resulting in the increased energy dissipation (Pedrizzetti et al. 2005). Therefore, measuring the energy dissipation could provide an insight into the cardiac adaptive remodeling. VFM can also offer an opportunity to measure intra-cardiac pressure difference. Although it underestimates the pressure difference compared to the conventional color Mmode based assessment, it can assess two-dimensional distribution of pressure difference that could give additional information on the pathophysiology of heart diseases. On the other hand, Garcia and Bermejo et al. 2014 have also created the software that can characterize vortex formation and furthermore assess the contribution of the vortex to blood transport (Figure 2.10) (Martinez-Legazpi et al. 2014). This assessment can clarify the role of vortex formation on the blood transport in the cardiac chambers. They have also established the unique tool to visualize two-dimensional flow propagation during diastole, using Lagrangian coherent structure analysis (Figure 2.11) (Hendabadi et al. 2013).This analysis enables

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qualitative and quantitative assessments of blood transport patterns and stasis in the cardiac chamber.

Figure 2.10. Extracting vortex features by vector flow mapping. Bermejo version of vector flow mapping identifies vortex with an established criterion. It can quantify the size and strength of vortices and track the center frame by frame. The panel A compares the vortex formation between dilated cardiomyopathy and normal. Larger vortices are formed inside the LV in dilated cardiomyopathy. This vector flow mapping enhances the vortex analysis by decomposing original flows into vortex and irrotational flow components, as illustrated in the panel B. (From Bermejo J et al. Am J Physiol Heart Circ Physiol. 2014; 306: H718-29 and Martínez-Legazpi P et al. J Am Coll Cardiol. 2014; 64: 1711-21, with permission).

Figure 2.11. LV filling topology illustrated by Lagrangian coherent structure. Lagrangian coherent structure revealed that two-dimensional flow propagation of LV inflows reveals two well-defined LCS that enable qualitative and quantitative assessment of the E-wave and A-wave filling topology into the LV. (From Hendabadi S et al. Ann Biomed Eng. 2013; 41: 2603-16, with permission).

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2.4.5. Color Doppler Based Methods: Blood Flow Imaging This emerging technique enhances color Doppler flow visualizations by displaying ultrasound backscatters, presumably from red blood cells, over the conventional color Doppler images (Løvstakken et al. 2006 and 2008). The backscatters create speckle patterns; their movements are expected to correspond to the direction and magnitude of the velocities in the blood flows. There has been a challenge in measuring flow vectors by tracking the speckles. Because the conventional color Doppler has a low temporal resolution that limits the speckle tracking, Lovstakken et al. has implemented the unfocused beam transmission and parallel receive beam-forming to achieve a high frame rate at around 100 frames per second. With this setup, they have successfully explored this technique in both vascular and pediatric cases (Figure 2.11) (Fadnes et al. 2014, Løvstakken et al. 2011). They demonstrated that the speckle tracking was able to depict recirculating flows and to give accurate flow measurements. This finding was confirmed by an experimental validation study in which velocities were slightly underestimated by 10-20% for both the axial and azimuthal velocity components (Swillens et al. 2010).

Figure 2.12. Flow trajectories displayed over a color Doppler image. This blood flow imaging intuitively illustrates that flows across the defect form a counter-clockwise vortex in the right ventricle in a baby with ventricular septal defect. (Image courtesy of Professor Lasse Løvstakken at Norwegian University of Science and Technology and Dr. Siri Ann Nyrnes, St. Olavs University Hospital).

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Figure 2.13. (Panel A) Echo PIV images with color coded streamlines during early diastole (left) to systole (right) from a healthy. (Panel B) Pressure gradients inside the LV in a patient with cardiac resynchronization therapy. The activation of the pacemaker creates synchronous LV contraction, resulting in the longitudinally directed intra-ventricular pressure gradients as illustrated by the color gradient aligned in the long axis (B-1). The compass graph displays the distribution of the direction of the pressure gradient vectors. In this setting, most of the vectors are directed in the longitudinal direction (B-2). On the other hand, the deactivation of the pacemaker produces the dyssynchronous LV wall motion. This inhomogeneous contraction and relaxation produces transverse directed pressure gradient as demonstrated in the color coded pressure gradient maps and the compass graph (B-3, 4). (From Sengupta PP et al. JACC Cardiovasc Imaging. 2012; 5: 305-16 and Pedrizzetti G et al. Nat Rev Cardiol. 2014; 11: 545-53, with permission).

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2.4.6. B-Mode Based Method B-mode ultrasound images the structure of the heart, but it cannot display blood flows inside the heart unless there is a spontaneous echocardiographic contrast that gives an opportunistic chance to visualize flow patterns. In a series of clinical studies, Sengupta et al. 2007 and Hong et al. 2008. used contrast agents to pacify the cardiac chamber and track blood flows. This method is called echo particle image velocimetry (echo-PIV) (Figure 2.13). Echo PIV does not track an individual bubble, but rather tracks the image patterns created by bubbles; the image patterns are tracked frame by frame using cross-correlation and the displacement data are translated into vectors. Theoretically, there should be an upper limit of velocity measurement which depends on the frame rate and the size of the interrogation window of the tracking. The limit of the measurement was verified in an experimental study using a simple phantom in which it was found that high velocities of over 60 cm/s were underestimated (Prinz et al. 2012). A computer-assisted validation using synthetic ultrasound datasets has revealed that in the pixel-by-pixel comparison between velocities measured with echo-PIV and corresponding original true velocities, there was no correlation at peak early and peak late diastole when the intra-cardiac flows ran fast, whereas there was a significant correlation during the other phases with slow intra-cardiac flows (Gao et al. 2012). However, echo-PIV was able to demonstrate similar flow patterns as the original synthetic flows throughout the cardiac cycle. Echo-PIV has been further validated in vitro against optical particle image velocimetry in a cardiac phantom (Kheradvar et al. 2010); it was able to create comparable, although slightly distorted, flow images to optical particle image velocimetry. The small-scale features of the flows were not accurately displayed because of the spatial resolution of current ultrasound imaging. The main advantage of this echo-PIV over color Doppler based methods is a high temporal resolution. It can characterize the flow sequences well for the phases of the cardiac cycle, even in the brief intervals of isovolumic contraction and relaxation (Sengupta et al. 2007). Echo-PIV provides the unique characterization of intra-cardiac flows, using Fourier analysis. It decomposes the time-dependent flows into steady-streaming and fluctuating components; the steady-streaming component represents a fingerprint of the intra-cardiac flows over the whole cardiac cycle, while the fluctuating component represents the timevarying feature created by the filling and ejection of the LV (Hong et al. 2008). It also quantifies energetic properties of flows, including the kinetic energy and energy dissipation (Agati et al. 2014). The clinical implications of evaluating the energy dissipation are discussed in the VFM section. It also plots the direction of flow thrusts estimated from vector datasets measured with echo-PIV, by solving a Navier-Stokes equation (Pedrizzetti et al. 2014). Healthy ventricles normally exhibit apex-to-base alignment, while dis-coordinated wall motion creates transverse oriented thrusts as easily imagined (Figure 2.13). This plot may have clinical relevance when assessing mechanical dyssynchrony and the therapeutic intervention for it.

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2.5. CLINICAL STUDIES ON THE INTRA-CARDIAC FLOWS Over the last decade, the ultrasound based methods for imaging blood streams have been emerged as a clinical research tool and been extensively explored in the clinical setting.

2.5.1. Heart Failure Analyzing intra-cardiac flow dynamics would provide incremental diagnostic and prognostic values over the conventional assessment of the cardiac chambers, as previous clinical studies suggested. Nogami et al. 2014 investigated an energetic aspect of flows inside the LV with heart failure, using VFM. They revealed that the timing of flow energy transfer from the base to the apex was delayed, although the amount of the energy transfer was similar, in the LV with elevated filling pressure, compared to the LV with normal filling pressure; the delay in energy transfer was associated with the LV spherical remodeling and reduced untwisting rate. These alterations in the energy transfer seemed to be reflected by reduced propagation velocity of the LV inflow. They also illustrated that there was a flow directed toward the apex in the apical region just before the mitral valve opening which seems to be generated by the LV suction force. The kinetic energy of this flow quantified with VFM was correlated with the untwisting rate, ellipsoidal LV geometry, LVEF and LV end-systolic volume. The transition from diastole to systole is not a mere shift between the two distinct phases, but rather a continuous process in which intra-cardiac flows form vortices which help redirect flows toward the outflow tract. This smooth flow transition may contribute to the pump efficiency. Abe et al. characterized the vortex sequence from the late diastole to isovolumic contraction, using echo-PIV (Figure 2.14) (Abe et al. 2013). The vortex strength was augmented during the phase in normal subjects, while it stayed the same in HFREF. The augmentation was correlated with LV longitudinal strain; low augmentation was associated with adverse outcomes in heart failure. These data suggested that the persistence of vortex strength from late diastole into isovolumic contraction is a marker of the fluid continuum of the cardiac cycle and helps coupling diastole to systole without any intervening periods of hemodynamic stasis.

2.5.2. Dilated Cardiomyopathy Previous studies have demonstrated that in dilated cardiomyopathy, there form large vortices inside the LV which may help optimize the efficiency and mix blood. Bermejo et al. characterized the LV vortex in those patients, using VFM (Bermejo et al. 2014). The features of the main vortex showed a biphasic time course during diastole, corresponding to the transmitral E and A waves. The vortex stored 26±20% of total kinetic energy delivered by the LV inflow. The vortex formed in dilated cardiomyopathy was larger and stronger than that formed in normal LV, even when corrected for the LV size. This vortex formation helped reduce convective pressure losses and facilitate blood transport. Martínez-Legazpi et al. 2014 further assessed the impact of the vortex formation on the LV filling in comparison to

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hypertrophic cardiomyopathy. The vortex formation enhanced the filling blood transport by 19±8% in dilated cardiomyopathy, while only by 5±5% in hypertrophic cardiomyopathy. There was a beneficial effect of the vortex formation on the intra-LV pressure gradients in dilated cardiomyopathy; it contributed to the augmentation of the pressure gradient during rapid filling and the reduction in the pressure gradient reversal during slow filling. This favorable effect was not observed in hypertrophic cardiomyopathy. These two observations suggested that the diastolic filling vortex serves as a key physiological contributor of the LV filling.

2.5.3. Hypertrophic Cardiomyopathy Hypertrophic cardiomyopathy is characterized by prolonged LV relaxation and chamber stiffness due to LV hypertrophy, myocardial disarray and fibrosis. These alterations result in elevated LV filling pressure. Prinz et al. 2014 investigated flows inside the LV in a group of those patients, using echo-PIV. They found that the intra-cardiac flows were disturbed with relatively small vortex formations. Accordingly, energy dissipation was progressively increased, depending on the diastolic functional grade. However, the flow-specific parameters were not related with heart failure symptoms and exercise capacity.

Figure 2.14. The comparison of flow sequences inside the LV between healthy and heart failure subjects. The vorticity map is displayed together with flow vectors from early diastole (A) to systole (F). In a healthy subject, clockwise and counter-clockwise rotating vortices rotating clockwise and counter-clockwise forms during early diastole and the clockwise rotating vortex becomes dominant in the later phase. A flow by atrial contraction increases the strength of the vortex that persists during isovolumic contraction phase. In contrast, the vortices are attenuated during isovolumic contraction phase in a heart failure subject. (From Abe H et al. Eur Heart J Cardiovasc Imaging. 2013; 14: 1049-60, with permission).

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Early clinical studies on obstructive hypertrophic cardiomyopathy observed that the anatomical narrowing and flow acceleration in the LV outflow tract were associated with the occurrence of systolic anterior motion (SAM) of the mitral valve. From these observations, the SAM was considered attributable to the lifting by the Venturi effect and the upper septal hypertrophy was implicated as a major culprit. However, this implication cannot explain a residual SAM after septal ablation or SAM without septal hypertrophy. Ro et al. 2014 used VFM to solve this longstanding question of the mechanism of the SAM. They demonstrated that during the isovolumic contraction phase, a swirling vortex generated at the LV base pushed up the posterior leaflet of the mitral valve and moved it anteriorly. This shift in the position of the mitral valve leaflet predisposed to the occurrence of the SAM. This observation emphasizes that investigating flow phenomena inside the LV could potentially reveal the unsolved physiology of heart diseases.

2.5.4. Mitral Valve Prosthesis From the numerical simulation and experimental studies using color Doppler and magnetic resonance, it has been inferred that prosthetic mitral valves seriously disturb intracardiac flows. Faludi et al. 2010 described in vivo flow patterns past the mitral prosthesis, using echo-PIV. They demonstrated that for the bileaflet mechanical valves, each of the two major orifices generated a jet directed differently with the larger one toward the interventricular septum and the smaller one toward the lateral wall. The jet toward the interventricular septum became dominant and formed a large vortex rotating in the opposite direction from that observed in healthy subjects. This observation suggested that the mechanical valves with anatomically symmetrical orifices are functionally asymmetrical when implanted in vivo. At the beginning of systole, the bloods flowing toward the outflow tract crossed the inflow tract. For the bioprosthetic valves, the flow through the valve generated a jet directed toward the apex and formed a vortex ring, seen as a pair of vortices in both sides of the central jet in the ultrasound plane. At the beginning of systole, the posterolateral part of the vortex became dominant and the bloods flowing toward the outflow tract crossed the inflow tract as observed for the bileaflet mechanical valves. For the both prosthetic valves, the non-physiological flows inside the LV lead to less energy efficiency, as indicated by the increased spatial variation in vorticity in the flow field. Investigating the intra-cardiac flows after the valve replacement would contribute to a better understanding of the hemodynamic consequences of the surgery, thus to the therapeutic optimization.

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tracking echocardiography: correlation with diabetic duration. Eur J Echocardiogr., 2009, 10, 926-32. Nogami, Y; Ishizu, T; Atsumi, A; Yamamoto, M; Kawamura, R; Seo, Y; Aonuma K. Abnormal early diastolic intraventricular flow 'kinetic energy index' assessed by vector flow mapping in patients with elevated filling pressure. Eur Heart J Cardiovasc Imaging., 2013, 14, 253-60. Nogami, Y; Ishizu, T; Atsumi, A; Yamamoto, M; Nakamura, A; Machino-Ohtsuka, T; Kawamura, R; Seo, Y; Aonuma, K. Diastolic suction in heart failure: impact of left ventricular geometry, untwist, and flow mechanics. Life Sci., 2014, 102, 111-7. Notomi, Y; Lysyansky, P; Setser, RM; Shiota, T; Popović, ZB; Martin-Miklovic, MG; Weaver, JA; Oryszak, SJ; Greenberg, NL; White, RD; Thomas, JD. Measurement of ventricular torsion by two-dimensional ultrasound speckle tracking imaging. J Am Coll Cardiol., 2005, 45, 2034-41. Ohtsuki, S; Tanaka, M. The flow velocity distribution from the Doppler information on a plane in three-dimensional flow. Journal of Visualization., 2006, 9, 69–82. Okura, H; Takada, Y; Yamabe, A; Kubo, T; Asawa, K; Ozaki, T; Yamagishi, H; Toda, I; Yoshiyama, M; Yoshikawa, J; Yoshida, K. Age- and gender-specific changes in the left ventricular relaxation: a Doppler echocardiographic study in healthy individuals. Circ Cardiovasc Imaging., 2009, 2, 41-6. Ommen, SR; Nishimura, RA; Appleton, CP; Miller, FA; Oh, JK; Redfield, MM; Tajik, AJ. Clinical utility of Doppler echocardiography and tissue Doppler imaging in the estimation of left ventricular filling pressures: A comparative simultaneous Dopplercatheterization study. Circulation., 2000, 102, 1788-94. Omoto, R; Yokote, Y; Takamoto, S; Kyo, S; Ueda, K; Asano, H; Nakekawa, K; Kasai, C; Kondo, Y; Koyano, A: The development ofreal-time two-dimensional Doppler echocardiography and its clinical significance in acquired valvular diseases: with specific reference to the evaluation of valvular regurgitation. Jpn Heart J., 1984, 25, 325. Pai, RG; Suzuki, M; Heywood, JT; Ferry, DR; Shah PM. Mitral A velocity wave transit time to the outflow tract as a measure of left ventricular diastolic stiffness. Hemodynamic correlations in patients with coronary artery disease. Circulation. 1994, 89, 553-7. Pedrizzetti, G; Domenichini, F. Nature optimizes the swirling flow in the human left ventricle. Phys Rev Lett., 2005, 95, 108101. Pedrizzetti, G; La Canna, G; Alfieri, O; Tonti, G. The vortex--an early predictor of cardiovascular outcome? Nat Rev Cardiol., 2014, 11, 545-53. Prinz, C; Faludi, R; Walker, A; Amzulescu, M; Gao, H; Uejima, T; Fraser, AG; Voigt, JU. Can echocardiographic particle image velocimetry correctly detect motion patterns as they occur in blood inside heart chambers? A validation study using moving phantoms. Cardiovasc Ultrasound., 2012, 10, 24. Prinz, C; Lehmann, R; Brandao da Silva, D; Jurczak, B; Bitter, T; Faber, L; Horstkotte, D. Echocardiographic particle image velocimetry for the evaluation of diastolic function in hypertrophic nonobstructive cardiomyopathy. Echocardiography., 2014, 31, 886-94. Ricci, S; Diciotti, S; Francalanci, L; Tortoli, P. Accuracy and reproducibility of a novel dualbeam vector Doppler method. Ultrasound Med Biol., 2009, 35, 829-38. Ritzema, JL; Richards, AM; Crozier, IG; Frampton, CF; Melton, IC; Doughty, RN; Stewart, JT; Eigler, N; Whiting, J; Abraham, WT; Troughton, RW. Serial Doppler echocardiography and tissue Doppler imaging in the detection of elevated directly

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measured left atrial pressure in ambulant subjects with chronic heart failure. JACC Cardiovasc Imaging., 2011, 4, 927-34. Ro, R; Halpern, D; Sahn, DJ; Homel, P; Arabadjian, M; Lopresto, C; Sherrid, MV. Vector flow mapping in obstructive hypertrophic cardiomyopathy to assess the relationship of early systolic left ventricular flow and the mitral valve. J Am Coll Cardiol., 2014, 64, 1984-95. Sengupta, PP; Khandheria, BK; Korinek, J; Jahangir, A; Yoshifuku, S; Milosevic, I; Belohlavek, M. Left ventricular isovolumic flow sequence during sinus and paced rhythms: new insights from use of high-resolution Doppler and ultrasonic digital particle imaging velocimetry. J Am Coll Cardiol., 2007, 49, 899-908. Shmuylovich, L; Kovács, SJ. Load-independent index of diastolic filling: model-based derivation with in vivo validation in control and diastolic dysfunction subjects. J Appl Physiol., 2006, 101, 92-101. Sohn, DW; Chai, IH; Lee, DJ; Kim, HC; Kim, HS; Oh, BH; Lee, MM; Park, YB; Choi, YS; Seo, JD; Lee, YW. Assessment of mitral annulus velocity by Doppler tissue imaging in the evaluation of left ventricular diastolic function. J Am Coll Cardiol., 1997, 30, 474-80. Steel, R; Ramnarine, KV; Criton, A; Davidson, F; Allan, PL; Humphries, N; Routh, HF; Fish, PJ; Hoskins, PR. Angle-dependence and reproducibility of dual-beam vector doppler ultrasound in the common carotid arteries of normal volunteers. Ultrasound Med Biol., 2004, 30, 271-6. Swillens, A; Segers, P; Torp, H; Løvstakken, L. Two-dimensional blood velocity estimation with ultrasound: speckle tracking versus crossed-beam vector Doppler based on flow simulations in a carotid bifurcation model. IEEE Trans Ultrason Ferroelectr Freq Control., 2010, 57, 327-39. Thavendiranathan, P; Poulin, F; Lim, KD; Plana, JC; Woo, A; Marwick, TH. Use of myocardial strain imaging by echocardiography for the early detection of cardiotoxicity in patients during and after cancer chemotherapy: a systematic review. J Am Coll Cardiol., 2014, 63, 2751-68. Troughton, RW; Prior, DL; Frampton, CM; Nash, PJ; Pereira, JJ; Martin, M; Fogarty, A; Morehead, AJ; Starling, RC; Young, JB; Thomas, JD; Lauer, MS; Klein, AL. Usefulness of tissue doppler and color M-mode indexes of left ventricular diastolic function in predicting outcomes in systolic left ventricular heart failure (from the ADEPT study). Am J Cardiol., 2005, 96, 257-62. Uejima, T; Koike, A; Sawada, H; Aizawa, T; Ohtsuki, S; Tanaka, M; Furukawa, T; Fraser, AG. A new echocardiographic method for identifying vortex flow in the left ventricle: numerical validation. Ultrasound Med Biol., 2010, 36, 772-88. Vinereanu, D; Florescu, N; Sculthorpe, N; Tweddel, AC; Stephens, MR; Fraser, AG. Differentiation between pathologic and physiologic left ventricular hypertrophy by tissue Doppler assessment of long-axis function in patients with hypertrophic cardiomyopathy or systemic hypertension and in athletes. Am J Cardiol., 2001, 88, 53-8. Wang, J; Fang, F; Wai-Kwok Yip, G; Sanderson, JE; Feng, W; Xie, JM; Luo, XX; Lee, AP; Lam, YY. Left ventricular long-axis performance during exercise is an important prognosticator in patients with heartfailure and preserved ejection fraction. Int J Cardiol., 2015, 178, 131-5.

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Wang, J; Khoury, DS; Yue, Y; Torre-Amione, G; Nagueh, SF. Preserved left ventricular twist and circumferential deformation, but depressed longitudinal and radial deformation in patients with diastolic heart failure. Eur Heart J., 2008, 29, 1283-9. Wang, M; Yip, G; Yu, CM; Zhang, Q; Zhang, Y; Tse, D; Kong, SL; Sanderson, JE. Independent and incremental prognostic value of early mitral annulus velocity in patients with impaired left ventricular systolic function. J Am Coll Cardiol., 2005, 45, 272-7. Wang, M; Yip, GW; Wang, AY; Zhang, Y; Ho, PY; Tse, MK; Lam, PK; Sanderson, JE. Peak early diastolic mitral annulus velocity by tissue Doppler imaging adds independent and incremental prognostic value. J Am Coll Cardiol., 2003, 41, 820-6. Weiss, JL; Frederiksen, JW; Weisfeldt, ML. Hemodynamic determinants of the time-course of fall in canine left ventricular pressure. J Clin Invest., 1976, 58: 751–760. Yamamoto, T; Oki, T; Yamada, H; Tanaka, H; Ishimoto, T; Wakatsuki, T; Tabata, T; Ito, S. Prognostic value of the atrial systolic mitral annular motion velocity in patients with left ventricular systolic dysfunction. J Am Soc Echocardiogr., 2003, 16, 333-9.

In: Advances in Hemodynamics Research Editor: Keiichi Itatani

ISBN: 978-1-63483-187-1 © 2015 Nova Science Publishers, Inc.

Chapter 3

FLOW VISUALIZATION IN MAGNETIC RESONANCE IMAGING (MRI) Yasuo Takehara* and Masataka Sugiyama Department of Radiology, Hamamatsu University School of Medicine, Japan

ABSTRACT Magnetic resonance imaging (MRI) is a unique modality that allows for localization and measurements of the velocities of the moving protons. This capability to chase flowing blood protons can be exploited by electrocardiography gated 3D phase contrast MRI (4D Flow). This technique used to be time consuming; however, recently innovated MR hardware and emerging technologies have made 4D Flow performable in a reasonable period of time. Combined use of appropriate post-processing software, in-vivo assessment of the flowing blood is readily available in a 3D fashion as 3D vector fields, streamlines or pathlines. Not just depiction of the flow, the accurate velocimetry allows for quantitative assessment of the blood flow velocities and flow volume supplying to specific organs. The capability of measuring temporal changes of the velocities and locations on the whole 3D axes of the flowing protons provide us an access to new hemodynamic derivatives such as wall shear stress or oscillatory shear index. Abnormally low WSS or significantly high OSI are known to trigger atherosclerotic changes by inappropriate stimuli to the mechanoreceptors of the vascular endothelium. MR flow visualization may not merely allow for the assessment of the current vascular pathologies, but open a door to predict the future integrities of the vessels, and thereby, contribute to the preventative medicine for the cardiovascular pathologies.

Keywords: flow visualization, phase contrast magnetic resonance imaging (PC MRI), 4D flow, streamline, pathline, and wall shear stress

*

Corresponding author: E-mail: [email protected].

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3.1. BASIC CONSIDERATIONS ON FLOW AND MAGNETIC RESONSNCE 3.1.1. Basic Principle of the Magnetic Resonance (MR) Signal Although magnetic resonance is capable of measuring signal from multiple nuclei, proton magnetic resonance is mainly utilized in clinical MR (magnetic resonance). We therefore focus on the proton MR, particularly specified to water protons hereafter. MR signals can be described as functions of several properties such as water proton density, longitudinal relaxation (T1), transverse relaxation (T2), diffusivity, and velocity (i.e., flow or motion of the proton). The signal acquired with MR is a function of these parameters. ( )

(

)

(

)

( )

( )

(3.1)

Figure 3.1. A: Proton or hydrogen nucleus is positively charged. The proton is rotating or spinning. The rotating charged object creates a small magnetic moment. B: Although there are numerous rotating protons within the tissues, which are small magnetic moments, the summation of the magnetic moments is virtually null. It is because individual moments are heading randomly. C: When protons are placed in the static magnetic field (Bo), the individual magnetic moments can point up (green) or down (pink), where equilibrium direction is up. The summation of the numerous magnetic moments represented by a net magnetization vector of M0 is headed up.

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Figure 3.2. In more detailed observations, individual moments precess at Larmor frequency of ω 0 that is proportional to the strength of B0. Although their rotating frequency is the same, their randomly varied rotating phases are not synchronized; therefore, the summation of the transverse (X-Y plane) magnetic moment Mxy is zero. The net magnetic moment M0 is only longitudinal (Z-axis).

where p: proton density, T1: longitudinal relaxation time, T2: transverse relaxation time, D: diffusivity of the water protons, v: flow velocity of the water protons In this article, we focus on the ―flow‖. In the field of clinical magnetic resonance, flow refers to water proton movement within the vessels, cisterns or ventricles during the time of MR data acquisitions. Such movements refer to blood flow, CSF flow, bile flow, urinary flow, pancreatic juice flow and other flows in the body.

3.1.2. MR Measurements of the Flow Spinning protons hold magnetic moment (Figure 3.1). When they are placed in a magnetic field, they experience torque, which causes them to precess what is called Larmor precession (Figure 3.2). The precession is a wobbling motion in the magnetic field occurring at a specific frequency termed ―Larmor frequency‖. The frequency of the precession is linearly proportional to the strength of the static magnetic field. (3.2) where ω is Larmor frequency, γ is the gyromagnetic ratio, B is static magnetic field strength. The application of an alpha pulse (the RF excitation pulse) forces some coherence, creates evolving transverse magnetization and generates an MR signal when a signal detecting coils are placed in the transverse plane (Figure 3.3). The angular position of each

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protons in this precessional path at any given time is called the phase of the spin. Using a combination of the main magnetic field and additionally applied local magnetic field gradients, dephasing and rephrasing of the protons can be controlled in a specified direction. The spins are in phase simultaneously after excitation; however, as a result of this gradient of static magnetic field (Figure 3.3), it follows that precession of in-phase spins become variable along the axis of the gradient. Since the Larmor frequency is proportional to static magnetic field strength, precessional frequency rate changes depending on the spin positions; therefore, cause the moving spins to dephase (Figure 3.4). As ―flow‖ means a physical changes of the location in a certain period of time, the faster the flow, the more dephasing that occurs. Roughly, MR signal is thus dependent on the flow velocities of the protons.

Figure 3.3. A: Once radiofrequency tuned to Larmor frequency is applied to the protons, randomly varied phases of each protons are synchronized, which creates transverse magnetization. Observing this on the rotating frame, this phenomenon is expressed as flipping the net magnetization towards the X-Y plane with a flip angle of θ. B: The behavior of the net magnetization after application of radiofrequency (RF) synchronized to Larmor frequency observed outside the rotating frame. After RF irradiation at Larmor frequency is applied, net magnetization is flipped towards X-Y plane or even toward -Z axis. After RF irradiation is off, the reverse trajectory of the net magnetization follows. During this process, an antenna or coil placed on the X-Y plane emits RF. Thus the transverse component of the net magnetization can be assessed. C: Focusing on the trajectory of the transverse magnetization projected onto the X-Y plane, it will reduce in its scalar. The reason for this reduction is due to the phase dispersions of each protons. D: After the RF pulse is off, synchronization of each magnetization vectors start to precess at the rotating velocity of ω0 based on each local static magnetic field strength. ω0 of each protons are not homogeneous due to the subtle differences of static local magnetic field strength. When this phase dispersion occurs, net magnetic moment is progressively reduced. This phase dispersion is deliberately caused by bi-polar magnetic gradients in phase contrast technique.

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Figure 3.4. When additional magnetic gradient is applied in addition to the static magnetic field in X directions, protons on the right side rotate faster than the left ones. Accordingly, phase differences are created depending on the location of the protons along the X axis. Flowing protons along X axis experience this progressive increase of static magnetic field and the accelerations of the phase shifts.

To chase the movements of the water protons within the blood flow, we employ additional gradients to MR pulse sequences (Figure 3.5). The amount of dephasing is dependent on the amplitude, the polarity, and the duration of the gradient and the locations of the spins along that gradient. We can measure the velocities of the flowing blood within the vessels by manipulating the bi-polar gradients that refocus stationary water proton phases to zero. If significant dephasing occurs due to their travel on non-laminar flow, water protons in the flowing blood experience variety of magnetic field strength, the vessel lumen appears as signal void. In PC, a pair of velocity encoding gradients (VENC) in addition to the imaging gradients play the role of bi-polar gradient. VENC is sensitive to flow in one direction only. PC quantifies those spins experiencing a regional magnetic field gradient and velocity-induced phase shift, and thereby, present velocity related signal intensities in contrast to stationary background protons. The amount of phase shift will be directly proportional to the velocity of the moving protons (Jones et al. 1998). This is how PC can measure the velocity and depict the flowing blood (Yucel EK. 1993). Utilizing the appropriate VENC, PC can measure or delineate even slower flow such as venous blood flow. This is a unique characteristic of PC as compared to other MR angiographic technique (Hausmann et al. 1991). The other strength of PC as compared to other MR angiography (MRA) is that PC MRA can effectively subtract out all undesirable positive background signal such as subacute hematoma.

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Figure 3.5. The scheme of phase shifts of moving protons when traveling through an additional bi-polar magnetic gradient. Phase differences of the precessions of each protons are observed from the top. Since the precessions of the protons are proportional to static magnetic field strength, the additional magnetic gradient is accelerated by the positive magnetic gradient. The faster the protons, the more phase shift protons experience due to the local gradient of the static magnetic field. Phase contrast MRI measures this phase shift as a signal loss. The velocities of the moving protons can be calculated by the amount of phase shift.

3.2. MRI TOOLS FOR FLOW MEASUREMENTS 3.2.1. 2D Phase Contrast (PC) MRI (2D PC) In addition to the capability to measure slow flow, the other strength of 2D PC is its speed of acquisition. For instance, flow sensitive gradients can be applied in multiple directions with multiple viewing sections in only a few minutes. If thicker slab is employed, the examination time is even more shortened, because the time required for spatial encoding in the slice direction can be omitted (Figure 3.6). Due to their ability to quickly document the direction of blood flow, 2D PC is often used as a convenient adjunct to a higher resolution 3D PC acquisition. Preliminary acquisitions of 2D PC also offer the information concerning the variety of velocities within the same area of interest. The use of multiple velocity acquisitions also allows the operator to select appropriate VENC before a time consuming high resolution 3D PC acquisition is performed.

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Figure 3.6. Slice selection of 2D phase contrast image. There is no geometrical information concerning slice selective direction; however, a projection image is acquired.

One of the weaknesses of it is that PC requires relatively long TE, because it requires by the time for additional bipolar gradient. Long minimal TE may exaggerate the grade of stenosis due to the signal loss due to phase dispersion created by the jet flow. PC also requires relatively higher spatial resolutions to avoid intra-voxel phase dispersion, which may further elongate the examination time.

3.2.2. Phase Resolved 2D Phase Contrast MRI (2D Cine PC) Another important option to 2D PC is an addition of temporal resolutions, which is enabled by electrocardiographic (ECG) gating (Naidich et al. 1993). The method can be characterized by higher temporal resolutions. In order to be reconstructed as an image, a certain amount of signal to noise ratio (SNR) is needed. For this purpose, summation of signals of every periodic or cyclically repeated flow patterns enables higher SNR; however, the summation of sporadic or non-cyclic flow will result in lower SNR. Therefore, data acquisitions of the blood flow or heart beat synchronized CSF flow are realistic since resultant signal can be higher after being summed up with ECG gating. With use of ECG gating, cardiac phase resolved flow assessment is also enabled. Blood flow velocity and directions varies from systole to diastole. Such an instantaneous flow diversions may not be reflected by single phase images averaging whole cardiac cycle. Therefore, cardiac phase resolved assessment is essential for further investigation of the flow dynamics-based vascular pathologies.

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3.2.3. 3D Phase Contrast MRI Unlike 2D PC, 3D PC allows for viewing vasculatures from multiple projections with high spatial resolution. Unlike 2D PC, velocity sensitivity gradients can be employed for all 3 directions, which enable the 3D PC protocols effective for imaging areas of complex multidirectional flow (Pelc et al.). Retrospectively determined multidirectional high resolution MIP projection images are also available with 3D PC (Figure 3.7). The limitation of the 3D PC is relatively long scan times as a result of its need to flow encode in multiple directions.

Figure 3.7. 3D phase contrast image is postprocessed with use of a bundle of 2D thin sections. The image therefore holds geometrical information of the slice selective direction.

Figure 3.8. A diagram of data acquisition scheme for cardiac phase resolved 3 dimensional phase contrast magnetic resonance imaging. Three sets of velocities (Vx,V y, Vz) and magnitude data are acquired during every 4xTR (repetition time). For each repetition time (TR), a bipolar gradient is on along x (red), y (dark pink), or z (pink) axes. As a reference image for subtraction, zero gradient (light pink) image is also acquired. Scheme from Markl M, et al. 2003.

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3.2.4. Phase Resolved 3D Phase Contrast MRI (3D Cine PC, 4D-Flow) Flow dynamics occurring within the cardiovascular system is not necessarily laminar, but helical, vortex or turbulent. Four dimensional (i.e., 3 spatial axes and one temporal axis), phase contrast image has therefore been awaited to investigate this hemodynamic complexities. The pulse sequence for 4D flow data acquisition consist of a fast spoiled gradient echo sequence with VENC along all three spatial directions. Measurements were performed synchronizing to ECG gated cycle in order to generate a cine series of 3D data set (Figure 3.8). The idea of ECG gated data acquisitions for 3D PC is not a new idea; however, it was previously not realistic because of its lengthy imaging time around one hour for one data acquisition. However, recent innovations in MR hardware and sophisticated flow encoding strategies (Pelc et al. 1991) have enabled considerably shorter TEs and TRs. Parallel imagings had also strong impact on shortening the imaging time. The 4D data can be reformatted onto freely selectable sub-volumes, planes, or regions of interest (ROIs). However, the acquisitions could not be concluded under breath holding period, data acquisitions are still performed under respiratory gating or respiratory compensations.

3.2.5. Cartesian and Non-Cartesian Data Sampling for Phase Resolved 3D PC MRI As mentioned, 4D Flow is a representative technique based on phase resolved 3D PC MRI with Cartesean data sampling (Markl et al. 2003)(Figure 3.9). On the other hand, representative method employing non-Cartesean data sampling is PC-VIPR (Gu et al. 2005)(Figure 3.10). PC-VIPR is a 3D radial highly undersampled PC-MRA with high spatial resolution capable of acquiring whole volume angiograms with quantitative velocity information. The VIPR sequence samples data along radial lines evenly spaced through a spherical volume each intersecting the origin of k-space (Gu et al. 2005). The type of this trajectory is likened to a ―koosh ball‖. VIPR benefits short acquisition times, large volume coverage, and small isotropic voxels.

Figure 3.9. The scheme of Cartesean data sampling for k-space (raw data) data filling. Data lines are placed from the initial phase encoding (ky 0) step to the last (ky +128). The reconstructed image on the right is Fourier transformed using the raw data. The trajectory is an example of a centric view ordering.

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Figure 3.10. The scheme of data sampling with vastly undersampled imaging with isotropic resolution projection reconstruction magnetic resonance (VIPR) style. The style data sampling for VIPR is ―radial data sampling‖. This trajectory is similized as ―Koosh ball‖ (upper left). Unlike Cartesean data sampling, filled data lines pass through k-space center of X-Y-Z0. Since the k-space center is related to the image contrast, this style of data sampling greatly contribute to the improved image contrast.

3.3. POST-PROSESSING IN MRI FLOW VISUALIZATION 3.3.1. Post-Processing for Flow Analysis Several previously described post-processing techniques can be used to analyze and visualize the 4D Flow results, including 2D vector field plots mapped onto arbitrarily reformatted planes (Figure 3.11A,B). Several commercially available applications can noninvasively visualize in vivo blood flow patterns using 3D vector fields (arrows)(Figure 3.11C), streamlines (Figure 3.11D), and particle pathlines (Napel et al. 1992). Blood flow patterns are traced as trajectories of blood movement through the vessel, which represents appreciable portions of the total blood volume, that exists for a measurable time interval and with measurable spatial fragments and that may evolve into another pattern during the entire cardiac cycle. By analyzing data of 4D F1ow using flow analysis software, blood flow measurement of the vital organs and analysis of the blood flow directions and blood flow volume measurement into the specific vessels or grafts can be performed.

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Figure 3.11. A. Sixty-three year old male with bilateral internal iliac artery aneurysms. Flow velocity and flow measurement are available at any arbitral sections. The figure is one systolic image picked out from the 20 cardiac phases. AA: abdominal aorta, RCIA: right common iliac artery, LCIA: left common iliac artery, RIIA: right internal iliac artery, LIIA: left internal iliac artery. B: The measured time-flow volume curves are readily depicted to the cardiac phase at each perpendicular section at abdominal aorta (AA), right common iliac artery (RCIA), left common iliac artery (LCIA), right internal iliac artery (RIIA), left internal iliac artery (LIIA). C: One 3D vector field map from systole. To depict all velocity vectors within whole vascular areas of interest in each cardiac phase, 3D vector field map is helpful. Note the velocity vectors within the aneurysm and the dilated segment of the right common iliac artery are very slow even in systole. The velocity of the points are expressed as vectors. The velocity is coded as the length and the color of each vector. D: One streamline analysis from systole. There are vortex flow within the right internal iliac aneurysm and turbulent flow within the left internal iliac aneurysm at one phase in systole. The flow patterns in the other arteries are almost laminar.

3.3.2. In-Vivo Flow Visualization There are several ways of expressions to visualize flow. The representative methods are 3D vector field, streamline and pathline.

3.3.3. 3D Vector Field 3D vector field is a type of expression of flowing fluid depicting as a collection of arrows with a given magnitude (speed) and direction each attached to a points within the voxel of interest. The method allows for the overview of the moving fluid throughout the 3D space.

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3.3.4. Streamline and Pathline Image Streamlines and pathlines are field lines resulting from the 3D vector field. They differ only when the flow changes with time. When the flow is steady, streamlines and pathlines are identical. Streamlines are the connections of curves instantaneously tangent to the velocity vector of the flow. Pathlines are the trajectories that individual fluid particles follow, which can be explained as a recorded path of a fluid element in the flow over a certain period of time. The direction the path takes is determined by the streamlines of the fluid at each moment in time.

3.3.5. WSS (Wall Shear Stress) and OSI (Oscillatory Shear Stress) Wall shear stress (WSS) is a dynamic frictional force induced by Newtonian fluid with some viscosity moving across a surface of solid material (Figure 3.12A). In the velocity distribution of intravascular blood flow, the speed is high in the central region, but slow near the vascular wall, forming a velocity gradient (Shear rate). The frictional force that the vascular wall receives from the blood viscosity is WSS, presented with the following equation. (3.3) τ represents shear stress, and μ represents viscosity of the blood. v is a velocity parallel to the wall and x is a distance from the wall. 3D WSS map can be drawn if we can determine the vascular wall boundary and all the velocities of the blood flow are known in a 3D fashion (Figure 3.12B). OSI that reflects instantaneous fluctuation of WSS was calculated by temporal changes in the local WSS vector. Oscillatory shear index (OSI) is defined as (He et al. 1996). (

( ) |∫ ⃗⃗⃗⃗⃗⃗⃗⃗⃗⃗⃗⃗⃗⃗⃗⃗ ( )| ∫|⃗⃗⃗⃗⃗⃗⃗⃗⃗⃗⃗⃗⃗⃗⃗⃗

|

)

(3.4)

OSI ranges from 0 to 1/2, and a large OSI implies that instantaneous WSS vectors greatly fluctuate in relation to the main stream direction at the calculated point during 1 cardiac cycle (Figure 3.13). WSS of each cardiac and phases, OSI can be displayed as a color coded 3D vascular model. The model readily allows for 3D overviews and recognitions of the WSS and OSI of the vascular walls throughout the cardiac phase. This type of observation has never been available in this field.

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3.4. CLINICAL APPLICATIONS 3.4.1. Flow Abnormalities and Vascular Pathologies The capabilites of measurements concerning flow velocity data in time and space indicates that endothelial shear stress is measurable on the vascular wall. Although various risk factors such as hyperlipidemia, diabetes, cigarette smoking, and Marfan syndrome are related to the development and progression of vascular lesions, hemodynamic factors are also closely related. Arteriosclerotic changes frequently occur in the coronary artery bifurcations, carotid artery bifurcations and infrarenal abdominal aorta where the flow turbulence occurs. Cerebral aneurysms also have predilection sites. These facts suggest the importance of hemodynamic factors in the generations of vascular pathologies. Among hemodynamic factors, the association between vascular walls shear stress (WSS) and vascular lesions has widely been studied. Vascular endothelial cells are constantly exposed to wall shear stress generated by blood stream. Endothelial cells are known to play a role of mechanoceptors sensing and responding to shear stress (Ando et al. 1990). Endothelial cells then release substances to promote atherogenic or anti-atherogenic effect. Morphologically, a loading of an about 1.5 Pa shear stress on the vascular endothelium causes a spindle-pattern rearrangements in parallel to the flow direction. Functionally, a physiological shear stress greater than 1.5 Pa acts against arteriosclerosis through reducing vasoconstrictor production, increasing of the vasodilator and anti-oxidative enzyme production, reducing growth factor expression，increasing growth inhibitor expression，and reducing inflammatory mediator, adhesive molecule expression, thrombus formation, and epithelial growth ability. In contrast, a low shear stress below 0.4 Pa and varying shear stress direction with time due to turbulence are known to act on vascular epithelium leading to arteriosclerosis (Malec et al. 1999). Involvement of shear stress of the vascular wall in aneurysm occurrence is also suspected. It has recently been considered that vascular wall shear stress is closely related to vascular degeneration through iNOS and NO. The association of vascular wall degeneration and apoptosis of the endothelium are also seen (Ando et al. 1990, 1999, and 2013, Malek et al. 1999).

3.4.2. Clinical Relevance of Flow Analysis Using 4D Flow, we have investigated abnormal flow patterns detected within the various vessels and the heart, to date. For example, we could depict arteriovenous fistula created in the vertebral body with use of 4D Flow. Not only the shunting point was depicted, but also shunting volume was measured with 4D Flow, which had significant impact on our correct management and the cure for the patient (Iwakura et al. 2012) (Figure 3.14).

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Figure 3.12 A. A scheme of WSS calculation. Wall Shear Stress (τ) can be understood as a friction forces of the flowing blood on the vascular wall. It is calculated by multiplying the viscosity of the flowing blood (μ) and wall shear speed ( ). B: Wall shear stress (WSS) map at systole. Local valves of WSS are color coded on the 3D artery model. Note significantly low WSS on the wall of the bilateral internal iliac aneurysms. The dilated segment of right common iliac artery shows also low WSS compared to other non-dilated arteries reflecting relatively slow flow.

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Figure 3.13. 3D oscillatory shear index (OSI) map at systole. Bilateral internal iliac artery aneurysms depict higher OSI as compare to other segments. Dilated common iliac artery also shows also relatively high OSI.

Using the 4D Flow we have also assessed diverted flow direction within the dilated pancreaticoduodenal arcade accompanied by celiac artery occlusions (Mano et al. 2013). 4DFlow identified vortex flow and heterogeneous distribution patterns of wall shear stress in not only PDA aneurysms but also across entire PDAs. Resected PDA aneurysms are all atherosclerotic. This study gained insights into the probable relations of the abnormal flow to the pathogenesis of PDA aneurysms. As a nature of PC flowmetry, 4D Flow can be used to measure the blood flow of all vascular structures. We found abnormal flow patterns affect the accuracy of the flowmetry in the vessels. Renovascular hypertension (RVH) is an important cause of hypertension in children. It is essential to assess the hemodynamics of RVH lesions in detail. Previously, we have reported a case of an infant with RVH caused by left renal artery stenosis in which the hemodynamics of the lesions were assessed with 3D PC VIPR before and after a percutaneous transluminal renal angioplasty (PTRA). Because of the vortex flow created in the post-stenotic segment of the renal artery, the correct placement of the flow measurement planes were critical in measuring the renal blood flow. 3D cine PC MRA played an essential role in measuring the correct renal flow for assessing the improved blood flow to the kidney (Ishikawa et al. 2015).

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Figure 3.14. A 93-year-old female with a paraspinal arteriovenous fistula (AVF) occurred within the lumbar spinal vertebral body was assessed with time resolved three-dimensional (3D) phase-contrast MRI (4D-Flow) on 1.5 Tesla MR scanner. A 3D vector field map taken at systole allows an overview of the whole vasculatures in the body including a huge vascular cavity in the lumbar spine (vascular cavity), which is paraspinal AVF. Note unusually fast blood flow (coded red) seen in the AVF and the dilated paravertebral veins (arrows) as numerous drainers to the IVC.

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Figure 3.15. A: Streamline analysis based on whole 20 phases acquired with 4D-Flow. The patient is 75 year-old male with slight mitral valve prolapse with regurgitation. The intra-LA vortex formation (large arrows) is developed during the late diastole and early systole reflecting the regurgitation. Intraventricular vortex flow (small arrows) is seen during the early diastole. B: Time velocity curves measured at the out flow of the ascending aorta (blue line) and the left atrium above the mitral valve (red line). The measurement plane was perpendicular to the tract. Note there is a reverse flow through mitral valve at systole.

Vortex flow is not always reflecting an abnormal hemodynamics. 4D-Flow clearly visualized the intra-LA vortex formation, and by viewing this with 4D Flow, we characterized that the intra-LA vortex formation was developed during the late systolic and early diastolic phases and was directed counter-clockwise when viewed from the subjects' cranial side. More importantly, the patients with vortex had less organic heart diseases. The vortex formation might depend on LV and LA volume and on flow velocity and blood flow volume from PVs (Suwa et al. 2014). We also found this vortex flow within the left atrium appears earlier in the cardiac cycle in mitral regurgitations (Figure 3.15A, B).

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CONCLUSION With the emerging technologies of phase resolved 3D phase contrast MRI, we are now at the line to study flow dynamics in normal and diseased cardiovascular systems, which has not fully been investigated previously. We expect further study will open a door to disclose the relationship between abnormal flow dynamics and vascular and other pathologies, and thereby contribute to the prevention and cure of the cardiovascular diseases.

REFERENCES Ando, J; Kamiya, A. Flow-dependent regulation of gene expression in vascular endothelial cells. Japanese heart journal., 1996, 37(1), 19-32. Ando, J; Ohtsuka, A; Katayama, Y; Araya, S; Kamiya, A. [Fluid shear stress effects on intracellular calcium concentrations in cultured vascular endothelial cells]. Kokyu to junkan Respiration & circulation., 1990, 38(11), 1107-13. Ando, J; Yamamoto, K. Flow detection and calcium signalling in vascular endothelial cells. Cardiovascular research., 2013, 99(2), 260-8. Gu, T; Korosec, FR; Block, WF; Fain, SB; Turk, Q; Lum, D; et al. PC VIPR: a high-speed 3D phase-contrast method for flow quantification and high-resolution angiography. AJNR American journal of neuroradiology., 2005, 26(4), 743-9. Hausmann, R; Lewin, JS; Laub, G. Phase-contrast MR angiography with reduced acquisition time: new concepts in sequence design. Journal of magnetic resonance imaging : JMRI., 1991, 1(4), 415-22. He, X; Ku, DN. Pulsatile flow in the human left coronary artery bifurcation: average conditions. Journal of biomechanical engineering., 1996, 118(1), 74-82. Ishikawa, T; Takehara, Y; Yamashita, S; Iwashima, S; Sugiyama, M; Wakayama, T; et al. Hemodynamic assessment in a child with renovascular hypertension using time-resolved three-dimensional cine phase-contrast MRI. Journal of magnetic resonance imaging : JMRI. 2015, 41(1), 165-8. Iwakura, T; Takehara, Y; Yamashita, S; Nasu, H; Unno, N; Nishiyama, M; et al. A case of paraspinal arteriovenous fistula in the lumbar spinal body assessed with time resolved three-dimensional phase contrast MRI. Journal of magnetic resonance imaging : JMRI. 2012, 36(5), 1231-3. Jones, L; Pressdee, DJ; Lamont, PM; Baird, RN; Murphy, KP. A phase contrast (PC) rephase/dephase sequence of magnetic resonance angiography (MRA): a new technique for imaging distal run-off in the pre-operative evaluation of peripheral vascular disease. Clinical radiology., 1998, 53(5), 333-7. Malek, AM; Alper, SL; Izumo, S. Hemodynamic shear stress and its role in atherosclerosis. Jama., 1999, 282(21), 2035-42. Mano, Y; Takehara, Y; Sakaguchi, T; Alley, MT; Isoda, H; Shimizu, T; et al. Hemodynamic assessment of celiaco-mesenteric anastomosis in patients with pancreaticoduodenal artery aneurysm concomitant with celiac artery occlusion using flow-sensitive four-dimensional magnetic resonance imaging. European journal of vascular and endovascular surgery : the official journal of the European Society for Vascular Surgery., 2013, 46(3), 321-8.

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Markl, M; Chan, FP; Alley, MT; Wedding, KL; Draney, MT; Elkins, CJ; et al. Time-resolved three-dimensional phase-contrast MRI. Journal of magnetic resonance imaging : JMRI., 2003, 17(4), 499-506. Naidich, TP; Altman, NR; Gonzalez-Arias SM. Phase contrast cine magnetic resonance imaging: normal cerebrospinal fluid oscillation and applications to hydrocephalus. Neurosurgery clinics of North America., 1993, 4(4), 677-705. Napel, S; Lee, DH; Frayne, R; Rutt, BK. Visualizing three-dimensional flow with simulated streamlines and three-dimensional phase-contrast MR imaging. Journal of magnetic resonance imaging : JMRI. 1992, 2(2), 143-53. Pelc, NJ; Bernstein, MA; Shimakawa, A; Glover, GH. Encoding strategies for three-direction phase-contrast MR imaging of flow. Journal of magnetic resonance imaging : JMRI., 1991, 1(4), 405-13. Suwa, K; Saitoh, T; Takehara, Y; Sano, M; Nobuhara, M; Saotome, M; et al. Characteristics of Intra-Left Atrial Flow Dynamics and Factors Affecting Formation of the Vortex Flow. Circulation journal : official journal of the Japanese Circulation Society. 2014. Yucel, EK. Magnetic resonance angiography of the peripheral arteries. Magnetic resonance imaging clinics of North America. 1993, 1(2), 229-38.

In: Advances in Hemodynamics Research Editor: Keiichi Itatani

ISBN: 978-1-63483-187-1 © 2015 Nova Science Publishers, Inc.

Chapter 4

COMPUTATIONAL MODELING OF BLOOD FLOW Masanori Nakamura* Department of Mechanical Engineering, Saitama University, Japan

ABSTRACT Blood accounts for approximately 8% of our body weight. Its behavior obeys the physical principles of so-called fluid mechanics. Fluids are classified into liquid and gas. The latter is more compressible, and thus its density can change more largely than the liquid. It would be quite interesting that almost the same physical disciplines can be applied to describe the behaviors of gas and fluid. We therefore are able to use the same governing equations to simulate their physical motions. Advances in computer technologies during the past decades have enabled the analysis of various phenomena that could not be studied previously. The widespread availability of powerful computers together with efficient solution algorithms and sophisticated pre- and post- processing facilities enable the use of computational fluid dynamics (CFD) with personal computers. The most successful application of CFD includes the analysis of blood flow, in particular, in the cardiovascular system. Investigators began with fairly simple objects and progressed to more complicated systems, thereby widening the horizon of computational research of biomechanics. While the researchers that have been involved in the blood flow analysis had a long learning curve with developments of CFD and are aware of limitations and problems in applying CFD to blood flow problems, new users do not always possess fundamental knowledge of fluid dynamics and problems when applying CFD to the analysis of blood flow. This chapter intends to help those readers understand fundamentals of fluid mechanics and the theoretical background required for the effective use of CFD. This chapter also describes issues and problems that still remain and disturb the application of computational methods to both direct and indirect clinical problems. Things described in this chapter would help fill a gap between advanced researchers and those who have just started CFD studies in blood flow analysis.

Keywords: Newtonian fluid, dimensionless numbers, discretization, finite volume method, mesh *

Corresponding author: E-mail: [email protected].

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4.1. CONCEPT OF A CONTINUUM MECHANICS Blood is not just a fluid. It is essentially a plasma suspension of blood cells. The physics of blood is basically determined by interactions of those blood cells. Therefore, ideally, all interactions of blood cells in the plasma must be solved to simulate hemodynamics. In reality, however, 5 million red blood cells are present in only 1 mm3 of blood. This means that the interaction of 1.6 x 109 red blood cells have to be solved if we want to analyze hemodynamics in a carotid artery with a diameter of 2 mm and a length of 100 mm. It is practically unfeasible even with state-of-art supercomputers. Limited computational resources have restricted complete expression of hemodynamics. The Knudsen number, Ku, is useful to determine whether we need to use statistical mechanics or the continuum mechanics formulation for a given problem. It is defined as (4.1) where λ is the molecular mean free path length and L is a representative physical length scale. The molecular mean free path length is the average distance traveled by a particle without collisions with other particles. If the Knudsen number is larger than one, a length scale of the problem is comparable to the mean free path, and we need to use statistical methods for taking account of motions of molecules to describe the phenomenon an interest. Alternatively, if the Knudsen number is sufficiently smaller than one, the presence of molecules or particles can be ignored to describe the phenomenon, and we can use fluid dynamics theories. Let us calculate the Knudsen number in various blood vessels. Here, the representative physical length L is a diameter of the blood vessel, D. Estimation of the molecular mean free path length of red blood cells is slightly difficult. For simplicity, suppose a one dimensional situation of Figure 4.1 where red blood cells are equidistantly aligned. In normal physiology, the red blood cells are present at a hematocrit, Hct, of 40%. If we consider an average distance between the red blood cells is equal to the molecular mean free path length, it can be gained as (4.2) where DRBC is a diameter of the red blood cell. Thus, the Kundsen number of blood flow is calculated from .

(4.3)

Figure 4.2 plots the Knudsen number against the blood vessel diameter D with assuming DRBC of 8 μm. As seen, the Knudsen number is sufficiently small (2.0 (Warnes et al. 2008). Researchers have already reported a method to calculate Qp/Qs using echocardiography. However, some researchers also demonstrated that there are several limitations to this method, such as the blood flow profiling and influences of the beam angle (Kitabatake et al. 1984, Sabry et al. 1995). Although Qp/Qs

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can be estimated based on MRI (Beerbaum et al. 2001), the use of MRI is also limited because of high heart rate and insufficient cooperation of patients in childhood. In order to evaluate the pulmonary arterial pressure concurrently, catheterization is still performed in Japan. We have focused on the intraventricular blood flow in patients with ventricular volume load, and hypothesized that the amount of intraventricular energy loss based on energy dispersion would increase in response to the volume load. We evaluated the perioperative changes in intraventricular blood flow and energy loss in a 7-month-old female with VSD (Figure 6.7).

Figure 6.7. The perioperative changes in the intraventricular energy loss in a 7-month-old female with ventricular septal defect (VSD). The peak energy loss in the diastolic phase decreased from 200.3 mW/m to 58.3 mW/m after the VSD closure.

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The peak amount of energy loss in the diastolic phase significantly decreased from 200.3 mW/m to 58.3 mW/m after the VSD closure. It is easy to speculate that an increase in intraventricular blood flow causes strong blood flow collisions, leading to high energy loss. Therefore, a reduction of volume load after the VSD closure is considered to be reflected by the decreased amount of intraventricular energy loss. Future studies with large populations will clarify the utility of assessing the intraventricular energy as a new parameter reflecting volume overload.

3. THE RIGHT VENTRICLE 3.1. Anatomical and Physiological Characteristics of Right Ventricle The right ventricle consists of inlet, apical trabecular and outlet components, and is the most anteriorly situated cardiac chamber (Haddad et al. 2008, Ho et al. 2006). The right ventricle is crescent-shaped when viewed in cross-section, and triangular when viewed from the side. The left ventricle has 3 muscle layers; an obliquely-oriented superficial layer, longitudinally-oriented deep layer, and predominantly circular muscle layer between them (Greenbaum et al. 1981). The circular muscle layer of the left ventricle is considered to make complex movements, such as twisting (Streeter et al. 1969) and untwisting (Notomi et al. 2008) possible. In contrast, the right ventricle has only 2 muscle layers; a superficial muscle layer parallel to the atrioventricular groove and a deep muscle layer is longitudinally aligned to the apex of the heart. The simpler structure of the right ventricular myocardium associates with the fact that the right ventricle has lower vascular resistance and greater pulmonary arterial distensibility than the left ventricle. Additionally, it is believed that this simplicity contributes to the high compliance of the right ventricle, and enables it to accommodate the changes in the preload on the heart. These anatomical and physiological characteristics also influence the blood flow pattern in the right ventricle. We observed the intraventricular blood flow based on 3-dimensional cine phase contrast MRI or 4D flow MRI (Figure 6.8), and found that in the left ventricle, a large vortex is formed that helps multidirectional streams of blood merge with minimal flow collision during the diastolic phase. Because the mitral inflow should be turned to the aortic outflow, large vortices are formed as if blood flow ―jumps on a spring‖. During the systolic phase, the vortex preferentially moves blood into the left ventricular outflow tract. In the right ventricle, the blood flow from the superior vena cava collides with that from the inferior vena cava, and helical blood flow streams into the right ventricle. In contrast to the left ventricle, no large vortex is formed in the right ventricle in the long axis plane (Frontal view in Figure 6.8), but helical spiral flow is formed inside the chamber (Lateral view in Figure 6.8). This helical flow called ―secondary vortex flow‖ in fluid mechanics, facilitates to enlarge the right ventricular free wall and this helical flow helps the right ventricle act as a flow volume reservoir. The anatomical and physiological characteristics of the ventricles greatly contribute to their features.

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Figure 6.8. The streamlines in normal biventricular hearts. In the right ventricle, no large vortex was found, and 2-dimensional blood flow moves into the pulmonary artery. In the left ventricle, a large vortex was confirmed during the diastolic phase. This large vortex helps multidirectional streams of blood merge with minimal flow collision, and preferentially moves blood into the left ventricular outflow tract in the systolic phase.

3.2. Consideration in Tetralogy of Fallot Tetralogy of Fallot (TOF) is characterized by 4 morphological features: (1) ventricular septal defect, (2) over-riding of the aorta, (3) right ventricular outflow obstruction, (4) right ventricular hypertrophy (Apitz et al. 2009, Chaturvedi et al. 2007). Many cases develop cyanosis in the first few weeks and months of life, although the pulmonary blood flow is adequate at birth. Most centers operate on children aged 3-6 months to improve the cyanosis. It is widely recognized that the long-term fate of the right ventricle is determined by the chronic pulmonary regurgitation (Apitz et al. 2009). Therefore, preservation of the pulmonary valvular function has recently been considered to be the most important policy in the surgery for TOF, even at the expense of modest residual stenosis (Van Arsdell et al. 2005). Right ventricular failure is related to pulmonary regurgitation in most cases, and the amount of pulmonary regurgitation is reported to correlate with the right ventricular volumes and exercise dysfunction (Carvalho et al. 1992). Therefore, pulmonary valve replacement, before irreversible myocardial change due to right ventricular volume load occurs, is of great importance. Therrien et al. 2005 have proposed the threshold for adequate reverse remodeling as 170 ml/m2 for the end-diastolic volume and 85 ml/m2 for end-systolic volume. In addition, the relationships between QRS duration and the occurrence of ventricular tachycardia and sudden death were reported (Gatzoulis et al. 1995). Gatzoulis et al. 2000 also reported that QRS duration >180msec and the rate of change in QRS duration can be used as parameters to predict the occurrence of ventricular arrhythmia and sudden death. Therefore, to determine the optimal timing for pulmonary valve replacement, RV volume measurement by MRI and

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QRS duration on ECG are clinically important. In addition, the clinical utilities of brain natriuretic peptide (BNP) and N-terminal pro-BNP levels to determine the indications for reoperation indication have recently been supported by several reports (Kitagawa et al. 2014, Hirono et al. 2014). Moreover, recent studies have demonstrated that ventricular fibrosis detected by late gadolinium enhancement cardiovascular MRI has relationships with late complications such as arrhythmia, ventricular function, exercise intolerance and neurohormonal activation (Babu-Narayan et al. 2006, Wald et al. 2009). However, further studies are warranted to establish the threshold for determining the timing for pulmonary valve replacement based on these new parameters. In order to elucidate the right ventricular function, ventricular-ventricular interaction is also considered to be an important concept, but is not yet fully understood. As the right and left ventricle share the same visceral cavity and common myocardial strands, the right ventricle influences the left ventricle, and vice versa. The concept of ventricular-ventricular interaction has been discussed for approximately 5 decades. Kelly et al. 1971 reported that right ventricular volume loading influences the left ventricle pressure-volume relationship and reduces the left ventricular function relative to left ventricular end-diastolic pressure. Bemis et al. 1974 also reported that an elevation in right ventricular end-diastolic pressure not only increases the left ventricular end-diastolic pressure, but also alters the geometry of the left ventricle. Several reports on TOF patients have indicated that there is a positive correlation between the right and left ventricular function (Geva et al. 2004, Tzemos et al. 2009), and ventricular-ventricular interaction has been considered to underlie this relationship. However, the clinical impact of ventricular-ventricular interaction has not fully clarified, and further studies will be needed to elucidate the importance of this interaction.

4. FONTAN PHYSIOLOGY 4.1. Fontan Procedure Fontan procedure is the surgery to establish the circulation of functional single ventricle (Fontan et al. 1971). We call this circulation ―Fontan circulation‖, and in the Fontan circulation, the superior and inferior vena cava directly connect to the bilateral pulmonary arteries. In 1971, Fontan and Baudet first reported this operation for a patient with tricuspid atresia, and the introduction of this procedure dramatically improved the life expectancy of children with single ventricle (Cetta et al. 1996, Mair et al. 2001, and d‘Udekem et al. 2007). As relatively low pulmonary vascular resistance and preserved ventricular function are essential for the formation of Fontan circulation, a bidirectional Glenn anastomosis is generally performed as an intermediate step. The bidirectional Glenn procedure is advantageous of providing an adequate amount of pulmonary blood flow and reducing the volume load on the main ventricle. The surgical method associated with the connection of venous return and pulmonary arteries has also been improved. Originally, the right atrium was isolated by the closure of atrial septal defect and tricuspid valve, and the right atrial appendage was anastomosed to the right pulmonary artery (atriopulmonary connection [APC] Fontan). Lateral tunnel was subsequently introduced to establish better streaming of the venous return by baffling the

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right atrium with an intraatrial patch. Recently, the venous return is routed by the insertion of an extracardiac conduit between the inferior vena cava and the right pulmonary artery, and extracardiac conduit modification leads to less supraventricular arrhythmia (d‘Udekem et al. 2007). Although the Fontan anastomosis is unique, the main ventricle, aortic arch, arteries and vena cava were also unique in the Fontan patients. Although better management and improved surgical techniques contributed to the better prognoses of Fontan patients, these patients frequently develop heart failure, arrhythmia and long-term complications such as protein losing enteropathy (PLE) (Mertens et al. 1998 and John et al. 2014), liver dysfunction (Baek et al. 2010), thrombosis (Jacobs et al. 2007), renal dysfunction (Dimopoulos et al. 2008) and plastic bronchitis (Do et al. 2009) as a consequence of the Fontan physiology. In this chapter, we will discuss the disadvantageous characteristics of the Fontan physiology.

4.2. Aortic Arch Some cases require aortic arch reconstruction in complicated congenital heart anomaly related to the single ventricle patients. Arch repair for the coarctation or interruption of the aortic arch, DKS (Damus-Kaye-Stansel) procedure for the restricted systemic outflow patients, and Norwood procedure are kind of procedures in aortic arch reconstruction. The Norwood procedure is the operation for HLHS involving the reconstruction of a sufficient systemic outflow. Recoarctation or obstruction of the aortic arch after the Norwood procedure deteriorates the function of the single right ventricle, leading to a high mortality rate; therefore, several surgical modifications have been introduced.

Figure 6.9 The streamlines and energy loss inside the aortic arch after the Norwood operation measured with echocardiography VFM. There was a large vortex formed in the dilated aortic arch. High amount of energy loss was confirmed in the dilated aortic arch during the systolic phase.

Cardis et al. 2006 has reported that patients with HLHS after the Norwood procedure had increased aortic stiffness and decreased dispensability in the reconstructed aorta. Itatani et al. 2012 also reported a CT-based simulation study analyzing the streamline and energy loss in aortic arches after the Norwood operation. We previously evaluated the streamlines and energy loss in the dilated aortic arch after reconstruction using echocardiography VFM (Figure 6.9). Our streamline analysis showed a large vortex inside the dilated aortic arch, and

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this finding was different from that of the CT-based simulation study. Echocardiography VFM has advantages in the examination of flow around the valve. Regarding the energy loss, high energy loss was confirmed at the dilated site. In addition, it is of great interest that the energy loss time curve obtained from VFM was similar to that obtained from the numerical simulation study (Itatani et al. 2012). The dilated aortic arch would be an afterload on the main ventricle.

4.3. Main Ventricle and Vessels Before the Glenn operation is performed, the oxygen supply to the heart is insufficient, because the oxygenation is not complete. And, as the main ventricle needs to supply blood with not only the systemic arteries but also pulmonary arteries with lower vascular resistance, volume overload negatively affects the main ventricle. This overload leads to ventricular hypertrophy, which has been reported to be related to the patient‘s prognosis (Seliem et al. 1989). In addition, after the Glenn operation, aortopulmonary shunts are sometimes formed. This complication can also negatively affect as a volume overload. Atrioventricular valve insufficiency also accompanies in the single-ventricle patients with a fixed frequency, and this complication could be a volume overload for the main ventricle. Moreover, especially in patients with HLHS, neoaortic valvular insufficiency would also cause volume overload. Meanwhile, the dilated aortic arch also works as a pressure load, as stated above. It is wellknown that the vascular resistance is high in the Fontan patients. This finding can be regarded as an adaptation that occurs to increase the venous capacity to propel the blood flow in the pulmonary arteries. There are other negative features, such as an impaired heart rate response, morphological abnormalities in the ventricle including the effect of the residual chamber (Ohuchi et al. 2001), the single coronary artery observed in the right single ventricle (Baffa et al. 1992) and RV-dependent coronary circulation in patients with pulmonary atresia. Therefore, the main ventricle is exposed to various and complicated negative factors.

Figure 6.10. The results of a streamline analysis in the normal left ventricle in VFM. In the early diastolic phase, 2 small vortices are formed around the mitral valve. The clockwise vortex on the right side gradually becomes larger in the end diastolic phase. The blood flow is consequently directed to the aorta in the systolic phase.

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Observations of the blood flow in hearts have recently shown preferable vortex formation in adults (Itatani 2014, Pedrizzetti et al. 2014, and Sengupta et al. 2014), which can also be observed in children. According to our preliminary data based on VFM echocardiography, two small vortices are formed around the mitral valve in the early diastolic phase (Figure 6.10). The clockwise vortex on the right side gradually becomes larger and occupies the ventricle in the end-diastolic phase. The blood flow is subsequently directed to the aorta in the systolic phase. Therefore, utilizing this inertial force, the intraventricular vortex preferentially moves the blood into the aorta. In addition, the observation of the energy loss based on VFM echocardiography revealed that high amount of energy loss is detected only at the outer periphery and center of the large vortex, indicating that the blood flow in the inner part of the vortex can preserve the kinetic energy.

Figure 6.11. The results of streamline and energy loss analysis in the main ventricle of an infant with tricuspid atresia. There was no significant large vortex in the ventricle. Instead, several small vortices were confirmed during the diastolic phase, and high amount of energy loss was detected around the vortices. The time-energy loss (time-EL) curve in this infant was significantly greater than that in a left ventricle of a normal biventricular infant. These findings indicate that this infant is not able to utilize the inertial force of the intraventricular vortex, leading to decreased energy efficiency.

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We show sequential images of the intraventricular blood flow in an infant with tricuspid atresia (Figure 6.11). No significant large vortex was confirmed in the main ventricle. Instead there were several small vortices coexisting and conflicting with each other. High amount of energy loss was consequently detected around these vortices, and this finding indicates that the energy efficiency is impaired in this single left ventricle. The pathophysiology underlying the impaired energy efficiency is unclear; however, the abnormal morphology may cause the inefficient intraventricular blood flow. In a 3-year-old male with hypoplastic left heart syndrome, two vortices were observed in the right single ventricle during the early diastolic phase; however, they vanished in the late diastolic phase, and these vortices did not consequently work as inertial forces in this patient (Figure 6.12). Therefore, this right single ventricle did not utilize any inertial force either. Future studies will be needed to elucidate the influences of abnormal intraventricular vortex formation on the impaired ventricular function in single-ventricle patients.

Figure 6.12. The results of a streamline analysis in the main ventricle of 3-year-old male with hypoplastic left heart syndrome. Although 2 vortices were formed in the early diastolic phase, they vanished in the late diastolic phase. Therefore, this right single ventricle did not utilize any inertial force.

4.4. Fontan Anastomosis Fontan anastomosis is an artificial structure, and a number of researchers have made efforts to elucidate the non-physiological blood flow at the Fontan anastomosis site. Although the flow drives of the pulmonary blood flow in the Fontan circulation have not yet been clarified, the heartbeat, respiration and muscles of the lower extremities are all considered to influence the blood flow pattern. Nakazawa et al. 1984 and DiSessa et al. 1984 revealed that the pulmonary blood flow increases during the atrial diastole. Redington et al. 1991 and Penny et al. 1991 clarified that the pulmonary blood flow increases in the inspiratory phase. Fogel et al. 1997 analyzed the flow based on MRI, and verified that the pulmonary blood flow increases from the end systolic phase to the early diastolic phase. Hjortdal et al. 2003 demonstrated that the pulmonary blood flow increases in response to the muscle contraction

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of the lower extremities. Future studies are needed to elucidate the mechanisms of these flow drives and the effects of complications on these flow drives. Energy loss in the Fontan anastomosis has been considered to reflect the energy efficiency, and several researches have focused on this novel parameter. Sharma et al. 1996 proposed the optimal connection site of the Fontan conduit with the lowest energy loss in the Fontan anastomosis, by using glass models based on in vivo cardiac MRI geometric data. This reported demonstrated that the energy losses of 1 and 1.5 times the diameter offset achieved the minimal energy loss. Subsequent studies using computational fluid dynamics (CFD) increased the understanding of the energy loss. de Lavel et al. 1996 subsequently demonstrated that the minimal energy loss and blood flow distribution to the bilateral pulmonary arteries could be achieved by enlarging the Fontan baffle (2.5 cm) and moving it alongside the pulmonary artery angling the Fontan baffle toward the right pulmonary artery. Itatani et al. 2011 reported that the lower limit of the pulmonary artery index was 110 mm2/m2, from the view of exercise tolerance. Marsden et al. 2007 also indicated that respiration and exercise considerably influence EL in the Fontan anastomosis. In order to determine the clinical importance of decreasing EL, we calculated the in vivo EL by measuring simultaneous pressure and velocity data at supra and inferior vena cava and bilateral pulmonary arteries, and compared EL with other cardiac functional parameters (Honda et al. 2014). This small study revealed that EL correlates with diastolic function of the main ventricle. A larger study reported by Khiabani et al. in 2015 clarified the relationship between EL and exercise capacity. In order to achieve clinical application of EL assessment in the Fontan anastomosis, it will be important to establish a further easy method for measuring EL in future studies.

REFERENCES Apitz C, Webb GD, Redington AN. Tetralogy of fallot. Lancet. 2009;374:1462-1471. Babu-Narayan SV, Kilner PJ, Li W, Moon JC, Goktekin O, Davlouros PA, Khan M, Ho SY, Pennell DJ, Gatzoulis MA. Ventricular fibrosis suggested by cardiovascular magnetic resonance in adults with repaired tetralogy of fallot and its relationship to adverse markers of clinical outcome. Circulation. 2006;113:405-413. Baek JS, Bae EJ, Ko JS, Kim GB, Kwon BS, Lee SY, Noh CI, Park EA, Lee W. Late hepatic complications after fontan operation; non-invasive markers of hepatic fibrosis and risk factors. Heart. 2010;96:1750-1755. Baffa JM, Chen SL, Guttenberg ME, Norwood WI, Weinberg PM. Coronary artery abnormalities and right ventricular histology in hypoplastic left heart syndrome. J. Am. Coll. Cardiol. 1992;20(2):350-8. Baumgartner H, Khan S, DeRobertis M, Czer L, Maurer G. Discrepancies between doppler and catheter gradients in aortic prosthetic valves in vitro. A manifestation of localized gradients and pressure recovery. Circulation. 1990;82:1467-1475. Beerbaum P, Korperich H, Barth P, Esdorn H, Gieseke J, Meyer H. Noninvasive quantification of left-to-right shunt in pediatric patients: Phase-contrast cine magnetic resonance imaging compared with invasive oximetry. Circulation. 2001;103:2476-2482.

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In: Advances in Hemodynamics Research Editor: Keiichi Itatani

ISBN: 978-1-63483-187-1 © 2015 Nova Science Publishers, Inc.

Chapter 7

VENTRICULAR SUCKING FORCES AND DIASTOLIC FUNCTION: INTRAVENTRICULAR PRESSURE GRADIENT IN VENTRICLE DURING EARLY DIASTOLE GIVES US NEW INSIGHTS INTO DIASTOLIC FUNCTION Ken Takahashi1 and Takahiro Ohara2 1

2

Department of Pediatrics, Juntendo University, Japan Department Cardiology, National Cerebral and Cardiovascular Center, Japan

ABSTRACT The intraventricular pressure difference (IVPD) from the left atrium to the left ventricular apex during early diastole, plays an important role in diastolic function. This pressure difference is well correlated with the Tau index, which is the gold standard of diastolic function. IVPD also plays an important role in exercise intolerance, which is thought to be one of the most important outcome predictors for various heart diseases. Additionally, the pressure difference can be estimated noninvasively either during exercise or at rest using echocardiography with digital processing of color Doppler Mmode recordings. When the IVPD is analyzed using color M-mode imaging, the spatial and temporal information can be analyzed simultaneously. This allows the pressure difference at each location to be determined, despite being limited to a one-dimensional scan line of the left ventricle. IVPD may also elucidate new aspects and mechanisms of diastolic function. Although at present, the original program in each institution, which is not commercially available is required to analyze color M-mode data to estimate IVPD, overcoming this difficulty will allow new insights into the diastolic function in both clinical and research settings. This chapter discusses the significance, advantages, and impacts of IVPD analyses in both settings.



Corresponding Author address E-mail: [email protected].

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Keywords: intraventricular pressure difference (IVPD), diastolic heart failure

1. WHY DO PEOPLE FOCUS ON INTRAVENTRICULAR PRESSURE DIFERENCE (IVPD) The cardiovascular system is very complex. The heart, especially the left ventricle (LV), plays the most important role in the circulatory system. There is growing recognition that congestive heart failure, caused predominantly by an abnormality in diastolic function, is both common and causes significant morbidity and mortality. (Aljaroudi W et al. 2012, Halley et al. 2011) However, the mechanisms underlying diastolic dysfunction remain unclear. The sucking force, which sucks blood from the left atrium into the LV, is now understood to play an important role in diastolic function during the early diastole. (Ohara et al. 2012, Yotti et al. 2005, Notomi et al.2008) The intraventricular pressure difference (IVPD) between the left atrium (LA) and the apex of the LV, which is the driving force of LV suction, ranges only from 2 to 5 mmHg in the adult human, and the IVPD duration is very short. (Ohara et al. 2012, Yotti et al. 2005, Notomi et al.2008) It begins around the time that the mitral valve opens and continues until the peak of the E wave at the mitral valve. Despite this small pressure difference and short duration, IVPD is the key force behind diastolic function. This chapter will first describe the history of the research and the theory for IVPD to explain the mechanisms of IVPD based on current research and clinical studies. Second, the chapter will explain with detailed, practical methods how to investigate IVPD using echocardiography. Third, it will provide data on some cardiac diseases related to new research projects using IVPD.

2. INTRAVENTRICULR PRESSURE DIFFERENCE (IVPD) 2.1. Definitions In this chapter, IVPD is defined as the pressure difference during early diastole between two points, the mitral annulus and the LV apex. (Popovi et al. 2006, Thomas et al. 2005) IVPD is defined as the change in pressure over a certain distance L, in this case the base to apex distance. The relationship between IVPD and the intraventricular pressure gradient (IVPG) is described by Equation (7.1) IVPG =

IVPD 𝐿

(7.1)

In other words, IVPG is the derivative of IVPD with respect to location. However, cardiologists tend to use “IVPG” to describe the pressure difference, whereas a physicist would use “IVPD”, reserving the word “gradient” to describe the rate of pressure change along a line. In this text, the physics definition is used. However, readers should be aware that this is not always the case in the cardiology literature. Later in the text, IVPD in the right

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ventricle (RV) is discussed. IVPD in the RV between the tricuspid valve and the RV apex is represented as RV-IVPD.

2.2. Clinical Background of IVPD and Development of IVPD In 1930, Katz 1930 speculated that the left ventricle relaxed actively and had the ability to “exert a sucking action to draw blood into its chamber.” Despite this speculation that diastole in the very early period was associated with active relaxation and was not an entirely passive process, this hypothesis was not supported until 1979 when Ling et al. Ling et al. 1979 reported the presence of regional IVPD between the base and apex of the LV in a canine model. They speculated that these gradients resulted in the active “sucking” of blood into the LV from the left atrium. Courtois and colleagues subsequently validated these findings in 1988 (Courtois et al. 1988). Later, they demonstrated a strong relationship between diastolic IVPD and systolic function, with regional ischemia-induced changes in LV function having a direct effect on IVPD (Courtois et al. 1990).Based on those results, they speculated that IVPD was related to regional elastic recoil, or the potential energy stored during LV systole, and that impairments in regional systolic function would have a significant effect on LV “suction.” Although the existence of the sucking force was proved, its mechanism still remained unclear. There had been two theories as to the mechanisms underlying IVPD. Ling et al. 1979 reported that IVPD could be due to viscoelastic myocardial properties and local acceleration of blood. In contrast to this theory, Courtois et al. 1990 reported that IVPD was due to differences in regional elastic recoil of the LV wall. To elucidate this issue, Nikolic et al. 1995 developed a very unique experimental system using a mitral valve occluder implanted in the mitral annulus. The mitral valve was occluded to produce non-filling diastole, and the base-to-apex pressure gradient was observed, regardless of the presence or absence of filling through the mitral valve from the LA to the LV. Thus, they concluded that IVPDs are related both to changes in LV shape and to the magnitude of elastic restoring forces and, furthermore, that the shape of the ventricle is not dependent on the hydrodynamics of blood inflow. As described above, although the presence of IVPD between the left ventricular base and apex during early diastole was reported, the clinical implications of this phenomenon were not fully appreciated. Before the methods to measure IVPD using echocardiography were developed, IVPD was not routinely measured in clinical practice because it required an invasive procedure with high-fidelity pressure measurements in the LV with cardiac catheterization. Greenberg et al. 2001 made a historical turning point for the measurements of IVPD. They developed a system to calculate transmitral pressure differences across a normal mitral valve into the unsteady flow from the Bernoulli equation using a full digital velocity map captured by echocardiography, based on color M-mode (Greenberg et al. 1996). Later, they extended this concept and applied basic hydrodynamic principles to the non-invasively obtained spatiotemporal velocity distribution of left ventricular inflow to calculate IVPD (Greenberg et al. 2001). These methods have since been used in several studies.

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2.3. The Mechanisms Underlying IVPD IPVD plays a key role in diastolic function. The mechanisms underlying diastolic function should be reviewed to provide insight into IVPD. Diastole encompasses the period of time beginning when the myocardium loses its ability to generate force and shortens until the time it returns to its resting force and length. The physical and physiologic properties that define diastolic filling are a complex interaction of active and passive components. The simultaneous interaction among (1) the dimensions of the mitral valve, (2) left atrial filling/emptying properties, (3) the passive compliance of the LV, and (4) the rate and duration of LV relaxation (tau: an active and energy-consuming process) defines the transmitral filling gradient that allows for diastolic filling (Yellin et al. 2000).At the organelle level, relaxation occurs in a series of energy-consuming steps beginning with the release of calcium from troponin C, detachment of the actin-myosin cross-bridge, phosphorylation of phospholamban, sarcoplasmic reticulum calcium ATPase–induced calcium sequestration into the sarcoplasmic reticulum, sodium/calcium exchanger–induced extrusion of calcium from the cytoplasm, slowing of the cross-bridge cycling rate, and extension of the sarcomere to its rest length (Brucks et al. 2005, Cheng et al. 1993, Cheng et al. 2005, Courtois et al. 1988, Dabiri et al. 2004). The mechanisms to supply adequate energy and regenerate them must work for this process at a sufficient rate and to a sufficient extent Cheng et al. 1993, Courtois et al. 1988, Dabiri et al. 2004) The rate and extent of these cellular processes determine the rate and extent of active ventricular relaxation. The actual location of this elastic storage remains controversial, but it likely involves both the myocyte and the myocardial interstitium. At the sarcomere level, titin is a molecular spring causing energy to be stored during systole that helps restore the sarcomere in early diastole (Helmes et al. 1996, Lahmers et al. 2004). Helmes et al. 1996 and 2003 explained titin-based restoring forces that the relengthening velocity of the sarcomere is inversely related to end-systolic length, a microscopic analogy of ventricular contraction below equilibrium volume. Therefore, diastolic suction involves deformation of the protein titin that occurs when sarcomeres are stretched above and shortened below slack length, (Kass et al. 2004) which affects acute deformation of the LV, such as the untwisting motion during isovolumic relaxation time (IVRT). (Notomi et al. 2006) At the chamber level, this process causes acute LV pressure decline during IVRT, then LV chamber filling, which occurs with variable LV pressures (auxotonic relaxation). The major determinant of diastolic suction is the elastic energy stored during systole. To generate elastic potential energy, the LV volume must fall under a critical value during contraction to generate suction (Nikolic et al. 1988, Beli et al. 2000, Solomon et al. 1998). This process is affected both by active relaxation and by passive stiffness. Nikolic et al. 1988 previously showed that the suction volume during diastole from the LA to the LV was directly related to the magnitude of the LV elastic recoil, or potential energy, forces. This finding means that IVPDs are directly related to LV geometry and influenced by the elastic recoil, reflecting the potential energy stored during systole and representing a mechanism by which the LV can adequately fill under low filling pressures. Early work investigating the determinants of IVPD by Courtois et al. 1988 demonstrated significant decreases in IVPD with acute coronary occlusion. In addition, they showed a relationship between decreases in IVPD and extensive regional systolic dysfunction. These findings contributed to their speculation of the relationship between IVPD and the elastic recoil of the LV and provided a mechanism to maintain LV filling at lower diastolic pressure.

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These observations are consistent with previous reports of both a relationship between IVPD and endo-systolic volume (ESV) and a relationship between the change in IVPD and changes in ESV (Firstenberg et al. 2001). Furthermore, the lack of a relationship between IVPD and left atrial pressures and the fact that these early pressure differences exist without inflow from the LA to the LV (Nikolic et al. 1995) suggest that they may represent intrinsic properties of the LV and transmitral pressure differences. From the view point of the energy store in the LV structure, Ashikaga et al. 2004 have shown significant deformation within the myocardium as the counter helixes contract against each other, storing significant energy in the interstitium as a global LV “spring”. (Robinson et al. 1986, Krams et al. 1994). The isovolumic pressure decay and rapid left ventricular (LV) filling during IVRT and early diastole are characterized by a series of consecutive events that partially overlap in time. As LV pressure starts to decline before mitral valve opening, conformational changes occur within the heart that are reflective of the release of energy stored during previous systole (Nikolic et al. 1988). Mitral valve opening is immediately followed by the development of IVPD. (Courtois et al. 1988) Finally, LV inflow is accelerated by IVPD to reach peak filling velocity. (Nakatani et al. 2001) It is widely accepted that the appearance of IVPD in early diastole reflects LV suction (Nikolic et al. 1995); in other words, the low-pressure field created by outward-directed elastic forces that aim to restore a non-stressed LV shape (Nikolic et al. 1988). It is also accepted that IVPD facilitates early LV filling (Little et al. 2005). LV systolic torsional deformation is one of the mechanisms by which potential energy is stored during ejection, to be later released during diastole, contributing to the creation of suction (Notomi et al. 2008). In systole, as the base and apex of the heart rotate in the opposite direction and generate twisting of the heart muscle, part of the energy used in contraction is stored within the extracellular collagen matrix (Waldman et al. 1988) and compresses titin within the myocytes (Granzier et al. 2005). During relaxation, this energy is promptly released and manifested by LV untwisting. About 40% of the LV untwisting occurs during IVRT (Rademakers et al. 1992); the untwisting rate is proportional to the rate of isovolumic pressure decay (Dong et al. 2002); and there is a positive association between the untwisting rate and IVPD (Notomi et al. 2006). These three phenomena have been shown to follow each other temporally, starting with isovolumic pressure decay, followed by untwisting, whose peak coincides with mitral valve opening, and ending with IVPD that peaks early during LV filling. From the view point of the coordination of ventricular motion, another aspect of the mechanisms causing IVPD can be realized. The timing of events during LV relaxation is programmed like a precision machine and is closely related to the mechanisms causing IVPD. The peak dP/dt at the apex is slightly delayed relative to that at the subaortic region and mitral tip (Steine et al. 2002). These small temporal differences probably reflect the ventricular activation time and lead to a small delay in the onset of relaxation in the apex relative to the basal region. (Sengupta PP et al. 2006, Ashikaga et al. 2007) During IVRT, however, pressure falls at a faster rate at the apex than at the base; therefore, early diastolic minimum pressure is reached first in the apex. During volume loading and after coronary micro-embolization, however, tau is similar in all regions. It seems likely that regional differences in tau contribute to the early diastolic mitral-to-apical pressure differences measured. (Steine et al. 2002) The twisting motion provides another aspect of the coordination of LV motion during diastole. Peak LV untwisting precedes IVPD (Notomi et al. 2006) and is a strong predictor of IVPD (Notomi et al. 2008), which is manifested in part by apical pressure decline. An obvious manner in which untwisting can affect LV suction is through a change of LV shape. As opposed to depolarization, repolarization, and therefore relaxation, progresses from the

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epi- toward the endocardial layers and occurs almost simultaneously at the basal and apical sites (Yan et al. 1998). Because subepicardial fibers are predominantly responsible for twisting due to the hammer theory, it is reasonable that the first motion detectable during relaxation is untwisting (Ashikaga et al. 2004). This is closely followed by a change of orientation in the myocardial sheets that becomes less perpendicular toward the long axis and that in turn leads to sub-endocardial radial thinning. (Rosen et al. 2004, Davis et al. 1999) This initial very early change causes a continuous apical LV pressure drop during the diastolic suction phase. The importance of this apical relaxation to LV suction was proved by Davis et al. 1999 and Steine et al. 1999.

2.4. Measuring IVPD Using Echocardiography Previously, cardiac catheterization was needed to measure IVPD, but Greenberg et al. 2001 reported a non-invasive method of IVPD measurement using echocardiography without the risk and expense of cardiac catheterization.

Figure 7.1. IVPD measurement. A Four-chamber view showing mitral inflow. B corresponding color M-mode Doppler image. C three dimensional profile of IVPD. Color M-mode Doppler images (B) are recorded with the cursor parallel to mitral inflow in an apical 4-chamber view (A). Euler’s equation, shown in Equation 7.2, is used to calculate the pressure gradient at each point. The pressure difference at each point along a scan line is measured relative to the position of the mitral annulus at the aortic valve closure by calculating the line integral between them. A three-dimensional profile of IVPD is generated, and the peak IVPD in early diastole is identified (C). IVPD: intraventricular pressure difference. AoV: aortic valve closure.

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Color M-mode images were obtained using the apical 4-chamber view (AsadaKamiguchi et al. 2006, Firstenberg et al. 2000, Yotti et al. 2005), apical long axis view (Steine et al. 2002) or 4-chamber view by trans-esophageal echocardiography (Ronber et al. 2003) and analyzed using an image-processing algorithm. (Figure 7.1). 𝜕𝑃 𝜕𝑠

𝜕𝑢

= 𝜌(

𝜕𝑡

+𝑢

𝜕𝑢 𝜕𝑠

)

(7.2)

Images were reconstructed using a de-aliasing technique, as shown in Equation (7.2), where P is the pressure, ρ is the constant blood density as 1060 kg/m3, u is the velocity, s is a position along the streamline of the transmitral flow measured with color Doppler M-mode line, and t is the time used to calculate the relative pressures within the region of interest from the reconstructed velocity field (Greenberg et al. 2001, Asada-Kamiguchi et al. 2006, Ronber et al. 2003, Firstenberg et al. 2000, Steine et al. 2002). The pressure difference at each point along a scan line was measured relative to the position of the mitral annulus at aortic closure by calculating the line integral between them (Greenberg et al. 2001, Yotti et al. 2005). (Figure 7.2) The first term on the right side of Equation 7.2 is the inertial component, and the second term is the convective component.

Figure 7.2. Left ventricular IVPD in normal subjects. A Three-dimensional profile of IVPD. B temporal profile of IVPD. C spatial profile of IVPD at the peak IVPD. The red line represents IVPD, the blue line represents inertial IVPD, and the green line represents convective IVPD. The positive pressure decrease is caused by the inertial acceleration. In contrast, convective forces decelerate blood flow and generate a negative gradient. The IVPD is the result of the instantaneous sum of these two pressure differences. IVPD, intraventricular pressure difference.

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Inertial and convective forces obey different physiological determinants. Theoretically, the inertial component of IVPD should be caused by the impulse developed by myocardial restoration forces. (Thomas et al. 1991, Greenberg e tal 1996) The convective IVPD should be determined by filling flow velocity and chamber geometry (Courtois et al. 1988). From the temporal profile of the LV apex pressure relative to left atrial pressure, the peak IVPD from the mitral valvular annulus to the LV apex is calculated. (Courtois et al. 1988) Color M-mode images were obtained using the apical 4-chamber view (Asada-Kamiguchi et al. 2006, Firstenberg et al. 2000, Yotti et al. 2005), apical long axis view (Steine et al. 2002) or 4-chamber view by trans-esophageal echocardiography (Ronber et al. 2003) and analyzed using an image-processing algorithm. (Figure 7.1) The resolution of the color Doppler and the temporal and spatial resolution of color Doppler M-mode images are important, as they determine the degree of accuracy for the partial derivative terms of the Euler equation (Greenberg et al. 2001). However, resolution was already acceptable using equipment in 2000 to 2005, and equipment has become much more developed in the past decade. Thus, this issue is resolved if the recent commercially available machines are used to measure IVPD. The LV inflow tract shows a complex three-dimensional geometry. Therefore, no straight line could ever be expected to coincide with a streamline throughout diastole. The accuracy of the pressure estimate is also related to the degree to which the ultrasound scan line approximates an inflow streamline through the center of the mitral valve. (Greenberg et al. 2001) It has been shown through a computational model that accurate results can be achieved when the scan line is placed within the central 60% of the valve orifice or when an angular misalignment is made up to 20°. The particular concern is the presence of vortices that form at the leaflet tips, which may affect the flow from the LA into the LV. During early diastolic filling, blood flows across the mitral valve from the LA into the LV, and the inflow jet produces a vortex ring (Domenichini et al. 2007, Hong et al. 2007, Kilner et al. 2000). The strength of the vortex ring continues to increase until the vortex ring is pinched off from the mitral leaflet tips. At the point when the inflow jet is terminated, the primary vortex ring detaches from the inflow jet and pinches off. Vortex ring formation within the LV inflow tract is predicted to improve LV filling efficiency and has been investigated as a possible metric of cardiac function. (Kilner et al. 2000) As these vortices are formed outside the central flow region, as long as the scan line is placed on the central stream line, the accuracy of the measurement of IVPD is proven. (Stewart et al. 2012).

3. CLINICAL IMPLICATION 3.1. Relationship between IVPD and Systolic and Diastolic Function Firstenberg et al. (Firstenberg et al. 2001) showed that IVPD is directly related to Emax, which is the gold standard measurement of systolic cardiac function and is assessed only by using cardiac catheterization with a micromanometer. Steine et al. 1999 also showed a strong correlation between IVPD and tau, which is the gold standard measurement of diastolic function and is assessed only by using cardiac catheterization with a micro manometer.

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Firstenberg et al. (Firstenberg et al. 2001, Firstenberg et al. 2008) showed that IVPD correlated linearly with improvements in regional tau.

3.2. Simultaneous Analysis of Spatial and Temporal Information The estimation of diastolic function using IVPD offers several advantages over the conventional diastolic parameters that are currently in clinical use. Pulsed Doppler techniques can measure velocity information at one point in space and at one point in time. In contrast, IVPD as measured by echocardiography from the color M-mode Doppler includes velocity information along the whole scan line from the mitral valve to the apex in space and during the whole diastolic duration in time. Ohara et al. 2012 effectively leveraged those benefits to determine the mechanisms of diastolic function. In their study, they divided the IVPD into two parts: from the left atrium to the mid-LV and from the mid-LV to the LV apex. With dobutamine infusion, total IVPD increased by a mean 2.20 ± 1.95 mmHg in normal controls and by only 0.73 ± 1.33 to 1.08 ± 1.57 mmHg in patients with diastolic dysfunction. Iwano et al. (Iwano et al. 2015) compared 151 patients with HFpEF, 101 patients with HFrEF and 28 normal controls. While basal IVPD were not significantly different among groups (HFpEF, 1.59 ± 0.62 mm Hg; HFrEF, 1.49 ± 0.75 mm Hg; controls, 1.80 ± 0.61 mm Hg; P = NS, analysis of variance), apical IVPDs were decreased in both HF groups (HFpEF, 1.18 ± 0.56 mm Hg [P < .01 vs controls]; HFrEF, 0.87 ± 0.48 mm Hg [P < .01 vs controls]; controls, 1.65 ± 0.62 mm Hg), resulting in decreased total IVPDs in patients with HF (HFpEF, 2.55 ± 0.80 mm Hg [P < .01 vs controls]; HFrEF, 2.16 ± 0.80 mm Hg [P < .01 vs controls]; controls, 3.17 ± 0.91 mm Hg). They concluded that in HF patients apical IVPD was reduced in relation to reduced longitudinal function and the basal IVPD was maintained by increased LA pressure manifested as preserved E wave. They concluded that, as the mechanism increasing IVPD, the augmentation of IVPD from the mid-LV to the apex was decreased in patients with diastolic dysfunction. Thus, the analysis of regional IVPD can detect the mechanisms of diastolic dysfunction. Yotti et al. 2005 applied this benefit to find the disc ordination of IVPD in patients with DCM by focusing on the timing of peak IVPD along the LV long axis. They found that IVPD originated near the base and propagated toward the apex. In the normal heart, the local temporal delay was very small, and IVPD reach its maximum almost simultaneously at both the base and apex. This propagation was slower in patients with dilated cardiomyopathy (DCM) compared to normal controls because their gradient time delay was significantly prolonged. As the peak value of the IVPD was reached at different moments along the long axis cavity, the suction became disorganized and IVPD was subsequently reduced (Yotti et al. 2005). These new approaches providing both location and temporal information enable the examination of the mechanisms underlying diastolic function. Like other diastolic parameters, IVPD is also affected both by diastolic function and LA pressure. Inertial component of Euler equation is influenced by both LV suction and LA pressure causing driving force from LA to LV. It is difficult to differentiate them. There are 2 ways to differentiate two components. First is to analyze spatial distribution of IVPD describe in this section. Second is to detect the response to sympathetic augmentation of IVPD by exercise or dobutamine infusion described at the section 7.3.4.

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3.3. Analysis of Inertial and Convective IVPD As shown in Euler’s equation, IVPD is calculated using two components: inertial and convective IVPD (Greenberg et al. 2001, Yotti et al. 2005, Ohara et al. 2012). The positive apex-to-base pressure drop was caused by the inertial acceleration of blood, which generated a suction force. In contrast, convective forces decelerated blood flow and generated a negative gradient as the pressure rose from base to apex in opposition to flow (Yotti et al. 2005). Because the total IVPD is the result of the instantaneous sum of these two pressure gradients of opposite sign, the total IVPD was smaller than the inertial IVPD component. Yotti et al. 2005 showed that although the peaks of the inertial and convective IVPD components were not reached simultaneously, the peak total IVPD closely correlated with the peak value of these two components: total IVPD = 0.2 + 0.88 × Inertial IVPD - 0.40 × Convective IVPD (adjusted R2 = 0.85, P < 0.0001) in normal subjects. They determined that the negative convective IVPG was generated close to the cardiac base. They also found that although patients with a restrictive filling pattern showed similar values of total IVPD, they showed a trend toward a higher inertial IVPD and a significantly higher absolute convective IVPD than did patients with nonrestrictive filling.

Figure 7.3. Left ventricular IVPD in patients with cardiac dysfunction: case 1. A Three-dimensional profile of IVPD. B temporal profile of IVPD. C spatial profile of IVPD at the peak IVPD. The data are from a patient with cancer using anthracycline for chemotherapy. In this case, the torsion and untwisting rate was decreased as assessed by speckle tracking imaging. The peak IVPD is relatively low due to the decreased inertial IVPD at the mid and apical portions of the LV. As the sucking force decreased, diastolic function is thought to be decreased in this case. IVPD, intraventricular pressure difference.

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Ohara et al. 2012 showed a similar trend in patients with diastolic dysfunction. In their study, with impaired relaxation, the reduced adrenergic response to dobutamine stress was predominately due to reduced inertial acceleration, whereas with more severe diastolic dysfunction, it was predominately due to greater convective deceleration. Their results provided very unique and useful information for assessing diastolic function in various cardiac diseases (Figure 7.3, Figure 7.4).

3.4. IVPD during Exercise and Dobutamine Infusion Currently, exercise intolerance is thought to be important in predicting outcomes in various heart diseases, (Piepoli et al. 2004, Diller et al. 2005) and IVPD is proven to play an important role in exercise intolerance. (Rovner et al. 2005) Left ventricular diastolic function has been considered to be essential in exercise tolerance and IVPD. During exercise, increased IVPD is associated with enhanced acceleration of blood flow across the mitral valve, while filling is maintained at a low pressure in the left atrium. (Rovner et al. 2005).

Figure 7.4. Left ventricular IVPD in patients with cardiac dysfunction: case 2. A Three-dimensional profile of IVPD. B temporal profile of IVPD. C spatial profile of IVPD at the peak IVPD. The data are from a patient undergoing chemotherapy with anthracycline for cancer. In this case, the LV shows uncoordinated abnormal motion as assessed by speckle tracking imaging. The uncoordinated motion of the LV might cause the larger convective IVPD. The peak IVPD is relatively small due to the large convective IVPD. IVPD, intraventricular pressure difference; LV, left ventricle.

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In the normal LV, adrenergic stimulation increases contractility, myocardial restoration forces, and the resulting ventricular suction. (Yotti et al. 2005) Increased adrenergic tone also decreases filling time, an effect that could reduce the filling volume and elevate diastolic pressure. However, increased diastolic suction causes rapid filling and lowers minimum LV pressure. (Nikolic et al. 1995, Cheng et al. 1993) Consequently, enhanced diastolic suction acts as a compensatory mechanism to maintain low pulmonary pressures in situations of increased contractility. During exercise, LV preload acutely increases, the heart rate increases with decreases in the duration of the diastolic stage, and the stroke volume increases; all of these physiological changes result in cardiac output (Ronver et al. 2005). Therefore, the ability of the LV to augment its relaxation potential and increase the suction of the blood from the LA may play an important role in increasing the filling rate at low filling pressures at a higher heart rate (Ronver et al. 2005). In patients with heart failure, this augmentation is diminished secondarily to abnormal LV diastolic function (MacGowan et al. 2001, McKelvie et al. 1995, Pepi et al. 1999), producing symptoms of dyspnea with exercise and providing for poor aerobic capacity. In most normal individuals, the limiting factors that influence V˙ O2 max are the skeletal muscle mass and the capacity of the cardiovascular system (Vanoverschel et al. 1993). In patients with heart failure, exercise capacity may be limited by the number of frequently coexisting factors, such as decreased contractility, diastolic dysfunction, chronotropic incompetence, oxygen metabolism, or skeletal muscle mass (Genovesi-Ebert et al. 1994). During peak exercise, the duration of diastasis is greatly diminished to account for the increase in heart rate. Yet, for the heart to increase cardiac output, the diastolic mechanics must adjust to the decrease in time to fill (Thomas et al. 1992), which is done at low filling pressures; rather, early relaxation is increased to provide for a “suction” force and high LV compliance (MacFarlane et al. 1991). Popović et al. 2006 showed that the change in stroke volume and IVPDs during exercise showed a strong correlation (r = 0.96, P = 0.0002). Ronver et al. 2005 clearly demonstrated the relationship of IVPD and exercise capacity in patients with diastolic heart failure. In their study, the change in IVPD was higher in normal subjects compared with patients with heart failure. Furthermore, increases in IVPD correlated with peak V˙ O2 max and were the strongest predictors of exercise capacity, which means that the ability to augment diastolic LV relaxation represented by increased IVPD with exercise has the strongest relationship with exercise intolerance. It is reasonable that a strong relationship exists between the ability to increase IVPD with exercise and V˙ O2 max max (Ronver et al. 2005), because both V˙ O2 max and IVPD are highly correlated with the Tau index (Rovner et al. 2005, Steine et al. 1999). Therefore, if these methods are used to evaluate cardiac function in acquired or congenital heart disease, it is possible that IVPD during exercise may be considered a strong predictor for outcomes.

3.5. IVPD in Patients with Dilated Cardiomyopathy The observation of a limited suction response to dobutamine in patients with DCM helps to explain why LV filling pressures may rise disproportionately during stress, leading to exercise-related dyspnea in these subjects. (Yotti et al. 2005)

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The mechanism to enhance diastolic suction could be important in patients with DCM, because they depend on an adequate end-diastolic volume to maintain cardiac output and because they have chronically elevated filling pressures at rest. However, Yotti et al. 1995 showed that the LV in DCM showed abnormal suction at baseline and had a limited ability to increase suction at inotropic stimulation. In their study, IVPD increased by 23% in patients with DCM, which was much lower than the 40% observed in volunteers. In contrast to that in the normal LV, the minimum diastolic pressure of failing ventricles rises during exercise (Cheng et al. 1993). It is very likely that the limited suction reserve recruitable by inotropic stimulation is a major determinant of the abnormal behavior induced by exercise in patients with DCM.

3.6. IVPD in Patients with Diastolic Heart Failure Ohara et al. 2012 demonstrated a reduction of the adrenogenic response of IVPD in patients with preserved ejection fraction and diastolic dysfunction. In their study, patients with impaired relaxation showed the lowest IVPD compared with pseudo-normal and restrictive filling. (Ohara et al. 2012) This result was due to a higher IVPD from the LA to the mid-LV in patients with pseudo-normal and restrictive filling than in patients with impaired relaxation, suggesting that LA pressure was higher in these patients. Interestingly, patients with impaired relaxation had the smallest augmentation, predominantly due to reduced inertial acceleration between the mid-LV and LV apex. The IVPD can be increased due to a decrease in LV diastolic pressure or increase in LA pressure. They speculated that IVPD between the LA to mid-LV represented elevated LA pressure, and IVPD between the mid-LV and LV apex represented LV suction. Even if total IVPD is not changed, the spatial pattern of IVPD will be helpful to consider the diastolic function.

3.7. IVPD in Patients with Hypertrophic Obstructive Cardiomyopathy Rovner et al. 2003 studied 19 patients with hypetrophic obstructive cardiomyopathy undergoing alcohol septal ablation. Reduction of LV outflow tract obstruction after alcohol septal ablation (62 ± 10 to 29 ± 5 mmHg, P < 0.001) was associated with an improvement in diastolic suction force. IVPD at baseline was 1.5 ± 0.2 mmHg and increased to 2.6 ± 0.3 mmHg (P < 0.001) at follow-up (5.6 ± 1.2 mo), which was accompanied with the improvement of symptoms and diastolic function detected by conventional diastolic measures. They speculated that the diastolic function improvement was associated with the improvement of some of the LV hypertrophy secondary to the increase in afterload caused by the LV outflow tract obstruction. IVPD may be useful to detect such changes in LV suction following the changes of the loading conditions.

3.8. Impact of Aging on Diastolic Function Most cardiac function assessed by echocardiography shows change with aging. A multitude of studies (Benjamin et al. 1992, Lakatta et al. 2003) have described profound

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effects of aging on LV filling patterns and it was usually assumed that aging impairs LV relaxation. Popović et al. 2006 showed that normal and vigorously healthy aging influences tau, indicating that aging itself invariably deteriorates calcium reuptake, as seen by slowing of relaxation (Yamakado et al. 1997), which in turn profoundly affects IVPD. Aging also profoundly affects passive diastolic properties (Arbab-Zadeh et al. 2004). It induces concentric remodeling, increases the chamber stiffness constant, and decreases equilibrium volume (a volume at which diastolic pressure equals 0 mmHg). For the study of IVPD, an equilibrium volume decrease is especially important because ventricular suction, of which IVPD is a major manifestation, depends on the ability to contract below the equilibrium volume during systole to engage passive restorative forces during relaxation. Thus, aging is associated with two processes that may lead to IVPD decreases. Aging has another aspect when considering younger populations. Cardiac function in infants and children shows different properties compared to that in adults. As shown previously, the untwisting rate directly relates with IVPD. We previously showed (Takahashi et al. 2010) that peak torsion and apical rotation increase with age. Furthermore, the peak untwisting rate decreased with aging, and greater untwisting occurred during IVRT in the younger heart compared to that in adults. As IVPD is linked with both active and passive relaxation, which change with aging, further evaluation is needed to understand IVPD in younger populations.

3.9. IVPD in Right Ventricle Right ventricular (RV) dysfunction is known to adversely affect prognosis in patients with a number of cardiovascular diseases. (Voelkel et al. 2006) Furthermore, RV function plays a major role in normal and abnormal cardiopulmonary interactions. (Di Salvo et al. 2005) It is now recognized that impaired RV systolic function is a major determinant of survival in patients suffering from ischemic or idiopathic dilated cardiomyopathy. (Afilalo et al. 2013, Gulati et al. 2013) In addition, RV function is among the most powerful predictors of long-term survival in patients with advanced heart failure, and is even more valuable than LV ejection fraction (Karatasakis et al. 1998). Because of its thin walls and low pressures, it could be hypothesized that the RV is filled passively. However, several studies have established a role of early diastolic suction as a determinant of RV filling during early diastole (Sabbah et al. 1981, Sun et al. 2006). During early diastole, the RV also is capable of lowering intracavitary pressure below RA values and of continuing to decrease its pressure despite its increasing volume. A high prevalence of RV diastolic dysfunction has been shown with pulse wave and tissue Doppler imaging. (Henein et al. 1998, Yu et al. 1996, Soinarova et al. 2005) The driving force for RV filling is the diastolic pressure difference between the right atrium and the RV apex along the RV inlet, as shown by catheterization procedures. (Pasipoularides et al. 2003) Later, Cortina et al. 2007 demonstrated the accuracy of measuring RV-IVPD using echocardiography. In their study, an anteriorly modified four-chamber apical view was used to obtain the color M-mode from the RV inflow to apex. Euler’s equation was used to calculate RV-IVPD, as done in LV. RV-IVPD was smaller compared to that of the LV (2.6 mmHg in young healthy volunteers, 1.4 mmHg in elderly population, and 1.0. mmHg in patients with DCM). In contrast to LV-IVPD, the peak RV-IVPD was almost completely

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determined by inertial component, and the convective component was very small. The tau index of the RV showed a significant liner relationship with RV-IVPD. Considering those results, the measurement of RV-IVPD using echocardiography is a useful tool for the clinical assessment of RV diastolic function (Figure 7.5).

Figure 7.5. Right ventricular IVPD in normal subjects (same subject as shown in Fig 7.3). A Threedimensional profile of IVPD. B temporal profile of IVPD. C spatial profile of IVPD at the peak IVPD. The red line represents IVPD, the blue line represents inertial IVPD, and the green line represents convective IVPD. Compared to the LV-IVPD as shown in Fig 7.2, RV-IVPD is smaller than LV-IVPD. The peak RV-IVPD is almost completely determined by its inertial component, as the convective component is very small in RV. IVPD, intraventricular pressure difference; LV-IVPD, left ventricular intraventricular pressure difference; RV-IVPD, right ventricular intraventricular pressure difference; RV, right ventricle.

3.10. IVPD in Left Ventricle with Different Size Humans develop from fetuses to adults. During this process, the size of the heart dramatically increases with aging. Therefore, the concept of scaling should be considered in the context of cardiac function. Zoran et al. 2006 showed very unique data related to both IVPD and IVPG, which is defined as IVPD divided by LV length, in humans and small mammals. They showed that as mammals get smaller, the IVPD also becomes smaller.

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However, IVPG increases as the heart becomes smaller. They speculated that with the decrease in the heart size, filling time duration proportionally decreases more than any other heart cycle interval. IVPG must be larger to produce a sufficient end-diastolic volume. This phenomenon corresponded with the fact that diastolic duration is shortened during exercise. In contrast to IVPG, the greater IVPD associated with larger mammals may be due to the larger LV length and volume, as there is more space to have a greater pressure difference from the valves to the apex. They concluded that IVPG changes with size may also help assess the diastolic function of pediatric patients, who would have smaller IVPD but larger IVPG compared with adults.

CONCLUSION This chapter discussed the history of the research into IVPD, mechanisms causing IVPD, methods for measuring IVPD using echocardiography, and the clinical implications of IVPD. The evaluation of IVPD will allow new insights into diastolic function in both clinical and research settings. This chapter may provide ideas to both clinicians and researchers for investigating the mechanisms underlying diastolic function, developing research projects, and using new findings to treat patients with diastolic dysfunction.

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Yu CM, Sanderson JE, Chan S, Yeung L, Hung YT, Woo KS. Right ventricular diastolic dysfunction in heart failure. Circulation. 1996;93:1509-14.

In: Advances in Hemodynamics Research Editor: Keiichi Itatani

ISBN: 978-1-63483-187-1 © 2015 Nova Science Publishers, Inc.

Chapter 8

HEMODYNAMICS IN CORONARY ARTERIAL DISEASE AND MYOCARDIAL PERFUSION Tadashi Yamamoto,1, Sachi Koyama2, Keiichi Itatani3 and Satoshi Yamada4 1

Department of Cardiology, Hokkaido Cardiovascular Hospital, Japan 2 Department of Cardiac Surgery, The University of Tokyo, Japan 3 Departments of Hemodynamic Analysis and Cardiovascular Surgery, Kitasato University School of Medicine, Japan 4 Department of Cardiovascular Medicine, Hokkaido University, Japan

ABSTRACT Coronary blood flow pattern is formed with each cardiac cycle, and its pattern is known to differ from the aortic flow pattern. The coronary blood flow is dominant during diastole, when the microcirculatory resistance is attenuated with the relaxation of the myocardium. The factors that affect hemodynamics in the coronary artery consist of the pressure distribution, coronary flow amount, peripheral myocardial resistance, coronary arterial geometrical configuration, and blood viscosity. In the assessment of the coronary arterial disease, evaluation of blood flow and pressure in each coronary vessel is one side of the approaches, and evaluation of the consequential myocardial perfusion is the other side. In addition to the pressure and flow measurement with catheter, that is used not only to detect the diseased stenotic site, but also to evaluate flow reserve with pressure related parameters including FFR (fractional flow reserve), recent novel technology with computational modeling enabled visualization of wall shear stress (WSS) distribution, which has been implicated in the plaque progression and rupture risk. Low WSS is believed to cause atherosclerosis development, resulting in effort angina, whereas high WSS is believed to cause plaque rupture, resulting in acute coronary syndrome. Recent results in coronary arterial hemodynamic research provide clue not only to the evaluation



Corresponding Author address E-mail: [email protected].

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Keywords: hemodynamic in coronary artery, myocardial perfusion, coronary artery disease, atherosclerosis

1.STRUCTURAL AND MECHANICAL FEATURES IN CORONARY CIRCULATION 1.1. Coronary Vessel Anatomy The coronary vessel system shown in Figure 8.1 consists of large arteries ranging from several mm to 400 μm in diameter and branching into small arteries and arterioles (< 400 μm in diameter). The coronary arteries run over the epicardial surface of the heart and branch off into arterioles. These arteries are 400-1300 μm in diameter, and repeat so many bifurcations as if it diverges to uncountable number of small vessels, then become arteriolar. There are 2 types of arterioles; one run into the cardiac muscle, the other reach to the deepest layer of the trabeculae carneae and the papillary muscle. The former supplies blood mainly to outer side of the ventricular muscle, and the latter supplies blood to the subendocardium (Estes et al. 1966).The arteries with less than 400 μm diameter are referred to as resistive vessels (Chilian et al. 1989). These arteries are not clearly at coronary angiography, but appear a myocardial brush of contrast medium. The coronary arterial system consists of two major vessels which are the left coronary artery (LCA) and the right coronary artery (RCA), and the LCA diverges to left anterior descending (LAD) artery and the left circumflex (LCX) artery from left main trunk (LMT) as shown in Figure 8.2.

Figure 8.1. The coronary vessel system.

The LAD artery runs anterior interventricular groove in the apex direction, branch off the septal branches and the diagonal branches which perform a nutrient of the septum and the anterior wall of left ventricular (LV). LCX artery runs from left atrium sulcus interventricularis cordis to post-lateral in LV wall, and performs a nutrient of lateral, posterior and anterior papillary muscle. RCA runs right ventricle anterior surface through right atrioventricular groove and diverges to posterior interventricular branch and atrioventricular branches in posterior interventricular groove. RCA performs a nutrient of right ventricle

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(RV), inferior in LV wall, posterior papillary muscle, a portion of the interventricular septum and the sinus node and the atrioventricular node. The coronary artery becomes small in diameter and has various shapes, for example bifurcation and bent shape. There are bifurcation point into LAD and LCX branches, that into LAD and lateral diagonal branches, LCX has bifurcation point into the obtuse marginal (OM) and posterolateral (PL) branches. RCA has bifurcation point into the atrioventricular node (AV) and posterior descending (PD) arteries. The Kawasaki et al. illustrated these divergence points of view using multi-detedtor CT (Figure 8.3) (Kawasaki et al. 2009). There are two types of bending sites in coronary arterial branches: the first one is the formed bending site due to ventricular contraction like the middle portion of LAD artery, and the other is the anatomically formed bending site like the proximal RCA portion.

Figure 8.2. The coronary artery system: Left main trunk (LMT), Left anterior descending (LAD), Left circumflex (LCX), Right coronary artery (RCA).

Figure 8.3. LMT bifurcation angles of the representative case. Each bifurcation angles can be measured on a volume rendering image using a three-dimensional workstation (Kawasaki et al. 2009).

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1.2. Coronary Vessel Tissue The normal coronary structure has three-laminar that consists of intima - media adventitia (Figure 8.4). The intima is comprised of one level of endothelial cell, and the media is of the vascular smooth muscle layer and a connective tissue. As for the adventitia, it becomes the layer of the connective tissue (Figure 10.5). From coronary arteries to arterioles, the media has three or more smooth muscular levels, and arterioles has 1-2 smooth muscular ones. Capillary is defined as a vessel without smooth muscle and/or media. The vascular beds from arterioles to venula are understood as a plexus and arterioles approximately 12-15 μm branch it and it is "net" before it continues and reaches the venula and is present in a capillary (Batson et al. 2000).

Figure 8.4. Coronary artery structure: three-laminar consists of intima – media – adventitia.

Figure 8.5. Histology of coronary artery: Masson staining (×2).

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1.3. Coronary Vessel Stiffness In general, when ―vascular hardness‖ is mentioned, hardness has two meanings: the first one is a material property of the vessel wall, and the second one is the force necessary for the unit diameter dilatation of the tube. The former ―hardness‖ as a material property of the vessel wall is called ―elastic modulus‖, and the latter ―hardness‖ as the dilatation force is called ―stiffness‖. The coronary artery is said to have approximately 10% diameter changes according to normal pulse with 40 mmHg of pulse pressure under 100 mmHg average blood pressure. On the other hand, the axial length is said to have nearly zero length changes even if the axially artery is said to extend 30-50% in the blood pressure measurements. Because the vascular pressure-diameter relationship is nonlinear, linear model can be applied only in the micro-deformation in the microsection. If the vessel diameter D0 increases ΔD0 with the pressure increases ΔPi from Pi, the elastic modulus (Ep) is expressed as follows.

.

/

(8.1)

If Ps, and Pd represent the systolic and diastolic pressure, and if Ds and Dd represent the systolic and diastolic vessel diameter, stiffness (β) is expressed as follows. ( .

) /

(8.2)

Representative value of β is reported to be around 29.8 in the human coronary arteries. Other than these calculated parameters based on physical models, direct measurement methods of the coronary artery properties has been report using an intravascular ultrasound (IVUS) device (Jeremias et al. 2000), and these measured properties are often mentioned in the discussion related to the balloon underexpansion in the stent delivery process and/or stent recoil detected by the quantitative coronary angiography (Quantitative Coronary Angiography: QCA). (Azis et al. 2007).

1.4. Coronary Vessel Movement In the heart, muscle fibers coil obliquely and covers the whole heart chamber (Figure 8.6). The cardiac muscle on the left ventricle repeats systole-diastole movements longitudinally, circumferentially and tortuously. Coronary vessel movements were classified into 3 types: the bend type, compression type, and displacement type. Especially the compression type was seen frequently in the proximal and mid left anterior descending artery, mid left circumflex artery. The compression movement may be an important mechanical stress inducing coronary atherosclerosis (Figure 8.7) (Konta et al. 1994). The coronary arteries are attached to the epicardial surface and move with contraction. Stresses due to coronary artery movement may cause the micro-tissue damage of in the

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atherosclerotic vessel walls, resulting in progression of the atherosclerogenetic diseases (Stein et al. 1994).

Figure 8.6. The image of myocardial structure from URL: http://www.anatomy.med.keio.ac.jp/funatoka/anatomy/Rauber-Kopsch/band1/png100/628.png.

Figure 8.7. Coronary artery movement: classification of coronary artery movement. Lines illustrate the coronary artery segment and arrows show the direction of coronary artery movement. Ostial C, ostial compressiontype; Lineal D, lineal displacement type; Parallel D, parallel displacement type (Konta et al. 2003).

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This is believed to be the cause of the facts that proximal coronary arterial segments is predisposed to the atherosclerosis progression and/or to the vulnerable plaque ruptures (Katritsis et al. 2008). The stretch-compression type of coronary artery movement is an independent predictor of the location of culprit lesions responsible for ST-segment elevation myocardial infarctions (O‘Louqhlin et al. 2007). Compression type of coronary artery movement may accelerate atherosclerosis and predispose to plaque vulnerability (Chan et al. 1957).

2.CORONARY ARTERY DISEASE ASSESMENT BASED ON THE GEOMETRICAL INFORMATION 2.1. Overview of the Geometry Measurements of Coronary Arterial Diseases Modalities to evaluate the coronary arterial shape, to Figure ure out the plague shape and size, ant to quantify the plaque include coronary computed tomography (Coronary CT) (Figure 8.8), coronary angiography (CAG) (Figure 8.9) and intravascular ultrasound (IVUS) (Figure 8.10). Coronary CT provides information of the 3D anatomical shape of the coronary arteries and the plaque.

Figure 8.8. Image of normal coronary artery. A and B: Left VR image, C and D: Right MPR image.

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Figure 8.9. CAG image of normal coronary artery. A: Left coronary artery. B: Right coronary artery.

Figure 8.10. IVUS images of plaque. A: Pre-balloon-dilatation was not performed because there was a small amount of calcification. B: Pre-balloon-dilatation was performed with heavy calcification lesion. C: Image of a case without pre-balloon-dilatation. D: Image of a case with pre-balloon-dilatation. Color legend: (Red) calcification (Yellow) dense fibrosis (Green) fibrosis (Blue) lipid pool.

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CAG is older modality than coronary CT, and is the finest diagnostic tool for the evaluation of the coronary arterial lumen even now, even though it provides 2D projection images formed by the contrast medium, which also provides rough information about blood flow direction and speed. IVUS enables plaque property and vascular tissue observation from the coronary artery lumen, and it enables a qualitative and qualitative evaluation of the plaque.

2.2. Image Acquisition in Coronary CT Coronary CT provides the anatomical feature of coronary arteries, and geometrical and qualitative information of the coronary arterial plaque, and it also quantifies the calcification. The image of coronary CT can be obtained with cardiac-gated multidetector-row. From the coronary CT different types of image reconstruction can be performed with different diagnostic meanings: VR (volume render) image, an MPR (multi-planar reconstruction) (Figure 8.8). Regarding the image acquisition process, patients are routinely administered betaadrenergic blocker and sublingual nitroglycerine. Sufficient image quality can be obtained under the condition of heart rate to < 65 bpm, and oral or intravenous beta-blocker is necessary to lower the heart rate. Cardiac electrocardiogram-gated multidetector computed tomography (MDCT) scan images are acquired during breath-hold. Typical contrast medium dose is 0.7 ml/kg with 3-5 ml/sec injection rate followed by 30 ml saline. The effective radiation exposure is said to be 0.78 mSv for 300 mA. Typical imaging resolutions are 0.28 mm pixel pitch, 0.4 mm slice thickness, and 0.21 sec temporal resolution under the typical image acquisition parameters: 120 kV(p) tube voltage, 580 mA tube current, 0.42 - 0.5 sec gantry rotation time. Regarding the timing of the image reconstruction, 40% and 75% R-R interval are set to be end-systole and end-diastole, respectively. CT image reconstruction are usually reconstructed in off-line analysis by a single experienced radiological technician with commercial workstation. The accuracy of the luminal size measurements has been proven in literatures (Budoff et al. 2006), and vessels under 50% stenosis can be detected with significant accuracy on a curved multiplanar image reconstruction (Curved MPR). Calcification is diagnosed with CT value over 130 (Leber et al. 2005).

2.3. Image Acquisition in Coronary Angiography (CAG) CAG is a 2D evaluation method with the projection shadow, and is currently the finest examination for stenosis site detection in a coronary lumen (Figure 8.9). Not only the disease site and stenosis ratio, CAG can detect the coronary flow speed such as delay due to stenosis and it can detect the collateral pathway, which often changes coronary flow direction. In CAG, after a sheath insertion from radial or femoral artery, a guide wire is carried to the Valsalva sinus, and a catheter is carried forward to the coronary ostium and testing injection of contrast medium into the coronary arteries is usually performed to evaluate coronary stenosis and/or obstruction under X-ray. Compared with coronary CT, which evaluates coronary artery plaque 3D geometry and quality, CAG has advantages in the quantification of the coronary artery stenosis site and in the detection of the flow direction

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and speed. The imaging quality depends on the CAG investigator, but fewer radiation doses and fewer contrast medium than coronary CT are necessary in CAG.

3. CORONARY ARTERY DISEASE ASSESMENT BASED ON THE HEMODYNAMIC OR FUNCTIONAL INFORMATION 3.1. Overview of the Measurements of Hemodynamics in Coronary Arterial Diseases The factors that influences on coronary blood flow as a resistance are a coronary artery stenosis and coronary microvascular resistance. The methods in coronary arterial disease assessment based on catheter includes IVUS, which provides geometrical and characteristic information of the plaque and FFR (Fractional Flow Reserve) and/or CFR (Coronary Flow Reserve) that provide functional information of myocardial perfusion and myocardial flow reserve. Only CFR can be used to evaluate coronary microvascular resistance. FFR is defined as the ratio of maximum coronary blood flow under the presence of stenosis to that under the assumed removal of the stenotic disease (Phijls et al. 1996). If a direct current electric circuit model is applied, the relationship of the coronary pressure, flow, and resistance can be expressed as Ohm's law. Thus, FFR under a certain critical value indicates myocardial ischemia. CFR reflects peripheral vascular resistance. The measurements of CFR are based either on Doppler method (CFR-Doppler) or on thermodilution method (CFR thermo), and correlations between these two methods has been proven (De Bruyne et al. 1996). Coronary blood flow at rest is not reported to decrease unless the stenosis ratio becomes over more than 90% (Miller et al. 1994), but is reported to decrease under the maximum hyperemia where peripheral resistance is completely reduced, if there is more than 50% stenosis in the vessel. CFR is defined as the ratio of coronary blood flow under maximum hyperemia to that at rest. Normal CFR value is between 3 and 5, and CFR below 2.0 indicates significant coronary arterial stenosis (Gould et al. 1974). CFR becomes low under the influence of peripheral vascular disease, diabetes, left ventricular hypertrophy and myocardial infarction in addition to coronary stenosis. h-MRv (velocity-based index of microvascular resistance) is used coronary arterial microvascular resistance, and is defined as follows. ( (

) )

(8.3)

Pd and APV are also measured under hyperemia (Meuwissen et al. 2001, Verhoeff et al. 2001). On the other hand true peripheral vascular resistance TMR (true microvascular resistance) under hyperemia is expressed as follows. (8.4)

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where Q represents coronary arterial flow, and venous pressure is assumed to be approximately 0. If Q is measured by thermodilution method, TMR is termed IMR (index of microcirculatory resistance), and its clinical utility is being established (Fearon et al. 2003). Recently application of coronary CT based computational flow simulation for calculation of FFR has been reported as FFRCT (Taylor et al. 2013), and because it is non-invasive, it is expected to be utilized in clinical practice (Koo et al., 2014).

3.2. Fractional Flow Reserve (FFR) Measurement Because coronary arterial pressure distal to the stenosis site is an important indicator of blood perfusion to myocardium, the maximum increase ratio of the blood volume under the maximum hyperemia to that when the stenosis disease is removed is defined to be FFR (Phijls et al. 1996). If we apply direct current electric circuit to coronary arterial circulation, the relationship between the coronary arterial pressure, flow volume, and resistance is governed by the Ohm‘s law (Chapter 1). Coronary arterial pressure is equivalent to the aortic pressure Pa unless there‘s stenosis region, and using the coronary venous pressure Pv and myocardial microvascular resistance R under hyperemia, maximal coronary arterial flow Qmax in normal cases can be expressed as follows (Figure 8.11).

Figure 8.11. Coronary arterial system without stenosis and myocardial resistance. Pa represents aortic pressure, Pv represents venous pressure, R represents resistance.

(8.5) If there‘s coronary arterial stenosis, coronary arterial pressure distal to the stenosis site Pd is lower than Pa, and peripheral coronary arterial pressure, which is a driving pressure to the coronary arterial flow supply becomes Pd – Pv. Thus, maximal flow supply under stenosis is (8.6) FFR is a ratio of Qmax under the stenosis to Qmax without stenosis, and becomes (

)

(

)

(8.7)

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)

(

)

(8.8)

under the constant resistance R condition, and when Pv becomes negligible compared with Pa and Pd, FFR is expressed as follows (Figure 8.12). (8.9)

Figure 8.12. Coronary arterial system with stenosis disease. Pd represents coronary arterial pressure distal to the stenosis site.

Figure 8.13. Coronary arterial system with stenosis disease and collateral vessels. Qc represents collateral flow and Qs represents coronary arterial flow through stenosis site.

FFR herein can be defined when there are no collateral circulation, and is defined as FFRmyo (myocardial fractional flow reserve). When there is collateral vessels, collateral flow Qc is additional flow to that through stenosis site Qs (Figure 8.13). (8.10) and FFRcor (coronary arterial fractional flow reserve) is defined with the formula below.

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When the coronary artery is occluded, collateral flow Qc is the only remaining flow and coronary arterial wedge pressure Pw is governed by the equation (8.12) where Rc represents the collateral arterial resistance. When the stenotic disease is removed, collateral arterial flow Qc becomes 0, Thus, FFRcor is defined as

(8.13)

In actual clinical measurement of FFRmyo, guide wire for FFR measurement is inserted into the coronary artery, after the catheter for the wire is engaged on the coronary orifice. The wire is inserted 3 cm from the edge of the catheter to locate the pressure measurement point at the tip of the catheter. Air inside the catheter is removed and the catheter is filled with water. Pressure measured with catheter should coincide with that with the wire (Equalization). After the equalization, wire go through the stenosis site and measure Pd. CFR and FFR are measured under the hyperemia condition, and to obtain the hyperemia state, papaverine hydrochloride and ATP is administered. After the pressure measurement under hyperemia, the wire is removed.

3.3. Index of Microcirculatory Resistance (IMR) Measurements Index of microcirculatory resistance (IMR) can be measured based on the thermodilution flow measurement. Because coronary arterial flow has inverse proportion to the mean transit time at peak hyperemia (Tmn), from equation (8.4) IMR becomes (8.14) Normal value of IMR is reported to be below 2.0, and IMR over 3.0 is reported to be abnormal (Gould et al. 1974). Recent research results revealed that long-term cardiac functional prognosis was significantly poor after primary PCI (percutaneous coronary intervention) when IMR was abnormally high in patients with STEMI (ST segment elevation myocardial infarction) (Cuculi et al. 2014). According to Cuculi et al. 2014, in PCI-treated patients with STEMI, coronary microcirculation begins to recover within 24 hours and recovery progresses further by 6 months. FFR significantly reduces from baseline to 6 months. The presence of microvascular obstruction indicates a highly dysfunctional microcirculation.

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3.4. Flow Wires and Simultaneous Measurement of Pressure and Velocity Not only the pressure, coronary flow velocity can be measured using coronary flow wire, in which microtip of the Doppler echo probe is embedded. FloWire or flow and pressure measurement wire ComboWire (Volcano Corporation, San Diego, CA). ComboWire is the first guide wire that obtains intravascular flow and pressure information simultaneously, and it enables the calculation of HSR (hyperemic stenosis resistance index). HSR is defined as follows (8.15) AVP represents the average of the instantaneous peak velocities. Normal HSR value was defined under 0.8. While both FFR and CFR are highly utilized to ascertain the physiological effect of a stenotic lesion, the best cutoff value of 0.75 and 2.0 for FFR and CFR respectively, does not always correspond in intermediate lesions (40% to 70% diameter stenosis). Abnormal FFR or abnormal CFR was documented in 31% of intermediate coronary lesions. Deferral of PCI in this group was associated with a high major adverse cardiac events (MACE) rate, which underscores the rationale of combined pressure and flow measurements providing a stenosis resistance index that is better suited for clinical decision making in these lesions (Meuwissen et al. 2008). ComboWire enables calculation of HMR (hyperemic microvascular resistance index) defined as follows (8.16) Intracoronary measurement of HMR was reported to detect increased microvascular resistance. Therefore, HMR may serve as a novel outcome measure in pre-clinical studies for serial assessment of microvascular circulation (Koudstaal et al. 2013).

4. CORONARY ATHEROSCLEROSIS 4.1. Pathological Process in Coronary Artery Atherosclerosis Myocardial infarction is one of the major cause of death in the developed countries today in addition to malignant neoplasms and cerebrovascular stroke. Most of the causes in myocardial infarction also the same in the cerebrovascular stroke, is the atherosclerotic disease. Atherosclerosis is a vascular disease, in which the progressive increase of plaque volume may cause ischemia in the perfused tissue (Figure 8.14). The favorite atherosclerosis sites are empirically known to be the LAD region. Myocardial ischemia is caused by the atherosclerotic plaque in coronary artery and combination of its properties, shape, and volume causes development to the different types of clinical manifestation such as acute myocardial infarction (AMI) or effort-induced angina pectoris (EAP). These differences are considered to be the results of the stability of the fibrous cap which covers the lipid plaque core. In the

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process of EAP development, initially tiny atheroma increases the arterial wall thickness gradually with the progression in plaque volume, but at the same time the entire vessel lumen attempts to maintain the cross-sectional area in the lumen to avoid ischemia, and this phenomenon is called ―compensatory enlargement‖.

Figure 8.14. Diagrammatic representation of anatomic sites (shown in black) and distribution of atherosclerosis sited from DeBakey et al. 1985.

However, if the atheroma lesion reaches to a certain stenosis level, this compensatory function ceases. This pattern of progression in vessel lumen narrowing leads to the EAP. On the other hand, the process of AMI development has completely different pathological mechanisms. Simple collapse of fibrous cap with lipid-rich plaque causes thrombus

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formation, resulting in acute coronary syndrome (ACS), in which cardiac muscle cells fall into necrosis (Figure 8.15). The previous pathological findings revealed that the plaque rupture risk is not always related to the intimal stenosis level (Fukuoka et al. 2008, Ross R. 1993) but to stability of the plaque caused by its hemodynamic environments. The next section describes the mechanism of plaque progression process under various hemodynamic environments.

Figure 8.15. Image of vascular section of the plaque lesion, and plaque rupture (arrow: a rupture site).

4.2. Mechanical Factors Related to the Progression in Coronary Atherosclerosis Atherosclerosis is induced from the atherosclerotic plaque formation inside the arterial wall. The most promising hypothesis of plaque formation was advocated by Ross R. 1993. Ross states that the damage of the endothelial cells are caused by the increase in the mechanical loads of endothelial cells by high blood pressure, high blood sugar, lipid abnormalities, and increase in oxidative stress. The monocytes and lymphocytes adhere or infiltrate into arterial walls and differentiate into macrophages. Then, the excessive accumulated macrophages accumulate oxidized LDL cholesterol and foams into plaques. Simultaneously, the phenotypically changed human smooth muscle cells are increased to cause intimal hyperplasia which progresses the atherosclerosis. There are also several hypotheses about endothelial cell damage induced by the mechanical stress caused by the blood flow. The most promising hypothesis believed today is the low endothelial or wall shear stress (ESS or WSS) theory. Low WSS site would be a determined as the progressive region of atherosclerosis (Malek et al. 1999). This low WSS theory seems consistent to clinical observations, because actual atherosclerotic plaque distributions are often compatible to the region reported to have low WSS. Low WSS theory is thought to be applied to the atherosclerosis progression in the carotid artery, in which the bifurcation site from the common carotid to the internal and external carotid arteries is the common plaque progression site. The blood flow at this site causes low WSS because of the turbulent flow detachment at the lateral site of the bifurcation. Coronary artery geometrical feature with branch and curvature would affect the developmental process of atherosclerosis, and the main cause is speculated to be mechanical stresses in addition to the metabolic factors such as diabetes mellitus with insulin resistance,

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dyslipidemia, or hypertension. The proximal bending feature detected in RCA and LAD, deviates the blood flow to the lateral high and medial low velocity profile.

Figure 8.16. Low WSS region at the curvature region in proximal RCA. A: experimental flow visualization from Fabregues et al. 1998. B: CFD results from Tada et al. 2005.

Figure 8.17. Mechanism of the deviation in wall shear around bifurcation. A: longitudinal cross-section. B: short-axis cross section.

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Figure 8.18. Stenosis site and blood flow around the plaque. A: No stenosis. B: Stenosis at the lesser curvature. C: Stenosis at the greater curvature.

The blood flow stagnation at the lesser curvature region causes low WSS in these region (Figure 8.16, Figure 8.17). Atherosclerotic region at the lesser curvature in proximal RCA, and LAD, which is quite familiar in clinical practice in ischemic heart disease, can be considered to be the results of the low WSS theorem (Figure 8.18). The lateral side of the bifurcation also has low WSS region with flow stagnation (Figure 8.17) (Nakazawa et al. 2010), whereas high WSS region at the bifurcation apex with flow split is reported to have low incidence of atherosclerosis progression. The lateral side of the bifurcation at LMT to LAD and LCX, and at LAD to diagonal branch are another a common location of plaque development. Thus non-laminar turbulent flow with flow detachment increases a plaque development risk. If we explain coronary blood flow as if it were a flow in a river, a river meanders (=atherosclerosis) gradually and the lateral side of the meandered region collects sediments (=LDL cholesterol) and creates a riverbed (=plaque), which reduces the width of the river (coronary artery stenosis) and creates another meander, as a proverb ―Life is like a river‖ says.

4.3. Definition of the Vulnerable Plaque As mentioned above, one of the main causes of ACS is thought to be the unstable coronary artery plaques. The plaque stability does not depend on the stenosis ratio but on its property and shape. More than half of the ACS cases occurs in coronary artery diseases less than 50% stenosis, and many plaque ruptures are observed at the edge of the fibrous cap lesion facing normal healthy arterial wall. Thrombus formation at the plaque rupture site develops into an ACS. The unstable plaques are described as unstable plaques, vulnerable plaques, or soft plaques, and their characteristics are the thin fibrous cap covering the lipid core. The stability and instability due to plaque shapes influence the mechanical property of the plaques. A pathological feature of unstable plaque is the existence of macrophage and T lymphocyte. Especially the invasion of macrophage emits the matrix metalloproteinase (MMPs), which degenerates the extra cellular matrix, and increase in MMP-1, -2, -3, -9 in arteries with atherosclerosis is reported (Terashima et al. 1999). Within those MMPs, MMP-3 (stromelysin) is said to play an important role in degeneration of extra cellular matrix protein.

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However, certain types of plaques are easier to cause ACS dependent on its present site or shape, or are easier to rupture due to the mechanical stress.

Figure 8.19. The relationship between WSS and plaque rupture risk from Fukuoka et al. 2008. High WSS region coincide with plaque rupture site observed in IVUS.

Setting an example at curvature region of RCA, a healthy coronary blood flow flows from the Valsalva into the RCA with diastolic dominant volume, high velocity region near the center of the blood stream, and low velocity near the artery wall. The high velocity region shifts towards the lateral side of the curvature region and returns to the center at the distal. When the plaque formed at the lesser curvature of the RCA, the plaque does not interfere with the blood flow, but it can be predicted that when the plaque forms at the lateral side, the plaque interferes with the blood flow and causes a greater loss in the coronary artery blood flow after the plaque. Thus it is possible to determine the stability of the coronary blood flow from the present site of the plaque and also the stability of the plaque from the hemodynamic stress applied at the plaque. Previous report revealed the relationship between the plaque rupture and WSS (Figure 8.19) based on the finite element analysis method (Fukuoka et al. 2008).

5. NUMERICAL MODELING OF HEMODYNAMICS IN CORONARY ARTERIAL SYSTEM 5.1. Motivation of the Numerical Coronary Flow Simulation Blood flow pattern in coronary artery is characteristic and different from that in the arterial system. The left coronary artery accepts blood flow in diastolic predominance. Because blood flow supplied to the left ventricle cardiac muscle depends on the diastolic phase, the perfusion pressure of the left coronary artery depends on the aortic diastolic

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pressure. As described above, coronary blood flow is determined by peripheral perfusion pressure and vascular resistance. The vascular resistance depends on the microvascular compression and expansion according to the contraction and relaxation of the ventricular muscle. Davies et al. 2006 demonstrated the coronary flow sucking force generated by the ventricular relaxation based on the wave intensity analysis (Chapter 1). In this meaning, coronary arterial microvascular resistance is highly dependent on the ventricular muscle viability of perfused region. Lim et al. 2009 demonstrated that IMR had inversely correlated with the ventricular muscle viability in patients with ACS. Not only the coronary arterial plaque and microvascular resistance, the geometrical conformation of diseased site suck as relationship between plaque location and coronary arterial branches, would affect the plaque progression speed or prognosis of the ischemic heart disease. Hahn et al. 2009 demonstrated the causal relationship between blood flow disturbance and atherosclerotic disease progression. As noted above, blood flow affects the WSS, which causes degeneration or regeneration of endothelial cells function, resulting in atherosclerosis progression. Therefore, detail observation in coronary arterial flow has been widely expected in prognostic diagnosis of the ischemic heart disease. Computational fluid dynamics (CFD) is a powerful tool to examine and evaluate blood flow detail even in small vessels (Chapter 4). CFD enables the quantitative evaluation of the severity of coronary ischemia based both on the anatomical features of the disease site and on the myocardial reserve of the perfused lesion in each branch (Koyama et al. 2014). Taylor et al. developed FFR derived from coronary CT angiography (FFRCT) based on the there-dimensional (3D) coronary patient-specific CFD models. Their system provide FFR non-invasively under virtual hyperemia by modifying boundary conditions (Taylor et al. 2013). Samady et al. 2011 created coronary CFD models based on intravascular ultrasound (IVUS) and evaluated WSS and its oscillation, oscillatory shear index (OSI) to predict atherosclerosis progression. Therefore, the CFD method is less-invasive and useful for evaluation and prediction of the severity of coronary diseases.

5.2. Model Creation in Coronary Arterial System Most of the previous CFD reports have dealt patient specific modeling based on medical imaging based geometries including coronary CT or IVUS. These patient specific models realized coronary arterial geometry and plaque morphology characteristic to each patient (Figure 8.20). Although CFD is a kind of modeling, these patient specific modeling requires data accumulation with statistical analysis to conduct a generalized results. On the other hands, Koyama et al. 2014 and several other research groups have developed simplified model ―Idealized model‖, based on the averaged data of large number of patients‘ geometrical data such as coronary CT and angiogram (Figure 8.21). Their method is easy to conduct generalized information such as indication of the surgical procedures, but validation of the system would be difficult, because simple experiment using a specific case is unrealistic.

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Figure 8.20. The process of patient specific model creation based on medical images.

Figure 8.21. The idealized model based on the averaged data from many patients.

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5.3. Boundary Condition Settings for Coronary Flow Simulation As we described above, coronary arterial flow is characteristic and takes quite different pattern from other splanchnic organ flow. Most of recent cardiovascular CFD reports adopt ―lumped parameter‖ models, which is an analogy of the electronic circuit in their inlet and outlet boundary conditions, because it reflects the peripheral vascular characteristics in system as noted in Chapter 1. Lumped parameter model is a circuit model composed of includes vascular resistance, compliance, and inertance. Although they are characteristics of peripheral vasculatures, these characteristics are passive effects in peripheral vessels. Coronary arterial flow has a sucking drive from the microvascular system according to the relaxation of the ventricular muscle during diastole, thus simple combination of electrical components dose not realize these sucking forces.

Figure 8.22. Coronary arterial impedance in one cardiac cycle.

Figure 8.22 illustrates the impedance change in two cardiac cycles obtained by the simultaneously measured pressure and flow using ComboWire in a normal coronary artery. During systole, impedance continues to increase with ventricular muscle contraction, but during diastole, it continues to decrease due to muscle relaxation. These time-varying impedance is an easier tool for the application to the boundary conditions in coronary arterial CFD models (Koyama et al. 2014 and 2015). Moreover, most of the problems in ischemic heart disease includes heterogeneous viability of the myocardial perfusion. Because diastolic coronary flow is a results of the ventricular sucking, viability should have close relationship with the ventricular sucking force and peripheral impedance. Current CFD reports related to the coronary arterial modeling has not mentioned the problems of viability distribution. Future modeling would include physiological effects specific to the coronary circulation into the boundary conditions.

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5.4. Evaluation of Hemodynamics in Coronary Artery with CFD Figure 8.23 illustrates the calculated results with CFD. From the calculated flow velocity and pressure, flow streamline, pressure distribution, WSS and its related parameters can be calculated. Diagnostic parameters of ischemic severity including flow rate and FFR can be calculated, but in addition, predictive diagnostic parameters reflecting plaque rapture and progression risk including WSS and OSI also can be calculated with CFD simulation.

Figure 8.23. CFD results of the coronary arterial model. Streamline, pressure distribution, WSS distribution, and their fluctuation in one cardiac cycle are shown from the calculated results.

Atherosclerosis progression related to the coronary shape such as flexion and bifurcation, or turbulence in the coronary arteries. Fluctuating WSS would be the cause. CFD can evaluate detail flow dynamics even inside the small capillary and a powerful tool for the investigation of pathophysiology of the coronary arterial and ischemic heart diseases.

6. MYOCARDIAL PERFUSION 6.1. Myocardial Oxygen Demand and Supply LV myocardial oxygen consumption is determined by 1) the LV myocardial mass, 2) LV work load which is influenced by the heart rate and the systemic blood pressure, 3) the LV pre-contraction volume, and 4) LV contractility. On the other hand, oxygen supply to the myocardium depends upon 1) the arterial oxygen concentration, and 2) coronary blood flow which is determined by the perfusion pressure and the resistance of the coronary blood vessels (Braunwald E. 1971). In order to preserve adequate myocardial oxygen supply in the presence of coronary artery stenosis, the resistance of distal perfusion beds is reduced by coronary autoregulation mechanism, resulting in the normal myocardial blood flow. Myocardial perfusion is thus a highly regulated process, and significant reductions in blood flow at rest cannot occur until an epicardial coronary stenosis exceeds 85% to 90% of luminal diameter. However, the maximal (hyperemic) myocardial

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flow, which can be unpeeled by vasodilator stimulus, has been shown to decrease when the coronary stenosis exceeds 45% of luminal diameter (Figure 8.24) (Gould et al. 1974).

Figure 8.24. Relationship between percent diameter stenosis of an epicardial coronary artery and resting coronary flow (dotted line) and hyperemic coronary flow (solid line) observed in 12 dogs (Gould et al. 1974).

Figure 8.25. Ischemic cascade. ECG, electrocardiogram.

These abnormalities of myocardial perfusion develop first in the sequence of events resulting from an imbalance between myocardial oxygen consumption and myocardial oxygen supply called as ―the ischemic cascade‖, and angina develops in the end of the

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sequence (Figure 8.25). The ischemic cascade represents the physiological basis of functional assessment of myocardial ischemia using various imaging modalities. Vasodilatory stress results in maldistribution of blood flow between regions supplied by normal and stenotic arteries, that is, the maldistribution of the maximal (hyperemic) myocardial blood flow. In this stress mode, therefore, myocardial ischemia is diagnosed primarily by the demonstration of the myocardial area with a hypoperfusion on the stress images which is not present on the resting images. Because perfusion abnormalities occur earlier than wall motion abnormalities in the ischemic cascade, the techniques that identify perfusion abnormalities have the better sensitivity and the techniques that identify wall motion abnormalities have the better specificity in the diagnosis of ischemia (Leong-Poi et al. 2002, Kamiya et al. 2014).

6.2. Evaluation of Myocardial Perfusion with Noninvasive Imaging Modalities Clinical diagnosis of coronary artery disease (CAD) and risk stratification of patients with known or suspected CAD depend heavily upon noninvasive assessment of myocardial perfusion. For this purpose, single-photon emission computed tomography (SPECT) as well as multiple modalities including positron emission tomography (PET), myocardial contrast echocardiography (MCE), cardiac MRI (CMR), and cardiac computed tomography (CT) are widely used.

6.3. Single Photon Emission CT The commonly used radiotracers are thallium-201 and technetium (Tc)-based agents such as Tc-99m sestamibi and Tc-99m tetrofosmin, the uptake of all of which is dependent on myocardial cellular integrity in addition to blood flow. Images are analyzed qualitatively using visual inspection or semi-quantitatively using differences in relative counts between resting and stress images. Ischemia is suspected when there is reduced uptake on the stress images which is reversible on the resting images. If a fixed defect, that is a defect present on both resting and stress images, is shown, myocardial infarction should be suggested. SPECT myocardial perfusion imaging is widely available and a large body of evidence concerning its diagnostic and prognostic value has been given. Because the imaging does not occur during first pass of the tracers, there is less demand for high temporal resolution. However, the acquisition protocols are relatively long, and spatial resolution is substantially poorer than other available modalities, resulting in limiting detection of subendocardial perfusion defects. The roll-off of tracer uptake at higher myocardial blood flow limits sensitivity in detecting mild-to-moderate coronary stenosis. Furthermore, there are artifacts in the inferior wall related to gut and biliary activity. Because only relative perfusion is generally assessed, the sensitivity for detecting 3-vessel disease is reduced. Finally, the tracers expose patients to nontrivial radiation doses.

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6.4. Positron Emission Tomography PET consists of perfusion imaging (rubidium-82, nitrogen-13 ammonia, or oxygen-15 water) and functional metabolic imaging, for example with 18-Ffluorodeoxyglucose (FDG). In general, when mismatch between the flow and metabolism, that is, reduced flow with normal FDG uptake is found, reversible ischemia should be suggested. PET had higher diagnostic accuracy than SPECT for coronary stenosis of > 50% of luminal diameter (Bateman et al. 2006). The diagnostic accuracy is also higher in patients with multi-vessel disease. There was less gut interference and fewer attenuation artifacts, resulting in superior quality images. PET thus has higher spatial resolution than SPECT, with spatial resolution of 2 to 3 mm as compared with that of 6 to 8 mm of SPECT imaging. PET tracers have significantly less roll-off of extraction at high flows as compared with SPECT agents. In addition, the acquisition protocols are shorter than SPECT because of the short half-life of the perfusion tracers. PET has the advantage over SPECT myocardial perfusion imaging of being able to measure myocardial blood flow in absolute units using data from dynamic acquisitions during first pass of the contrast agent (Camici et al. 2009). Deriving the arterial input function from the blood pool, myocardial tissue-activity curves are fit to a 2-compartment kinetic model for determining the absolute perfusion. This has been shown to strongly correlate with myocardial blood flow measured by microspheres in animal models. Finally, radiation doses are lower in PET than SPECT because of the short half-lives of the PET agents. However, the widespread use of PET is hampered. One of the major limitations to PET is higher costs including the requirement for a cyclotron or rubidium generators.

6.5. Myocardial Contrast Echocardiography MCE allows the assessment of myocardial perfusion and viability as well as the quantitative assessment of myocardial blood flow velocity and myocardial blood volume by using intravenous ultrasound contrast agents. The contrast agents consist of air- or gas-filled small microbubbles (