Springer KK T. Yamaguchi (Ed.)

Clinical Application of Computational Mechanics to the Cardiovascular System

With 229 Figures, Including 45 in Color

'Springer Takami Yamaguchi, M.D., Ph.D. Professor, Department of Mechanical and Systems Engineering Nagoya Institute ofTechnology Gokiso-cho, Showa-ku, Nagoya 466-8555, Japan

ISBN 978-4-431-67989-9 ISBN 978-4-431-67921-9 (eBook) DOI 10.1007/978-4-431-67921-9 Library of Congress Cataloging-in-Publication Data

Clinical application of computatii>nal mechanics to the cardiovascular system I T. Yamaguchi (ed.). p.;cm. Includes bibliographical references and index. ISBN 4431702881 (hard cover: a1k. paper) 1. B1ood flow-Mathematical models. 2. Biomechanics. I. Yamaguchi, T. (Takami), 1948- [DNLM: 1. Cardiovascu1ar Physiology. 2. Biomechanics. 3. Computing Methodologies. 4. Models, Cardiovascu1ar. WG 102 C6403 2000] QP105.4 .C565 2000 612.1'181-dc21 00-028462

Printed on acid-free paper

© Springer Japan 2000 Originally published by Springer-Verlag Tokyo 2000 Softcover reprint of the hardcover 1st edition 2000 This work is subject to copyright. All rights are reserved, whether the whole or part of the material is concemed, specifically the rights of translation, reprinting, reuse of illustrations, recitation, broadcasting, reproduction on microfilms or in other ways, and storage in data banks. The use of registered names, trademarks, etc. in this publication does not imply, even in the absence of a specific Statement, that such names are exempt from the relevant proteelive laws and regulations and therefore free for generat use. Product liability: The publisher can give no guarantee for information about drug dosage and application thereof contained in this book. In every individual case the respective user must check its accuracy by consulting other pharmaceuticalliterature. 1)rpesetting: Camera-ready by the editors and authors

SPIN: 10763749 Foreword

Vascular diseases, particularly atherosclerosis, are the most frequent and critical underlying fatal disorders in the industrialized world. Cardiovascular deaths are the leading cause of death in the Western world. Although cancer or malignant neoplasms recently have topped the list of causes of deaths in Japan, cardiovascular and cerebrovascular diseases bring about more deaths than cancer if they are reclassified into a unified category of diseases of the vascular system. The National Cardiovascular Center was established by the Ministry of Health and Welfare of Japan to combat cardiovascular and cerebrovascular diseases. Since the Center was opened, we have continued to support basic and clinical sturlies of cardiovascular and cerebrovascular diseases within as weil as outside the Center. Clinical studies that we have supported in modern diagnostic and therapeutic measures against cardio- and cerebrovascular diseases have made remarkable advances in recent years, especially in medical imaging technology including CT and MRI, and in interventional measures including balloon angioplasty and other catheter-based treatments. We are proud of the significant improvement in the overall survival rate and the quality of life of patients suffering from vascular disorders. However, there are still many essential difficulties remaining in the diagnosis and treatment of vascular disorders. Such difficulties necessitate further fundamental studies not only from the practical aspect but also from the integrated perspectives of medicine, biology, and engineering. Fortunately, extremely rapid advancement of computer science based on the development of electronics technology has enabled us to study the very complex phenomena of fluid-wall interactions by computational or numerical methods. At the same time, the establishment of vascular biology in recent decades has made possible an increase in biological knowledge of the reactions and adaptations of the vascular system, and this may in turn provide a firm basis for computational studies. Against this background, we are now able to consider computational biomechanics as a third approach to vascular sturlies in addition to the experimental and theoretical paths, particularly for practical application in real clinical situations. For this reason, the National Cardiovascular Center opened its supercomputer center in 1997 to promote sturlies using high-performance computing. At the same time, a project to study the application of computational mechanics to various fields of clinical medicine began, and the results are presented in this book. We are very pleased that the project was so fruitful, and we hope that those results presented here will be widely utilized in fundamental and clinical sturlies and in the practice of cardio- and cerebrovascular medicine. H. Kikuchi, M.D., Ph.D. President National Cardiovascular Center

V Preface

The computational approach is one of the most important methods for scientific and engineering studies, paralleling experimental and theoretical approaches. lt has already been used in many fields of engineering and is regarded as the sine qua non tool for design and manufacturing in industry. Although its application in the fields of medicine and biology has been limited to date, the computational approach can also be extended to a wide range of medical disciplines. In addition, the explosion of Internet technology today undoubtedly enhances and accelerates the development of applications of computational mechanics to biology and medicine. The subject of this book is computational biomechanics applied to clinical cardiovascular medicine. A broad spectrum of computational approaches is discussed in the book to widen the horizons of computational biomechanics, with special reference to recent attempts in realistic modeling and simulations in the field of cardiovascular medicine. This book is a compilation of studies in a 3-year project promoted by the National Cardiovascular Center of Japan, and includes various aspects of computational mechanical studies of the cardiovascular system. Computational biomechanics is a term used to describe the project's approach to integrate the fluid and solid mechanics of the heart and the vascular system and finally to create a comprehensive new methodology in cardiovascular research. Electrophysiological studies as well as radiological studies are also included to make the approach as comprehensive as possible. The entire book is dedicated to computational studies at the cutting edge, from the supercomputer at the National Cardiovascular Center to individual PCs. Application of theory, rather than the development of theory itself, is emphasized in each chapter, to interest researchers with little or no special background in computation, as well as clinical practitioners and graduate students in biomedical engineering. The editor and the authors would like to thank the National Cardiovascular Center for their support of the project, the results of which now can be presented in this book. T. Yamaguchi, M.D., Ph.D. Department ofMechanical and Systems Engineering Nagoya Institute of Technology Nagoya, Japan

VII Acknowledgment

This book is a compilation of the results of studies supported by a project promoted by the National Cardiovascular Center through the Research Grant for Cardiovascular Disease 9A-1 from the Ministry of Health and Welfare of Japan (1997-1999). The contributions from the authors and the editorial assistance of Ms. Miyuki Kato are gratefully acknowledged.

VIII Contents

Part 1. General Aspects of Computational Cardiovascular Mechanics

1.1 Computational Mechanical Model Studies in the Cardiovascular System ...... 3 Takami Yamaguchi 1.2 Inelastic Constitutive Models of Blood Vessels in Physiological Conditions ...... 19 Hiroshi Yamada 1.3 Stress and Strain Analyses of Blood Vessels in Physiological and Pathological Conditions ...... 29 Hiroshi Yamada 1.4 Development of lnteractive Modeling System for the Computational Biomechanics Simulation Using Medical Imaging Data ...... 39 Tomoaki Hayasaka, Ryutaro Himeno, Hao Liu, and Takami Yamaguchi 1.5 A Modeling System of 3-Dimensional Blood Vessel Configuration for CFD Analysis ...... 43 Makoto Misawa, Yusuke Kimura, Hao Liu, and Takami Yamaguchi

Part 2. Wall Motion and Blood Flow in the Heart

2.1 Computational Analysis for Mechanical Functions of Left Yentriele ...... 49 Yutaka Sawaki, Tadashi Inaba, Kazuo Yagi, Kiyotsugu Sekioka, and Masataka Tokuda 2.2 Automated Tracking of Tagged Magnetic Resonance Image for Assessment of Regional Cardiac Wall Function ...... 59 Kiyotsugu Sekioka, Hiroshi Yamada, Giovanni V. D. Ciofalo, and Wataru Ohyama 2.3 Error Estimation and Smoothing for Regional Deformation Analysis of the Heart with Tagged Magnetic Resonance Images ...... 70 Hiroshi Yamada and Kiyotsugu Sekioka

IX X

2.4 Deformation Analysis of Human Left Ventricular Wall Using Magnetic Resonance Tagging Technique ...... 76 Tadashi lnaba, Yutaka Sawaki, and Masataka Tokuda 2.5 Motion and Strain Analyses of Left Ventricular Wall Using Optical Flow .... 83 Kazuo Yagi, Yutaka Sawaki, and Masataka Tokuda 2.6 Intraventricular Blood Flow Analysis Using Robust CFD Models ...... 93 Yuko Kusaka, Shinichi Fujimoto, Reiko Mizuno, Hiroshi Nakano, Kazuhiro Dohi, Liu Hao, and Takami Yamaguchi

Part 3. Interactions Between the Blood Flow and Wall Motion in Vascular System

3.1 Computational Fluid Mechanics of the Blood Flow in an Aortic Vessel with Realistic Geometry ...... 99 Hideki Fujioka and Kazuo Tanishita 3.2 Numerical Simulation and Experiment of Pulsatile Flow in Modeled Aortic Arch ...... 118 Kenkichi Ohba, Kiyoshi Bando, Hiroyuki Kamino, Takeharn Urabe, Shigeo Ikedo, and Yoshizumi Fujita 3.3 Flow Simulation of the Aortic Arch -Effect of the 3D Distortion on Flows in the Ordinary Helix Circular Tube- ...... 132 Daisuke Mori, Hao Liu, and Takami Yamaguchi

3.4 Computational Fluid Mechanics of the Vortical Flow in Blood Vessel ...... 136 Hao Liu and Takami Yamaguchi 3.5 Computational Study on LDL Transfer from Flowing Blood to Arterial Walls ...... 157 Shigeo Wada and Takeshi Karino 3.6 Numerical Simulationnf Co-operative Regulation in the Cerebra! Microvascular Arcadal Network ...... 174 Hideyuki Niimi, Yutaka Komai, and Saburo Yamaguchi 3.7 Computational Fluid Dynamic Simulation ofthe Flow Through Venous Valve ...... 186 Tsuyoshi Ohashi, Hao Liu, and Takami Yamaguchi Contents XI

Part 4. Clinical and Electrophysiological Aspacts of Computational Mechanics of the Heart

4.1 A High-Performance Computation Method for Simulation ofCardiac Excitation Propagation Using a Supercomputer ...... 193 Tohru Suzuki, Takashi Ashihara, Masashi Inagaki, Tsunetoyo Namba, Takanori Ikeda, and Kazuo Nakazawa 4.2 Simulated Electrocardiogram of Spiral Wave Reentry in a Mathematical Ventricular Model ...... 205 Takashi Ashihara, Tohru Suzuki, Tsunetoyo Namba, Masashi Inagaki, Takanori Ikeda, Makoto Ito, Masahiko Kinoshita, and Kazuo Nakazawa 4.3 Computational Analysis and Visualization of Spiral Wave Reentry in a Virtual Heart Model ...... 217 Kazuo Nakazawa, Tohru Suzuki, Takashi Ashihara, Masashi Inagaki, Tsunetoyo Namba, Takanori Ikeda, and Ryoji Suzuki 4.4 Simulation of Platelet Adhesion U sing a Discrete Element Method ...... 242 Hisako Miyazaki, Hao Liu, and Takami Yamaguchi 4.5 Computational Fluid Dynamics as a Tool to Develop the Artificial Heart .. 246 Toru Masuzawa, Takashi Yamane, and Yuki Tsukamoto 4.6 Three-Dimensional Image Processing and Motion Analysis of the Heart Using Radionuclide Medical Images ...... 258 Yoshio Ishida, Naozo Sugimoto, Shigeo Kawano, Tetsuro Katafuchi, Makoto Takamiya, Chikao Uyama, and Hyoji Hasegawa 4. 7 The Modeling of the Heart and the Aortic Arch Applying Differential Geometrical Method and Simulation of Blood Flow ...... 269 Daisuke Mori, Hao Liu, and Takami Yamaguchi 4.8 Orientation Response of Stress Fibers in Cultured Cells Under Biaxial Cyclic Stretch: Hypothesis and Theoretical Prediction ...... 273 Hiroshi Yamada, Tohru Takemasa, and Takami Yamaguchi

Index ...... 283 List of Contributors

Takashi Ashihara First Department of Interna! Medicine, Shiga University of Medical Science, Seta Tsukinowa-cho, Otsu 520-2192 Chapters 4.1, 4.2, 4.3 Kiyoshi Bando Department of Mechanical Systems Engineering, , Yamate-cho 3-3-35, Suita, Osaka 564-8680 Chapter 3.2 Giovanni V. D. Ciofalo First Department of Interna! Medicine, School of Medicine, Mie University, Tsu 514-0001 Chapter2.2 Shinichi Fujimoto Department of Clinico - Laboratory Diagnostics, Nara Medical University, Nara 634-8522 Chapter2.6 Hideki Fujioka Department of Biological and Medical Systems, Imperial College of Science, Technology and Medicine, London, SW7 2BX, U.K. Email: [email protected] Chapter 3.1 Yoshizumi Fujita Mitsubishi Heavy lndustries, Ltd., Oe-cho 10, Minato-ku, Nagoya 455-0024 Chapter 3.2 Tomoaki Hayasaka Division of Computer and Information, The Institute of Physical and Chemical Research (RIKEN), Wako 351-0198 Email: [email protected] Chapter 1.4 Hyoji Hasegawa Toshiba Medical Co., Ootawara, Tochigi 324 Chapter 4.6 Ryutaro Himeno Division of Computer and Information, The Institute of Physical and Chemical Research (RIKEN), Wako 351-0198 Chapter 1.4 Takanori Ikeda Third Department of Interna! Medicine, Ohashi Hospital, Toho University, Ohashi, Meguro-ku, Tokyo 153-8515 Chapters 4.1, 4.2, 4.3 Shigeo Ikedo Sharp Corporation., Nagaike-cho, Abeno-ku, Osaka 545-0013 Chapter 3.2 Tadashi lnaba Department ofMechanica1 Engineering, Mie University, Tsu 514-8507 Email: [email protected] Chapters 2.1, 2.4

XII List of Contributors XIII

Masashi Inagaki Department of Cardiovascular Dynamics, National Cardiovascular Center Research Institute, Fujishiro-dai, Suita 565-8565 Chapters 4.1, 4.2, 4.3 Yoshio Ishida Department of Radiology and Nuclear Medicine, National Cardiovascular Center Hospital, Suita, Osaka 565-8565 Email: [email protected] Chapter 4.6 Makoto Ito First Department of Internal Medicine, Shiga University of Medical Science, Seta Tsukinowa-cho, Otsu 520-2192 Chapter4.2 Hiroyuk.i Kamino Mitsubishi Heavy Industries, Ltd., Oe-cho 10, Minato-ku, Nagoya 455-0024 Chapter 3.2 Takeshi Karino Research Institute for Electronic Science, , North 12, West 6, North District, Sapporo 060-0812 Chapter 3.5 Tetsuro Katafuchi Department of Radiology and Nuclear Medicine, National Cardiovascular Center Hospital, Suita, Osaka 565-8565 Chapter 4.6 Shigeo Kawano Department ofRadiology and Nuclear Medicine, National Cardiovascular Center Hospital, Suita, Osaka 565-8565 Chapter 4.6 Yusuke Kimura Department of Mechanical and Systems Engineering, Nagoya Institute of Technology, Nagoya 466-8555 Chapter 1.5 Masahiko Kinoshita First Department of Interna! Medicine, Shiga University of Medical Science, Seta Tsukinowa-cho, Otsu 520-2192 Chapter4.2 Yutaka Komai Department ofVascular Physiology, National Cardiovascular Center Research Institute, Suita, Osaka 565-6565 Chapter 3.6 Yuko Kusaka Department of Mechanical and Systems Engineering, Nagoya Institute of Technology, Nagoya 466-8555 Email: [email protected] Chapter 2.6 Hao Liu Division of Computer and Information, The Institute of Physical and Chemical Research (RIKEN), Wako 351-0198 Email: [email protected] Chapters 1.4, 1.5, 3.3, 3.4, 3.7, 4.4, 4.7 XIV

Toru Masuzawa Department of Mechanical Engineering, School of Engineering, Ibaraki University, Nakanarusawa, Hitachi 316-8511 Email: [email protected] Chapter4.5 Makoto Misawa Department of Mechanical and Systems Engineering, Nagoya Institute of Technology, Nagoya 466-8555 Chapter 1.5 Hisako Miyazaki Department of Mechanical and Systems Engineering, Nagoya Institute ofTechnology, Nagoya 466-8555 Email: [email protected] Chapter 4.4 Reiko Mizuno First Department of Interna! Medicine, Nara Medical University, Nara 634-8522 Chapter 2.6 Daisuke Mori Department of Mechanical and Systems Engineering, Nagoya Institute of Technology, Nagoya 466-8555 Email: [email protected] Chapters 3.3, 4.7 Hiroshi Nakano Department of Clinico - Laboratory Diagnostics, Nara Medical University, Nara 634-8522 Chapter 2.6 Kazuo Nakazawa Department of Epidemiology, National Cardiovascular Center Research Institute, Fujishiro-dai, Suita 565-8565 Chapters 4.1, 4.2, 4.3 Tsunetoyo Namba Department of Cardiovascular Medicine, Medical School, Shikata-cho, Okayama 700-8558 Chapters 4.1, 4.2, 4.3 Hideyuki Niimi Department of Vascular Physiology, National Cardiovascular Center Research Institute, Suita, Osaka 565-6565 Email: [email protected] Chapter 3.6 Kenkichi Ohba Department of Mechanical Systems Engineering, Kansai University, Yamate-cho 3-3-35, Suita, Osaka 564-8680 Email:[email protected] Chapter 3.2 Tsuyoshi Ohashi Department of Mechanical and Systems Engineering, Nagoya Institute of Technology, Nagoya 466-8555 Email: [email protected] Chapter 3.7 Wataru Ohyama Department of Information Engineering, Faculty of Engineering, Mie University, Tsu 514-8507 Chapter 2.2 List of Contributors XV

Yutaka Sawaki Department of Mechanical Engineering, Mie University, Tsu 514-8507 Email: [email protected] Chapters 2.1, 2.4, 2.5 K.iyotsugu Sekioka First Department oflnternal Medicine, School ofMedicine, Mie University, Tsu 514-0001 Chapters 2.1, 2.2, 2.3 Naozo Sugimoto Department of Investigative Radiology, National Cardiovascular Center Research Institute, Suita, Osaka 565-8565 Chapter 4.6 Ryoji Suzuki Human Information Systems Laboratories, Kanazawa Institute of Technology, Yatsukaho, Matto 924-0838 Chapter 4.3 Tohru Suzuki Department ofEpidemiology, National Cardiovascular Center Research Institute, Fujishiro-dai, Suita 565-8565 Email: [email protected] Chapters 4.1, 4.2, 4.3 Makoto Takamiya Department of Radiology and Nuclear Medicine, National Cardiovascular Center Hospital, Suita, Osaka 565-8565 Chapter 4.6 Tohru Takemasa Institute of Health and Sports Sciences, University ofTsukuba, Tsukuba, Ibaraki 305-8574 Chapter4.8 Kazuo Tanishita Department of System Design Engineering, , Kohoku-ku, Yokohama 223-8522 Email: [email protected] Chapter 3.1 Masataka Tokuda Department of Mechanical Engineering, Mie University, Tsu 514-8507 Chapters 2.1, 2.4, 2.5 Yuki Tsukamoto R&D Center, Shizuoka Plant, Nikkiso Co., Haibara-cho, Haibara-gun 421-0496 Email: [email protected] Chapter 4.5 Takeharn Urabe Matsushita Electric Industrial Co., Ltd., Kadoma, Osaka 571-0050 Chapter 3.2 Chikao Uyama Department of Investigative Radiology, National Cardiovascular Center Research Institute, Suita, Osaka 565-8565 Chapter 4.6 XVI

Shigeo Wada Research Institute for Electronic Science, Hokkaido University, North 12, West 6, North District, Sapporo 060-0812 Email: [email protected] Chapter 3.5 Kazuo Yagi Department of Mechanical Engineering, Mie University, Tsu 514-8507 Email: [email protected] Chapters 2.1, 2.5 Hiroshi Yamada Department of Micro System Engineering, Graduate School of Engineering, Nagoya University, Nagoya 464-8603 Email: [email protected] Chapters 1.2, 1.3, 2.2, 2.3, 4.8 Saburo Yamaguchi Department ofVascular Physiology, National Cardiovascular Center Research Institute, Suita, Osaka 565-6565 Chapter 3.6 TakamiYamaguchi Department of Mechanical and Systems Engineering, Nagoya Institute of Technology, Nagoya 466-8555 Email: [email protected] Chapters 1.1, 1.4, 1.5, 3.3, 3.4, 3.7, 4.4, 4.7,4.8 Takashi Yamane Biomimetics Division, Mechanical Engineering Laboratory, Namiki, Tsukuba 305-8564 Email: [email protected] Chapter 4.5 XVII

Color Plates

Chapter 1.1 (by T. Yamaguchi) Fig. 2 (p. 7) Spatial distribution of stretch of the wall and the blood flow in the arterial Iumen. There is a significant concentration of stretch at the shoullders of the atherosclerotic plaque

Chapter 1.1 (by T. Yamaguchi) Fig. 3 (p. 10) Models of single endothelium using 2D Gaussina distribution function. XVIII

Chapter 1.1 (by T. Yamaguchi) Fig. 4 (p. 11) (a) (top left) the bottom grid of the endothelial model at initial condition; (b) (right) the velocity vectors adjacent to the cellular surface;(c) (bottom Ieft) the wall shear stress distribution on the cellular surface.

Chapter 1.1 (by T. Yamaguchi) Fig. 5 (p. II) (a) (top left) the bottom grid of the endothelial model after very ]arge computational steps; (b) (right) the velocity vectors adjacent to the cellular surface;(c) (bottom Ieft) the wall shear stress distribution on the cellular surface. XIX

Chapter 2.2 (by K. Sekioka, et al.) Fig. 5 (p. 65) Regional wall motion vectors in a case of hypertrophic cardiomyopathy. The lower and mid portion of this image correspond to the lateral wall and interventricular septum, respectively. The upper area with no motion is the anterior ehest. In this case, the wall motion in the mid portion of the interventricular septum and apical region decreased. The right ventricular free wall in the upper left shows normal wall motion. XX

Chapter 2.2 (by K. Sekioka, et al.) Fig. 7 (p. 66) Minimal principal strains (maximum shortening) in the short axis slice calculated from tracked grid lines. The line length indicates the magnitude of strain. The left strains were calculated with Snake method and the rights were from manually tracked grid lines. Results in the two methods are closely correlated.

End Diastole

E",;11 = -6% E",;11 = -17% Emin= -22%

Chapter 2.3 (by H. Yamada & K. Sekioka) Fig. 2 (p. 7 4) Result of smoothing in a selected region of the normal left ventricular wall and the minimum strain with respect to the end diastote in a cardiac cycle. XXI

a b

c d

g h Chapter 2.4 (by T. Inaba, et al.) Fig. 5 (p. 81) Images with distributions of circumferential strains at end systole in normal humans (a and b), patients with HCM (c and d), patients with HHD (e and f), and patients with LBBB (g and h) XXII

Chapter 2.6 (by Y. Kusaka, et al.) Fig.l (p. 95) The flow field in the Ieft ventricle at an early stage of dilatation.

Chapter 2.6 (by Y. Kusaka, et al.) Fig.2 (p. 95) The flow field in the left ventricle at the final stage of dilatation. XXIII

.. f \ c ' 1

. I I ;: • ~ · (J I) ~ . \ 1>.,, · 00 ' J fJ•!• O(J l ( U'J•· f)l i . •, fJ-:1: 0 1 . ) t) (,l: 01 Re = IIIIHI r.. () . 0 01_;• 00

Chapter 2.6 (by Y. Kusaka, et al.) Fig.3 (p. 96) The flow field in the left ventricle at the middle stage of contraction. XXIV

Chapter 3.3 (by D. Mori, et al.) Fig. 3 (p. 135) The streamline patterns near the top of the arch.

outflov viev from +Z inflov inflov viev from -Z outflov rPal

outflov viev from +Z inflov inflov viev from -Z outflov rPal

outflov viev from +Z inflov inflov viev from -Z outflov

Chapter 3.3 (by D. Mori, et al.) Fig. 4 (p. 136) Wall shear distribution for NR=800 XXV

1=0.75 r:.H

1=0.9

a: Velocity b: Pressure Chapter 3.4 (by H. Liu & T. Yamaguchi) Fig. 4 (p. 144) This figure shows a train öf propagating vortex wave behind a flush-in indentation at ten instants during a complete cycle, at Re=300, St=0.057 with the amplitude, E =0.4. a, iso• velocity contour in which red color expresses high velocity and blue color is lower velocity. b, iso-pressure contour in which red color represents high pressure and blue is Iower pressure. lt can be seen that the pressure gradient throughout the channel changes markedly during one cycle and the local pressure distribution is obviously sensitive to the vortices. XXVI

'1.-J.I,•• ,,_

Chapter 3.4 (by H. Liu & T. Yamaguchi) Fig. 10 (p. 153) This figure shows iso-speed contour of a train of propagating vortex wave downstream of the constriction at the end of systole of a physiological waveform of flow rate (at instant d in Fig. 2), at Re=750, St=0.024 with variation in width and configuration of the constriction. It is seen that the vortex wave grows and strengthens with increasing depth of the constriction but shows a distinguishable change at some critical value, E =0.7 when the vortex wave tends to collapse. XXVII

Re 0 = 200 V[cm/sb.o d0 = 0.6 cm 3.0 = 135deg 6.0 e 9.0 Q, = Qz = 0.5Qo 12.0 15 .0 18.0 21.0 24.0

B

't [ dynes/cm2] Re 0 = 200 d0 = 0.6 cm - 2.00 e = 135 deg 4.0 6.0 Q, = Q2 = 0.5Qo 8.0 10.0 - 12.0 - 14.0 - 16.0 18.0 c

Re0 = 200 Vw = I x I 0·6 cm/s I 7 2 1.037 D = 5x I o- cm /s 1.073 K = 2x J0-8 cm/s 1.110 1.146 1.1 83 1.219 1.256 1.292 - 1.329 Chapter 3.5 (by S. Wada & T. Karino) Fig. 10 (p. 169) LDL transpoft in blood flowing through a T -junction. A: flow pattems, 8 : distribution of wall shear stress, and C: distribution of surface concentration of LDL around the junction. XXVIII

Chapter 3.7 (by T. Ohashi, et al.) Fig. 1 (p. 188) This figure shows velocity vectors and flow pattems found in Model I (left) and Model 3 (right). Upper panels: velocity vectors; lower panels: streamlines.

(a)

T= 200 T= 400 T= 600 T= 800 T=1000

(b)

~T= 800 T=1000 (c) Chapter 4.1 (by T. Suzuki, et al.) Fig. 4 (p. 202) Evaluation of the precision of piecewise linearization, based on the excitation propagation in !wo-dimensional Luo-Rudy medium. (T: msec) (a) With piecewise linearization in the SX-4 (b) Without piecewise linearization in the SX-4 (c) With piecewise linearization in a personal computer XXIX

0 1.6 .u 4.8 6.4 Vclocily (mlsl

J rnm

Chapter 4.5 (by T. Masuzawa, et al.) Fig. 7 (p. 252) Shown are results of flow visualization. Velocity vectors, which were obtained from about 900 images during a single impeller rotation, were summed and indicated to analyze the change of the local flow pattem at the tongue region for Group 2.

Chapter 4.5 (by T. Masuzawa, et al.) Fig.S (p. 253) Shear stress distribution in the pumps. High shear regions over 120 Pa are indicated by hatched area. The area of high shear stress was enlarged by reducing the gap size. XXX

Modell Model2 Model3

[m/s]

Chapter 4.5 (by T. Masuzawa, et al.) Fig. 9 (p. 254) Velocity vector plots for Group 2.

Modell Model2 Model3

[Pa] 2 15 Pa 1158 Pa 903 Pa

Chapter 4.5 (by T. Masuzawa, et al.) Fig.lO (p. 254) Shear stress distribution in the volute and outlet diffuser for Group 2. Maximum shear stresses in the volute and outlet diffuser are indicated in the figure. XXXI

%S WT Map

I · : C<:-~:atcd M~u ~a r · dial l'erfu5ion SI'EC'r wi th Tc-99m Sc~tam ib i = 100 c nd-dia~loli c 1

ESC - EDC , IOO EOC max

Chapter 4.6 (by Y. Ishida, et al.) Fig. 3 (p. 262) Measurement and display of regional wall thickening based on the end-diastolic and end• systolic perfusion images. Systolic wall thickening in the area with reduced perfusion is overestimated in the conventionally used %SWT (upper right), we utilized a new parameter indicating the extent of systolic wall thickening, ßSWT/EDCmax (lower right).

C:"~ I : J-: . \ . F

.\nl<' r·ior ~ II

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RC.\ 11 1 100% 25'Yo 1995. 5. 10. (2 •.rck' aftcr) 1995. 6. 1-1. (1.6 monrh aflcr)

Chapter 4.6 (by Y. Ishida, et al.) Fig. 5 (p. 264) Usefulness of a /::,. SWT/EDCmax Bull's eye map for monitaring regional myocardial function in the follow-up study of patients with acute myocardial infarction (upper : a case with anteroseptal infarction and with functional recovery, lower : a case with inferior infarction and without functional recovery). XXXII

Superimosed Display of Coronary Artery Trees and End-diastolic SPECT Images

Y. S. 47 M: Acute Myocardial Infarction

- 4days after the

Chapter 4.6 (by Y. Ishida, et al.) Fig. 7 (p. 267) A three-dimensionally superimposed display of coronary artery trees from CAG and left ventricular myocardial perfusion from myocardial SPEer with 99"'Tc-sestamibi in a patient with acute myocardial infarction (4 days after the onset).

Superimosed Display of Coronary Artery Trees and End-diastolic SPECT Images

Y. S. 47 M: Acute Myocardial Infarction

- 1 month after the onset -

Chapter 4.6 (by Y. Ishida, et al.) Fig. 8 (p. 267) A three-dimensionally superimposed display of coronary artery trees from CAG and Ieft ventricular myocardial perfusion from myocardial SPEer with 99"'Tc-sestamibi in a patient with acute myocardial infarction (I month after the onset).