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Vortexformationinthecardiovasc.Pdf Vortex Formation in the Cardiovascular System Arash Kheradvar • Gianni Pedrizzetti Vortex Formation in the Cardiovascular System Authors Arash Kheradvar, M.D., Ph.D. Gianni Pedrizzetti, Ph.D. University of California, Irvine Università degli Studi di Trieste 2410 Engineering Hall Dipto. Ingegneria Civile e The Edwards Lifesciences Center for Architettura Advanced Cardiovascular Technology P. Europa 1 Irvine 34127 Trieste California 92697 Italy USA ISBN 978-1-4471-2287-6 e-ISBN 978-1-4471-2288-3 DOI 10.1007/978-1-4471-2288-3 Springer London Dordrecht Heidelberg New York British Library Cataloguing in Publication Data A catalogue record for this book is available from the British Library Library of Congress Control Number: 2011944219 © Springer-Verlag London Limited 2012 Apart from any fair dealing for the purposes of research or private study, or criticism or review, as permitted under the Copyright, Designs and Patents Act 1988, this publication may only be reproduced, stored or transmitted, in any form or by any means, with the prior permission in writing of the publishers, or in the case of reprographic reproduction in accordance with the terms of licenses issued by the Copyright Licensing Agency. Enquiries concerning reproduction outside those terms should be sent to the publishers. The use of registered names, trademarks, etc., in this publication does not imply, even in the absence of a specifi c statement, that such names are exempt from the relevant laws and regulations and therefore free for general 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 pharmaceutical literature. Printed on acid-free paper Springer is part of Springer Science+Business Media (www.springer.com) To my wife Ladan and our children Aryana and Ario for their love and support Arash Kheradvar To my wife Ilaria and our children Giulia, Guglielmo, Greta for accompanying with smiles and infi nite love. Gianni Pedrizzetti Preface The topic of vortex formation has received much attention over the past few years. Vortices occur in nature wherever propulsive fl ow exists; from erupting volcanoes to the ones generated by squid and jellyfi sh to propel them. Vortices drive the atmo- spheric circulation; smaller ones like hurricanes and tornado contain an enormous amount of destructive energy. They are also present in the heart. A wide variety of vortices develop in the cardiovascular system, particularly in the cardiac chambers, and in large arteries. These vortices play fundamental roles in the normal physiology and provide proper balance between blood motion and stresses on the surrounding tissues. In contrast, formation of unnatural vortices may alter the momentum transfer in the blood fl ow and increase energy dissipation. In the present book, we have tried to recapitulate the current knowledge on the vortex formation in the cardiovascular system, from physics to physiology. The fi rst two chapters of the book cover the fundamental aspects of fl uid mechanics and in particular vortex dynamics. Through these, the reader’s attention is driven toward the lifespan of vortices – from formation to dissipation and interaction. The third chapter describes vortex formation in heart. Through this chapters, formation of vortices at different locations inside the heart, and their physiological and clinical signifi cances are discussed. Chapter four discusses the effects of cardiac devices and surgery on vortex formation. In a nutshell, the fl uid dynamics of the artifi cial heart valves and ventricular assist devices are described, and the effect of each device on cardiovascular vortex formation is comprehensively reviewed. The last chapter is focused on diagnostic vortex imaging in which we have reviewed existing methods to visualize vortices in the cardiac chambers, and the experimental and computational techniques to model the vortex formation in cardiovascular system. The material described in the book has been brought together from the published and unpublished work of the authors and the invited contributors. Through this work, we desire to translate physical, mathematical and engineering concepts related vii viii Preface to vortex formation into a clinical perspective with the objectives that these notions fi nally advance the cardiovascular patient care. This work is the product of three years of transatlantic collaboration on various cardiovascular projects between Kheradvar’s and Pedrizzetti’s groups. In addition, we owe debt of gratitude to the invited contributors who permitted to span over the multidisciplinary expertise involved in this fi eld; without their support and involve- ment, completion of the book seemed impossible. We would also like to acknowl- edge our students and postdoctoral scholars, Ahmad Falahatpisheh, Hamed Alavi, Jan Mangual, Brandon Dueitt, and our colleague Federico Domenichini who helped us preparing the fi gures, plots, etc. At the end, we would like to acknowledge the American Heart Association for providing funding support for the right ventricular vortex project (10BGIA4170011). The funding deeply helped us contribute to understanding of vortex formation in the right heart and enhanced our collaboration that gave rise to the present book. Arash Kheradvar, M.D., Ph.D. Irvine, CA, USA Gianni Pedrizzetti, Ph.D. Trieste, Italy Acknowledgements The authors would like to thank the below authors for their contributions to this book: Haruhiko Abe, M.D., Chapter 3: Sects. 3.5 and 3.6.1, 3.6.2, 3.6.3. Osaka Minami Medical Center , Japan Idit Avrahami, Ph.D., Chapter 4: Sects. 4.2 and 4.3. Chapter 5: Sect. 5.4. Ariel University Center of Samaria, and Afeka Academic College of Engineering , Tel Aviv, Israel Giuseppe Caracciolo, M.D., Chapter 3: Sects. 3.5 and 3.6.1, 3.6.2, 3.6.3. Mount Sinai School of Medicine , New York, NY, USA Gabriele Dubini, Ph.D., Chapter 4: Sect. 4.4. Politecnico di Milano , Milano, Italy Tino Ebbers, Ph.D., Chapter 5: Sect. 5.1 Linköping University , Linköping, Sweden Jan Engval, Ph.D., Chapter 5: Sect. 5.1 Linköping University , Linköping, Sweden Kambiz Ghafourian, M.D., Chapter 3: Sects. 3.6.4. and 3.6.5. Washington Hospital Center , Washington, D.C., USA Helene Houle. Chapter 5: Sect. 5.2. Siemens Medical Solutions , Mountain View, CA, USA Francesco Migliavacca, Ph.D., Chapter 4: Sect. 4.4. Politecnico di Milano , Milano, Italy Laura Miller, Ph.D., Chapter 3: Sect. 3.4. University of North Carolina , Chapel Hill, NC, USA Partho P. Sengupta, M.D., Chapter 3: Sects. 3.5 and 3.6.1, 3.6.2, 3.6.3. Mount Sinai School of Medicine , New York, NY, USA ix Contents 1 Fundamental Fluid Mechanics ................................................................ 1 1.1 Fluids and Solids, Blood and Tissues ................................................ 1 1.2 Conservation of Mass ........................................................................ 3 1.3 Conservation of Momentum and Bernoulli Theorem ........................ 6 1.4 Conservation of Momentum and Viscosity ....................................... 9 1.5 Boundary Layer and Wall Shear Stress ............................................. 11 1.6 Simple Flows and Concepts of Cardiovascular Interest .................... 13 References ......................................................................................... 16 2 Vortex Dynamics ....................................................................................... 17 2.1 Defi nitions ......................................................................................... 17 2.2 Dynamics of Vorticity ....................................................................... 20 2.3 Boundary Layer Separation ............................................................... 22 2.4 Vortex Formation ............................................................................... 25 2.5 Three-Dimensional Vortex Formation ............................................... 29 2.6 Energy Loss and Force of Vortex Formation ..................................... 33 2.7 Vortex Interactions............................................................................. 38 2.8 A Mention to Turbulence .................................................................. 40 References ......................................................................................... 43 3 Vortex Formation in the Heart ................................................................ 45 3.1 Mitral Valve and Transmitral Flow ................................................... 45 3.1.1 Mitral Valve Functional Anatomy ......................................... 45 3.1.2 Transmitral Flow ................................................................... 46 3.1.3 Transmitral Vortex Formation ............................................... 47 3.1.4 Transmitral Vortex Formation Time Index: A Parameter to Couple Diastole and Systole ............................................. 50 3.1.5 Mitral Annulus Recoil ........................................................... 51 3.1.6 Grading Diastolic Dysfunction .............................................. 52 3.1.7 Outcome Planning for Diastolic Dysfunction ....................... 53 xi xii Contents 3.2 Aortic Valve and Sinuses of Valsalva ................................................ 54 3.2.1 Functional Anatomy .............................................................. 54 3.2.2 Vortex Formation in Aortic Sinus .........................................
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