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BIOLOGICAL AND MEDICAL PHYSICS BIOMEDICAL ENGINEERING M. Zamir The Physics of Coronary Blood Flow With 269 Illustrations . . With Foreword by Y C Fung Series Preface The fields of biological and medical physics and biomedical engineering are broad, multidisciplinary and dyanmic. They lie at the crossroads of frontier re- search in physics, biology, chemistry, and medicine. The Biological & Medi- cal Physics/Biomedical Engineering Series is intended to be comprehensive, covering a broad range of topics important to the study of the physical, chemi- cal and biological sciences. Its goal is to provide scientists and engineers with textbooks, monographs, and reference works to address the growing need for information. Books in the series emphasize established and emergent areas of science in- cluding molecular,membrane, andmathematical biophysics;photosynthetic energy harvesting and conversion; information processing; physical principles of genetics; sensory communications; automata networks, neural networks, and cellularautomata.Equallyimportantwillbecoverageofappliedaspectsofbio- logicalandmedicalphysicsandbiomedicalengineeringsuchasmolecularelec- tronic components and devices, biosensors, medicine, imaging, physical principles of renewable energy production, advanced prostheses, and environmental control and engineering. Elias Greenbaum Oak Ridge, TN M.Zamir DepartmentofAppliedMathematics UniversityofWesternOntario London,Ontario,N6A5B7 CANADA [email protected] LibraryofCongressCataloging-in-PublicationData Zamir,M.(Mair) Thephysicsofcoronarybloodflow/M.Zamir. p.cm.—(Biologicalandmedicalphysics,biomedicalengineering) Includesbibliographicalreferencesandindex. 1.Coronarycirculation. 2.Hemodynamics. 3.Bloodflow. I.Title. II.Series. QP108.Z362005 612.1′7—dc22 2005042502 ISBN-10:0-387-25297-5 e-ISBN:0-387-26019-6 Printedonacid-freepaper. ISBN-13:978-0387-25297-1 ©2005SpringerScience+BusinessMedia,Inc. AIPPressisanimprintofSpringerScience+BusinessMedia,Inc. Allrightsreserved.Thisworkmaynotbetranslatedorcopiedinwholeorinpartwithoutthe writtenpermissionofthepublisher(SpringerScience+BusinessMedia,Inc.,233SpringStreet, NewYork,NY10013,USA),exceptforbriefexcerptsinconnectionwithreviewsorscholarly analysis.Useinconnectionwithanyformofinformationstorageandretrieval,electronicadap- tation,computersoftware,orbysimilarordissimilarmethodologynowknownorhereafterde- velopedisforbidden. Theuseinthispublicationoftradenames,trademarks,servicemarks,andsimilarterms,even iftheyarenotidentifiedassuch,isnottobetakenasanexpressionofopinionastowhether ornottheyaresubjecttoproprietaryrights. PrintedintheUnitedStatesofAmerica. (MP) 9 8 7 6 5 4 3 2 1 springeronline.com To the memory of my father – how well I know him now. Foreword Everybody is interested in his/her coronary blood flow. I am delighted to read Dr Zamir’s clear exposition of the dynamics of the coronary blood flow in this book. I have read many of his scientific papers published in profes- sional journals, as well as his book The Physics of Pulsatile Flow, published by Springer-Verlag New York in 2000. His writing is a model of clarity. In an unhurried manner, he dwells on points of conceptual difficulty, and takes his reader to look at the difficulties from as many angles as possible. He offers solutions of difficulties. He enhances true understanding, but never dogmati- cally. As a reader, I am grateful for that. He loves the word conundrum. For example, the heading of Section 10.3 of this book is “Coronary Heart Disease andtheConundrumofCoronaryFlowReserve.”Thatsectionis,ofcourse,the heart of this book: every reader would be interested in this topic. What does conundrummean?AccordingtoWebster’sDictionary,conundrummeans“(1) a riddle whose answer involves a pun, (2) anything that puzzles [1590-1600; pseudo-L word of obscure orig.]” That word prepares the reader. Be patient. Listen! Then I became patient, and I got a great deal of enlightenment out of the book. The book opens with a beautiful introductory Chapter 1, and concludes with a very serious Chapter 10. I read the whole book, but I would like to make a recommendation to any reader: read these two chapters first. Then you can get a clear picture of the whole book right away. Then, again, for every chapter, I would suggest to a reader to read the first and the last sec- tions of that chapter first, in order to get a completely clear picture of that chapter. Dr Zamir’s writing is especially clear and persuasive in these sec- tions.Chapters2-7aredevotedtolumpedmodels.Chapters8-10aredevoted to unlumped models. The lumped models are extremely clearly described in thisbook.Theyaremature.Theyareblackboxes.Theunlumpedmodelsare clearly less mature. But they are transparent. We can expect many future developments in the unlumped models, especially for the myocytes which are nourished by the coronary blood flow. Thus, we expect attention to microcirculation,venousreturn,cellularmechanics,effectsofstressandstrainonand VIII Foreword inthecells,heartmuscletissueremodeling,geneexpressionactivities,protein configuration changes, cell membrane behavior, integrins, enzymes, kinases, and their activities. Before long, besides learning about the heart, we have to learn how to engineer the coronary blood vessels for health and longevity. Physics and mathematics will have a lot more to do with biology! Y.C. Fung La Jolla, California November 20, 2004 Preface Coronary blood flow is blood flow to the heart for its own metabolic needs. In the most common form of heart disease there is a disruption in this flow becauseofobstructivediseaseinthevesselsthatcarrytheflow.Thesubjectof coronary blood flow is therefore associated mostly with the pathophysiology of this disease, rarely with dynamics or physics. Yet, the system responsible forcoronarybloodflow,namelythe“coronarycirculation,”isahighlysophis- ticated dynamical system in which the dynamics and physics of the flow are as important as the integrity of the conducting vessels. While an obstruction in the conducting vessels is a fairly obvious and clearly visible cause of disruption in coronary blood flow, any discord in the complex dynamics of the system can cause an equally grave, though less conspicuous, disruption in the flow. This book is devoted specifically to the dynamics and physics of coronary blood flow. While it upholds the clinical and pathophysiological issues involved, the book focuses on dynamics and physics, approaching the subject from a strictly biomedical engineering viewpoint. The rationale for this approach is simply that the coronary circulation involves many issues in dynamics and physics, as the book will demonstrate. Also, with this particular focus, the book will complement other books on the subject, that have so far focused largely on clinical and pathophysiological issues. A study of the dynamics of the coronary circulation requires far more information about the system than is currently available. Whether in terms ofanatomicaldetailsofthevasculature,systempropertiessuchascapacitance andelasticityoftheconductingvessels,orthebasicandregulatoryconditions underwhichthesystemoperates,theinformationcurrentlyavailableishighly incomplete. Thus, the scope of this book is limited to dynamical aspects of coronary blood flow, but within these limits it is also constrained to deal necessarily with an incomplete picture of these dynamics. In particular, the book does not include the microcirculation, the venous part of the coronary circulation, Thebesian veins or the lymphatic system. Also, the many-faceted regulatory mechanisms of the coronary circulation are not considered in any XII Preface systematic or factual way, but only tangentially in how they may affect the dynamics of the system. These omissions reflect the degree of complexity of the coronary circulation and serve as a sober reminder that it may never be possible or practical to deal with this complexity in a single book. What seems possible at this time is to use known elements or properties of the system in such a way as to construct a meaningful, though incomplete, model of the system. This is the spirit in which the content of this book is presented. The book deals essentially with the dynamics of that part of the coronary circulation extending from the coronary ostia at the base of the aorta to the capillary level of coronary vasculature. It is meaningful to consider this part of the system in isolation because this is where the largest part of the pressure drop driving the flow occurs. While the dynamics of this part of the system may not represent the dynamics of the system as a whole, they demonstrate clearly the role of dynamics in the coronary circulation and illustrate how a disruption in these dynamics can affect coronary blood flow as significantly as can the obstruction of a blood vessel. This is indeed what the present book is about. Other books have in the past focused in a similar way on clinical or pathophysiological aspects of the system, or on the microcirculation. Each of these must clearly be seen as representing an important, though equally incomplete, view of the system. My foray into the subject of coronary blood flow began in earnest in 1984 whenIspentasabbaticalleaveintheDepartmentofPathologyatUniversity Hospital in London, ON, and it is fair to say that this book would not have comeintobeingwithoutmyensuingcollaborationwithProfessorMalcolmD. Silver,thendepartmentchairandchiefofpathology.Hispassionfortheheart andcoronaryarteries,andthedepthofhisexpertiseincardiovascularpathol- ogy in general, was a haven for an engineer/applied mathematician seeking entryintothesubject.WithhishelpIcametoknowthecoronaryarterieslit- erally “in the flesh” as I attended weekly autopsy review sessions and learned to dissect, cast and measure coronary vasculature. The collaboration was not a hit from the start - he was as puzzled by my preoccupation with branching angles and branch diameters as I was by his preoccupation with shades of pink in myocardial tissue. But a meeting of the minds soon prevailed, and together we embarked on several studies that have since formed the basis of allmysubsequentworkonthesubject.IamdeeplyindebtedtoDr.Silvernot only for his continued guidance over the years but also for reading a draft of this book and offering many valuable comments and suggestions. I am indebted by equal measure to my long-time friend and colleague Dr. Gerry Klassen, formerly professor of medicine, physiology and biophysics at Dalhousie University. His passion for the subject, combined with his love of science and engineering, made him an invaluable “resource” for me for more than two decades. Always ready to explain and ready to help, he made a lasting contribution to my education in the field of coronary blood flow. His enthusiasm for the subject was always a source of inspiration to me. I am grateful to Dr. Klassen for these “hidden” contributions to this book as well