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Biofluid
Mechanics
The Human Circulation
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Biofluid
Mechanics
The Human Circulation
Krishan B. Chandran
Ajit P. Yoganathan
Stanley E. Rittgers
Boca Raton London New York
CRC is an imprint of the Taylor & Francis Group,
an informa business
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Library of Congress Cataloging-in-Publication Data
Chandran, K. B.
Biofluid mechanics : the human circulation / Krishnan B. Chandran, Ajit P.
Yoganathan, and Stanley E. Rittgers.
p. ; cm.
Includes bibliographical references and index.
ISBN-13: 978-0-8493-7328-2 (hardcover : alk. paper)
ISBN-10: 0-8493-7328-X (hardcover : alk. paper)
1. Blood flow. 2. Fluid mechanics. I. Yoganathan, A. P. (Ajit Prithiviraj), 1951- II.
Rittgers, Stanley E. III. Title.
[DNLM: 1. Blood Circulation--physiology. 2. Cardiovascular Physiology. 3. Heart
Valves--physiology. WG 103 C456b 2007]
QP105.C43 2007
612.1’181--dc22 2006031653
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Dedication
To my wife, Vanaja, and daughters, Aruna and Anjana, for their loving support.
KBC
To my wife, Tripti, and daughter, Anila, for their love, encouragement and support.
APY
To my wife, Eva, and sons, David and Andrew, who have taught me so much.
SER
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Preface
The field of biomedical engineering has seen a rapid growth in the past
decade and numerous new undergraduate and graduate programs have
been established in many universities. With the increasing number of stu-
dents enrolled in these programs, there is also an increase in demand for
suitable text books. This work is an attempt to provide such a text book for
a course in the application of fluid mechanics to the study of the human
circulatory system. This book is intended as a first course on fluid mechanics
in the human circulation, which is suitable for senior undergraduate or for
first-year graduate students in biomedical engineering. The topics contained
in the various chapters were organized based on the experience gained by
the three authors in teaching courses on cardiovascular fluid mechanics in
their respective programs.
The book is organized into three parts. Part I consists of introductory
review material on fluid and solid mechanics and also a review of cardio-
vascular physiology pertinent to the topics covered in the subsequent chap-
ters. The first two chapters are an introduction to foundational material in
fluid and solid mechanics for those students not having had prior exposure
to these topics. In curricula where the students would have previously
enrolled in courses in fluid mechanics, mechanics of deformable bodies, and
in human physiology, this section may serve as a brief review.
Part II of the book discusses the fluid mechanics in the human circulation,
primarily applied to blood flow at the arterial level. The first chapter in this
section (Chapter 4) examines viscometry and the rheological behavior of
human blood. The solid mechanics of the arterial wall subject to transmural
pressure is also briefly discussed in this chapter, since the interaction
between blood and the arterial wall needs to be considered in unsteady
flow simulation. The application of steady flow models to derive some
useful diagnostic parameters, such as vascular resistance and Gorlin’s equa-
tions to describe time-averaged flow behavior past heart valves, is treated
next (Chapter 5). The third chapter in this section (Chapter 6) briefly
describes the Windkessel model for unsteady flow followed by a detailed
treatment of the Moens–Korteweg and Womersley models of pulsatile flow
in the human circulation. The relationship between flow-induced stresses
and the initiation and growth of atherosclerosis is also discussed with
qualitative treatment of flow in curved vessels, branches, and bifurcations,
as well as unsteady flow past stenoses and aneurysms. The final chapter in
this section (Chapter 7) examines the flow through native heart valves and
cardiac chambers.
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In Part III, vascular implants and measurements in the cardiovascular
system are discussed. The first chapter in this section (Chapter 8) examines
in detail the design and fluid mechanical evaluation of artificial heart
valves. The following chapter (Chapter 9) deals with the fluid mechanical
alterations related to vascular graft and stent implants. The final chapter
(Chapter 10) details measurement of blood flow, pressure, velocity, and
vascular impedance. The chapter concludes with discussions on sophisti-
cated fluid mechanical measurements employed in vitro and in vivo to
assess the complex time-dependent, three-dimensional flow in human
circulation.
Because this book is intended as a first course for exposing students to
fluid mechanics in the human circulation, only the heart and major arteries
are considered, while flow in other organ systems, such as the lungs, kidneys,
and the brain or flow in the microcirculation is not included.
The material contained in this book was developed over several years of
teaching these particular courses to undergraduate and graduate-level stu-
dents. The figures have been selectively included from publications of
numerous eminent researchers in the field and the captions include the
sources from which the figures were obtained (with permission). Citations
of references in the text, however, have not been included so as not to
distract the students from the subject matter. A reference list for each chapter
is provided at the end of the book. Students also are referred to leading
journals dealing with relevant subject matter (e.g., the Annals of Biomedical
Engineering; Journal of Biomechanical Engineering; Journal of Biomechanics;
Medical Engineering and Physics; Atherosclerosis; Circulation; Circulation Research;
Journal of Thoracic and Cardiovascular Surgery; and Annals of Thoracic Surgery)
as well as numerous other sources for current advances in the field.
Krishnan B. Chandran
Ajit P. Yoganathan
Stanley E. Rittgers
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Contents
Part I Fluid and Solid Mechanics
and Cardiovascular Physiology
Chapter 1 Fundamentals of Fluid Mechanics.....................................3
Chapter 2 Introduction to Solid Mechanics......................................47
Chapter 3 Cardiovascular Physiology................................................69
Part II Biomechanics of the Human Circulation
Chapter 4 Rheology of Blood and Blood Vessel Mechanics.........115
Chapter 5 Static and Steady Flow Models......................................167
Chapter 6 Unsteady Flow and Nonuniform
Geometric Models............................................................191
Chapter 7 Native Heart Valves.........................................................257
Part III Cardiovascular Implants and Biomechanical
Measurements
Chapter 8 Prosthetic Heart Valve Fluid Dynamics........................277
Chapter 9 Vascular Therapeutic Techniques...................................315
Chapter 10 Fluid Dynamic Measurement Techiques.....................343
Bibliography........................................................................................405
Index.....................................................................................................411
Description:Part medicine, part biology, and part engineering, biomedicine and bioengineering are by their nature hybrid disciplines. To make these disciplines work, engineers need to speak ''medicine,'' and clinicians and scientists need to speak ''engineering.'' Building a bridge between these two worlds, Bio
