The Physics of Coronary Blood Flow

The fields of biological and medical physics and biomedical engineering are broad, multidisciplinary and dyanmic. They lie at the crossroads of frontier - search in physics, biology, chemistry, and medicine. The Biological & Me- cal Physics/Biomedical Engineering Series is intended to be comprehensive, covering a broad range of topics important to the study of the physical, che- 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 - cluding molecular, membrane, and mathematical biophysics; photosynthetic - ergy harvesting and conversion; information processing; physical principles of genetics; sensory communications; automata networks, neural networks, and cellular automata. Equally important will be coverage of applied aspects of b- logical and medical physics and biomedical engineering such as molecular el- tronic components and devices, biosensors, medicine, imaging, physical prin- ples of renewable energy production, advanced prostheses, and environmental control and engineering. Elias Greenbaum Oak Ridge, TN M. Zamir Department of Applied Mathematics University of Western Ontario London, Ontario, N6A 5B7 CANADA zamir@uwo.ca Library of Congress Cataloging-in-Publication Data Zamir, M. (Mair) The physics of coronary blood flow / M. Zamir. p. cm. — (Biological and medical physics, biomedical engineering) Includes bibliographical references and index. 1. Coronary circulation. 2. Hemodynamics. 3. Blood flow. I. Title. II. Series. QP108.Z36 2005 612.1?7—dc22 2005042502 ISBN-10: 0-387-25297-5 e-ISBN: 0-387-26019-6 Printed on acid-free paper.

The Lone Pump. -Heart 'Disease'? . -Origin of Coronary Blood Supply. -Coronary Arteries. -Left/Right Dominance. -Branching Structure. -Underlying Design?. -Coronary Flow Reserve.- Design Conflict?. -Summary. -Modelling Preliminaries. -Why Modelling?. -The 'Lumped Model' Concept. -Flow in a Tube. -Fluid Viscosity: Resistance to Flow. -Fluid Inertia: Inductance. -Elasticity of the Tube Wall: Capacitance. -Elasticity of the Tube Wall: Wave Propagation. -Mechanical Analogy. -Electrical Analogy. -Summary. -Basic Lumped Elements. -Introduction. -RLC System in Series. -Free Dynamics of the RLC System in Series. -R1,R2 in Parallel. -R,L in Parallel. -R,C in Parallel. -RLC System in Parallel Under Constant Pressure. -RLC System in Parallel Under Constant Flow. -Summary. -Forced Dynamics of the RLC System. -Introduction. -The Particular Solution. -Using the Complex Exponential Function. -Overdamped Forced Dynamics. -Underdamped Forced Dynamics. -Critically Damped Forced Dynamics. -Transient and Steady States. -The Concept of Reactance. -The Concepts of Impedance, Complex Impedance. -Summary. -The Analysis of Composite Waveforms. -Introduction. -Basic Theory. -Example: Single-Step Waveform. -Example: Piecewise Waveform. -Numerical Formulation. -Example: Cardiac Waveform. -Summary. -Composite Pressure-Flow Relations. -Introduction. -Composite Pressure-Flow Relations Under Pure Resistance. -Example: Cardiac Pressure Wave. -Composite Pressure-Flow Relations Under General Impedance. -Composite Pressure-Flow Relations Under Inertial Effects. -Composite Pressure-Flow Relations Under Capacitance Effects. -Composite Pressure-Flow Relations Under RLC in Series. -Composite Pressure-Flow Relations Under RLC in Parallel. -Summary. -Lumped Models. -Introduction. -LM0: {R,C}. -LM1: {R1,{R2+C}}. -LM2: {{R1+L},{R2+C}}. -LM3: {{R1+(pb)},{R2+C}}. -Inflow-Outflow. -Summary. -Elements of Unlumped-Model Analysis. -Introduction. -The Streamwise Space Dimension. -Steady Flow along Tube Segments. -Steady Flow Through a Bifurcation. -Pulsatile Flow in a Rigid Tube. -Pulsatile Flow in an Elastic Tube. -Wave Reflections. -Summary. -Basic Unlumped Models. -Introduction. -Steady Flow in Branching Tubes. -Pulsatile Flow in Rigid Branching Tubes. -Elastic Branching Tubes. -Effective Impedance, Admittance. -Pulsatile Flow in Elastic Branching Tubes. -Cardiac Pressure Wave in Elastic Branching Tubes. -Summary. -Dynamic Pathologies. -Introduction. -Magic Norms? -Coronary Heart Disease, Physical Exercise, and the Conundrum of Coronary Flow Reserve. -Wave Propagation Through a Coronary Bypass. -Wave Propagation Through a Coronary Stent. -Sudden Cardiac Death. -Broken Heart Syndrome. -Summary. -References. -Index.