The Physics of Coronary Blood Flow

by Zamir, M.; Fung, Y. C.

• ISBN13: 9780387252971
• ISBN10: 0387252975
• Format: Hardcover
• Copyright: 2005-06-30
• Publisher: Springer Verlag

Summary

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 because of obstructive disease in the vessels that carry the flow. The subject of coronary blood flow is therefore associated mostly with the pathophysiology of this disease, rarely with dynamics or physics. Yet, the system responsible for coronary blood flow, namely the "coronary circulation", is a highly sophisticated 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 to the dynamics and physics of coronary blood flow. While it recognizes the range of clinical and pathophysiological issues involved, the book focuses on dynamics and physics, approaching the subject from a biomedical engineering viewpoint. With this approach, the book will complement other books on the subject that have so far focused largely on clinical and pathophysiological issues. The author, originally trained in fluid dynamics, has been teaching and working on the dynamics of blood flow in general and coronary blood flow in particular for the past thirty years and has produced a book that will appeal to physicians, physicists and engineers.

Author Biography

The author, originally trained in fluid dynamics, has been teaching and working on the dynamics of blood flow in general and coronary blood flow in particular for the past thirty years and has produced a book that will appeal to physicians, physicists and engineers.

Table of Contents

Foreword	vii
Series Preface	ix
Preface	xi
Static Design Issues	1	(34)
The Lone Pump	1	(2)
Heart ``Disease''?	3	(2)
Origin of Coronary Blood Supply	5	(2)
Coronary Arteries	7	(5)
Left/Right Dominance	12	(2)
Branching Structure	14	(7)
Underlying Design?	21	(6)
Coronary Flow Reserve	27	(4)
Design Conflict?	31	(1)
Summary	32	(3)
Modelling Preliminaries	35	(44)
Why Modelling?	35	(2)
The ``Lumped Model'' Concept	37	(1)
Flow in a Tube	38	(3)
Fluid Viscosity: Resistance to Flow	41	(4)
Fluid Inertia: Inductance	45	(11)
Elasticity of the Tube Wall: Capacitance	56	(6)
Elasticity of the Tube Wall: Wave Propagation	62	(4)
Mechanical Analogy	66	(5)
Electrical Analogy	71	(4)
Summary	75	(4)
Basic Lumped Elements	79	(36)
Introduction	79	(2)
RLC System in Series	81	(3)
Free Dynamics of the RLC System in Series	84	(4)
R1, R2 in Parallel	88	(4)
R.L in Parallel	92	(5)
R.C in Parallel	97	(4)
RLC System in Parallel Under Constant Pressure	101	(2)
RLC System in Parallel Under Constant Flow	103	(9)
Summary	112	(3)
Forced Dynamics of the RLC System	115	(30)
Introduction	115	(1)
The Particular Solution	116	(1)
Using the Complex Exponential Function	117	(2)
Overdamped Forced Dynamics	119	(3)
Underdamped Forced Dynamics	122	(2)
Critically Damped Forced Dynamics	124	(2)
Transient and Steady States	126	(5)
The Concept of Reactance	131	(6)
The Concepts of Impedance, Complex Impedance	137	(5)
Summary	142	(3)
The Analysis of Composite Waveforms	145	(32)
Introduction	145	(3)
Basic Theory	148	(3)
Example: Single-Step Waveform	151	(6)
Example: Piecewise Waveform	157	(7)
Numerical Formulation	164	(5)
Example: Cardiac Waveform	169	(5)
Summary	174	(3)
Composite Pressure-Flow Relations	177	(44)
Introduction	177	(2)
Composite Pressure-Flow Relations Under Pure Resistance	179	(2)
Example: Cardiac Pressure Wave	181	(5)
Composite Pressure-Flow Relations Under General Impedance	186	(4)
Composite Pressure-Flow Relations Under Inertial Effects	190	(8)
Composite Pressure-Flow Relations Under Capacitance Effects	198	(9)
Composite Pressure-Flow Relations Under RLC in Series	207	(6)
Composite Pressure-Flow Relations Under RLC in Parallel	213	(6)
Summary	219	(2)
Lumped Models	221	(34)
Introduction	221	(1)
LM0: {R, C}	222	(7)
LM1: {R1, {R2+C}}	229	(6)
LM2: {{R1+L}.{R2+C}}	235	(6)
LM3: {{R1+(pb)},{R2+C}}	241	(8)
Inflow-Outflow	249	(3)
Summary	252	(3)
Elements of Unlumped-Model Analysis	255	(44)
Introduction	255	(1)
The Streamwise Space Dimension	256	(2)
Steady Flow along Tube Segments	258	(7)
Steady Flow Through a Bifurcation	265	(7)
Pulsatile Flow in a Rigid Tube	272	(7)
Pulsatile Flow in an Elastic Tube	279	(8)
Wave Reflections	287	(10)
Summary	297	(2)
Basic Unlumped Models	299	(62)
Introduction	299	(1)
Steady Flow in Branching Tubes	300	(7)
Pulsatile Flow in Rigid Branching Tubes	307	(6)
Elastic Branching Tubes	313	(4)
Effective Impedance, Admittance	317	(12)
Pulsatile Flow in Elastic Branching Tubes	329	(14)
Cardiac Pressure Wave in Elastic Branching Tubes	343	(15)
Summary	358	(3)
Dynamic Pathologies	361	(30)
Introduction	361	(1)
Magic Norms?	362	(8)
Coronary Heart Disease, Physical Exercise, and the Conundrum of Coronary Flow Reserve	370	(8)
Wave Propagation Through a Coronary Bypass	378	(3)
Wave Propagation Through a Coronary Stent	381	(3)
Sudden Cardiac Death	384	(3)
Broken Heart Syndrome	387	(1)
Summary	388	(3)
References	391	(12)
Index	403