The Physics of Coronary Blood Flow

Cover......Page 1
Title......Page 3
Series Preface......Page 5
Copyright......Page 6
Dedication......Page 7
Foreword......Page 8
Preface......Page 12
Contents......Page 16
1.1 The Lone Pump......Page 19
1.2 Heart “Disease”?......Page 21
1.3 Origin of Coronary Blood Supply......Page 23
1.4 Coronary Arteries......Page 25
1.5 Left/Right Dominance......Page 30
1.6 Branching Structure......Page 32
1.7 Underlying Design?......Page 39
1.8 Coronary Flow Reserve......Page 45
1.9 Design Conflict?......Page 49
1.10 Summary......Page 50
2.1 Why Modelling?......Page 53
2.2 The “Lumped Model” Concept......Page 55
2.3 Flow in a Tube......Page 56
2.4 Fluid Viscosity: Resistance to Flow......Page 59
2.5 Fluid Inertia: Inductance......Page 63
2.6 Elasticity of the Tube Wall: Capacitance......Page 74
2.7 Elasticity of the Tube Wall: Wave Propagation......Page 80
2.8 Mechanical Analogy......Page 84
2.9 Electrical Analogy......Page 89
2.10 Summary......Page 93
3.1 Introduction......Page 96
3.2 RLC System in Series......Page 98
3.3 Free Dynamics of the RLC System in Series......Page 101
3.4 R1, R2 in Parallel......Page 105
3.5 R,L in Parallel......Page 109
3.6 R,C in Parallel......Page 114
3.7 RLC System in Parallel Under Constant Pressure......Page 118
3.8 RLC System in Parallel Under Constant Flow......Page 120
3.9 Summary......Page 129
4.1 Introduction......Page 132
4.2 The Particular Solution......Page 133
4.3 Using the Complex Exponential Function......Page 134
4.4 Overdamped Forced Dynamics......Page 136
4.5 Underdamped Forced Dynamics......Page 139
4.6 Critically Damped Forced Dynamics......Page 141
4.7 Transient and Steady States......Page 143
4.8 The Concept of Reactance......Page 148
4.9 The Concepts of Impedance, Complex Impedance......Page 154
4.10 Summary......Page 159
5.1 Introduction......Page 161
5.2 Basic Theory......Page 164
5.3 Example: Single-Step Waveform......Page 167
5.4 Example: Piecewise Waveform......Page 173
5.5 Numerical Formulation......Page 180
5.6 Example: Cardiac Waveform......Page 185
5.7 Summary......Page 190
6.1 Introduction......Page 192
6.2 Composite Pressure-Flow Relations Under Pure Resistance......Page 194
6.3 Example: Cardiac Pressure Wave......Page 196
6.4 Composite Pressure-Flow Relations Under General Impedance......Page 201
6.5 Composite Pressure-Flow Relations Under Inertial Effects......Page 205
6.6 Composite Pressure-Flow Relations Under Capacitance Effects......Page 213
6.7 Composite Pressure-Flow Relations Under RLC in Series......Page 222
6.8 Composite Pressure-Flow Relations Under RLC in Parallel......Page 228
6.9 Summary......Page 234
7.1 Introduction......Page 236
7.2 LM0: {R,C}......Page 237
7.3 LM1: {R1,{R2+C}}......Page 244
7.4 LM2: {{R1+L},{R2+C}}......Page 250
7.5 LM3: {{R1+(pb)},{R2+C}}......Page 256
7.6 Inflow-Outflow......Page 264
7.7 Summary......Page 267
8.1 Introduction......Page 270
8.2 The Streamwise Space Dimension......Page 271
8.3 Steady Flow along Tube Segments......Page 273
8.4 Steady Flow Through a Bifurcation......Page 280
8.5 Pulsatile Flow in a Rigid Tube......Page 287
8.6 Pulsatile Flow in an Elastic Tube......Page 294
8.7 Wave Reflections......Page 302
8.8 Summary......Page 312
9.1 Introduction......Page 314
9.2 Steady Flow in Branching Tubes......Page 315
9.3 Pulsatile Flow in Rigid Branching Tubes......Page 322
9.4 Elastic Branching Tubes......Page 328
9.5 Effective Impedance, Admittance......Page 332
9.6 Pulsatile Flow in Elastic Branching Tubes......Page 344
9.7 Cardiac Pressure Wave in Elastic Branching Tubes......Page 358
9.8 Summary......Page 373
10.1 Introduction......Page 376
10.2 Magic Norms?......Page 377
10.3 Coronary Heart Disease, Physical Exercise, and the Conundrum of Coronary Flow Reserve......Page 385
10.4 Wave Propagation Through a Coronary Bypass......Page 393
10.5 Wave Propagation Through a Coronary Stent......Page 396
10.6 Sudden Cardiac Death......Page 399
10.7 Broken Heart Syndrome......Page 402
10.8 Summary......Page 403
References......Page 405
Index......Page 416