Contents

Preface xi Acknowledgments xiii

Chapter 1. Review of Basic Fluid Mechanics Concepts 1

1.1 A Brief History of Biomedical Fluid Mechanics 1

1.2 Fluid Characteristics and Viscosity 4

1.2.1 Displacement 4

1.2.2 Shear stress 6

1.3 Fundamental Method for Measuring Viscosity 9

1.4 Introduction to Pipe Flow 11

1.4.1 Reynolds number 12

1.4.2 Poiseuille's law 14

1.4.3 Flow rate 16

1.5 Bernoulli Equation 18

1.6 Conservation of Mass 18

1.6.1 Venturi meter example 19

1.7 Example Problem: Fluid Statics 20

1.7.1 Example problem: fluid statics 21

1.8 The Wormersley Number, a, a Frequency Parameter for Pulsatile Flow 22

Chapter 2. Cardiovascular Structure and Function 25

2.1 Introduction 25

2.2 Clinical Features 26

2.3 Functional Anatomy 27

2.4 The Heart as a Pump 28

2.5 Cardiac Muscle 29

2.5.1 Biopotential in myocardium 30

2.5.2 Excitability 31

2.5.3 Automaticity 33

2.6 Heart Valves 33

2.6.1 Clinical features 34

2.7 Cardiac Cycle 34

2.8 Heart Sounds 36

2.8.1 Clinical features 36

2.9 Factors Influencing Flow and Pressure 38

2.10 Coronary Circulation 40

2.10.1 Control of the coronary circulation 41

2.10.2 Clinical features 41

2.11 Microcirculation 41

2.11.1 Capillary structure 42

2.11.2 Capillary wall structure 42

Chapter 3. Pulmonary Anatomy, Pulmonary Physiology, and Respiration 45

3.1 Introduction 45

3.2 Clinical Features 46

3.3 Alveolar Ventilation 47

3.3.1 Tidal volume 47

3.3.2 Residual volume 47

3.3.3 Expiratory reserve volume 48

3.3.4 Inspiratory reserve volume 48

3.3.5 Functional residual capacity 48

3.3.6 Inspiratory capacity 48

3.3.7 Total lung capacity 48

3.3.8 Vital capacity 49

3.4 Ventilation—Perfusion Relationships 49

3.5 Mechanics of Breathing 50

3.5.1 Muscles of inspiration 50

3.5.2 Muscles of expiration 51

3.5.3 Compliance of the lung and chest wall 51

3.6 Work of Breathing 51

3.7 Airway Resistance 54

3.8 Gas Exchange and Transport 57

3.8.1 Diffusion 58

3.8.2 Diffusing capacity 58

3.8.3 Resistance to diffusion 59

3.8.4 Oxygen dissociation curve 60

3.9 Pulmonary Pathophysiology 61

3.9.1 Bronchitis 61

3.9.2 Emphysema 61

3.9.3 Asthma 61

3.9.4 Pulmonary fibrosis 61

3.9.5 Chronic obstructive pulmonary disease 62

3.9.6 Heart disease 63

3.9.7 Comparison of pulmonary pathologies 63 3.10 Respiration in Extreme Environments 63

3.10.1 Barometric pressure 63

3.10.2 Partial pressure of oxygen 65

3.10.3 Hyperventilation 66

3.10.4 Alkalosis 67

3.10.5 Acute mountain sickness (AMS) 67

3.10.6 High-altitude pulmonary edema 67

3.10.7 High-altitude cerebral edema 68

3.10.8 Acclimatization 68

3.10.9 Drugs stimulating red blood cell production 69

Chapter 4. Hematology and Blood Rheology 71

4.1 Introduction 71

4.2 Elements of Blood 71

4.3 Blood Characteristics 71

4.4 Erythrocytes 72

4.4.1 Hemoglobin 74

4.4.2 Clinical Features 75

4.4.3 Erythrocyte indices 76

4.4.4 Abnormalities of the blood 77

4.5 Leukocytes 77

4.5.1 Neutrophils 78

4.5.2 Lymphocytes 79

4.5.3 Monocytes 80

4.5.4 Eosinophils 80

4.5.5 Basophils 81

4.5.6 Leukemia 81

4.5.7 Thrombocytes 81

4.6 Blood Types 81

4.6.1 Rh blood groups 83

4.6.2 M and N blood group system 84

4.7 Plasma 84

4.7.1 Plasma viscosity 85

4.7.2 Electrolyte composition of plasma 85

4.8 Blood pH 86

4.9 Clinical Features 86

Chapter 5. Anatomy and Physiology of Blood Vessels 89

5.1 Introduction 89

5.2 General Structure of Arteries 89

5.2.1 Tunica intima 90

5.2.2 Tunica media 90

5.2.3 Tunica externa 91

5.3 Types of Arteries 91

5.3.1 Elastic arteries 92

5.3.2 Muscular arteries 92

5.3.3 Arterioles 92

5.4 Mechanics of Arterial Walls 92

5.5 Compliance 94

5.6 Pressure-Strain Modulus 99

5.7 Vascular Pathologies 100

5.7.1 Atherosclerosis 100

5.7.2 Stenosis 100

5.7.3 Aneurysm 100

5.7.4 Thrombosis 101

5.7.5 Clinical aspects 101

5.8 Stents 102

5.9 Coronary Artery Bypass Grafting 102

5.9.1 Arterial grafts 103

Chapter 6. Mechanics of Heart Valves 105

6.1 Introduction 105

6.2 Aortic and Pulmonic Valves 106

6.3 Mitral and Tricuspid Valves 109

6.4 Clinical Features 111

6.5 Prosthetic Mechanical Valves 111

6.5.1 Case study-the Bjork-Shiley convexo-concave heart valve 112

6.6 Prosthetic Tissue Valves 114

Chapter 7. Pulsatile Flow in Large Arteries 117

7.1 Fluid Kinematics 117

7.2 Continuity 118

7.3 Complex Numbers 119

7.4 Fourier Series Representation 121

7.5 Navier-Stokes Equations 123

7.6 Pulsatile Flow in Rigid Tubes: Wormersley Solution 126

7.7 Pulsatile Flow in Rigid Tubes: Fry Solution 131

7.8 Instability in Pulsatile Flow 135

Chapter 8. Flow and Pressure Measurement 137

8.1 Introduction 137

8.2 Indirect Pressure Measurements 137

8.3 Direct Pressure Measurement 138

8.3.1 Intravascular: strain gauge-tipped pressure transducer 138

8.3.2 Extravascular: catheter-transducer measuring system 144

8.3.3 Electrical analog of the catheter measuring system 145

8.3.4 Characteristics for an extravascular pressure measuring system 147

8.3.5 Case 1—the undamped catheter measurement system 149

8.3.6 Case 2—the undriven, damped catheter measurement system 150

8.3.7 Pop test—measurement of transient step response 154

8.4 Flow Measurement 155

8.4.1 Indicator dilution method 155

8.4.2 Fick technique for measuring cardiac output 156

8.4.3 Fick technique example 156

8.4.4 Rapid injection indicator-dilution method—dye dilution technique 156

8.4.5 Thermodilution 157

8.4.6 Electromagnetic flowmeters 158

8.4.7 Continuous wave ultrasonic flowmeters 159

8.4.8 Continuous wave Doppler ultrasound example 160

8.5 Summary and Clinical Applications 160

Chapter 9. Modeling 163

9.1 Introduction 163

9.2 Theory of Models 164

9.2.1 Dimensional analysis and the Buckingham Pi theorem 164

9.2.2 Synthesizing Pi terms 166

9.3 Geometric Similarity 168

9.4 Dynamic Similarity 169

9.5 Kinematic Similarity 169

9.6 Common Dimensionless Parameters in Fluid Mechanics 170

9.7 Modeling Example 1—Does the Flea Model the Man? 170

9.8 Modeling Example 2 173

9.9 Modeling Example 3 173

Chapter 10. Lumped Parameter Mathematical Models 177

10.1 Introduction 177

10.2 Electrical Analog Model of Flow in a Tube 178

10.2.1 Nodes and the equations at each node 179

10.2.2 Terminal load 180

10.2.3 Summary of the lumped parameter electrical analog model 182

10.3 Modeling of Flow through the Mitral Valve 182

10.3.1 Model description 184

10.3.2 Active ventricular relaxation 186

10.3.3 Meaning of convective resistance 186

10.3.4 Variable area mitral valve model description 187

10.3.5 Variable area mitral valve model parameters 188

10.3.6 Solving the system of differential equations 188

10.3.7 Model trials 188

10.3.8 Results 189

10.4 Summary 190

Index 193

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