Dynamics of the vascular system / John K-J. Li.

Format:

Book

Author/Creator:

Li, John K-J., 1950-

Series:

Series on bioengineering and biomedical engineering ; v. 1.

Series on bioengineering and biomedical engineering ; v. 1

Language:

English

Subjects (All):

Cardiovascular system.

Hemodynamics.

Blood--Circulation.

Blood.

Cardiovascular System.

Hemodynamic Processes.

Blood Circulation.

Medical Subjects:

Cardiovascular System.

Hemodynamic Processes.

Blood Circulation.

Physical Description:

xii, 257 pages : illustrations ; 24 cm.

Place of Publication:

River Edge, N.J. : World Scientific, [2004]

Summary:

Li (biomedical engineering, Rutgers U.) begins the series he will edit with a study that can serve as a companion to his The Arterial Circulation: Physical Principles and Clinical Applications. He uses mathematical techniques to formulate the physical principles involved in the structural and functional correlates of the vascular system's underlying physiology. Control and geometric perspectives are also included wherever possible. He writes for professionals and students in bioengineering and related fields. Annotation ©2004 Book News, Inc., Portland, OR (booknews.com)

Contents:

1 Historical Backgrounds and Book Contents

1.1 Discoveries of the Circulation 1

1.2 Importance of the Vascular System 7

1.3 Modern Concepts 8

2 Vascular Biology, Structure and Function

2.1 Anatomical Organization of the Vasculature 14

2.1.1 The Circulatory System 14

2.1.2 The Heart 14

2.1.3 The Arteries 18

2.1.4 The Veins 18

2.1.5 The Microvasculature 19

2.2 Mechanical Properties of Blood Vessels 20

2.2.1 Some Geometric Aspects of Blood Vessels 20

2.2.2 Vascular Stiffness and Elastic Properties 25

2.3 Functional Properties of Blood 30

2.3.1 Blood Plasma and Blood Gas 30

2.3.2 Oxygen Saturation Curves and Hemoglobin 31

2.3.3 Red Blood Cells, Hematocrit and Blood Volume 33

2.4 Control Aspects of the Vascular System 35

2.4.1 Control of the Central Cardiovascular System 36

2.4.2 Functions of the Baroreceptors 37

2.4.3 Arterial Chemoreceptors 39

3 Physical Concepts and Basic Fluid Mechanics

3.1 Basic Mechanics and Dimensional Analysis 41

3.1.1 Mass, Length and Time System and the Pi-Theorem of Buckingham 41

3.1.2 Dimensional Matrix 43

3.1.3 Dynamic Similitude in Vascular Biology 44

3.1.4 Elastic and Viscoelastic Properties of Blood Vessels 46

3.2 Frequency Domain and Fourier Analysis 54

3.2.1 Periodic Functions 54

3.2.2 Trigonometric Fourier Series 55

3.2.3 Complex Form of Fourier Series 58

3.2.4 Other Aspects of Frequency Domain Analysis 60

3.2.4.1 Dirichlet Conditions 60

3.2.4.2 Line Spectrum and Nyquist Criterion 61

3.2.4.3 Correlation, Coherence and Power Spectrum 61

3.3 Fluid Mechanics and Rheology 63

3.3.1 Steady Flow and Poiseuille Equation 63

3.3.2 Bernoulli's Equation and Narrowing Vessel Lumen 67

3.3.3 Orifice Flow and Torricelli's Equation 68

3.3.4 The Gorlin Equation 69

3.3.5 Flow and Flow Acceleration 69

3.3.6 Newtonian Fluid, No-Slip, Boundary Conditions and Entry Length 72

3.3.6.1 Newtonian Fluid 72

3.3.6.2 No-Slip Boundary Conditions 73

3.3.6.3 Laminar and Turbulent Flow 73

3.3.6.4 Entry Length 75

4 Hemodynamics of Large Arteries

4.1 Ventricular Outflow and the Aorta 76

4.1.1 Ventricular Ejection 76

4.1.2 Cardiac Muscle Contraction and Force-Length-Velocity Relation 78

4.1.3 The Pressure-Volume Curve and Contractility of the Heart 81

4.1.4 Ejection Fraction, Cardiac Performance, Preload and Afterload 82

4.1.5 Coupling of the Ventricle and the Arterial System 83

4.1.6 Dynamic of Heart-Arterial System Interactions 87

4.2 Pressure-Flow Relations and Vascular Impedance 89

4.2.1 Pressure and Flow Waveforms in Large and Small Arteries 89

4.2.2 Vascular Impedance to Blood Flow 94

4.3 Wave Propagation Phenomena 99

4.3.1 The Propagation Constant 99

4.3.2 Foot-to-Foot Velocity 100

4.3.3 Apparent Propagation Constant and Transfer Function 103

4.3.4 Determination of the Propagation Constant 107

4.4 Wave Reflection Phenomena 110

4.4.1 Influence of Wave Reflections on Pressure and Flow Waveforms 110

4.4.2 The Reflection Coefficients 116

4.4.3 Augmentation Index 118

4.4.4 Wave Reflection Sites 119

4.5 Modeling Aspects of the Arterial System 120

4.5.1 Mathematical Formulations 120

4.5.2 Linear Theories of Oscillatory Blood Flow in Arteries 124

4.5.3 The Lumped Model of the Arterial System: The Windkessel 130

4.5.4 Nonlinear Aspects and Pressure-Dependent Arterial Compliance 136

5 Vascular Branching

5.1 Branching Geometry 142

5.1.1 Complexity of Vascular Branching 142

5.1.2 Nonuniform Branching and 3-D Branching Structure 144

5.1.3 Space-Filling Properties and Modeling 146

5.2 Fluid Mechanics of Vascular Branching 148

5.2.1 Branching Geometry and Fluid Dynamic Considerations 148

5.2.2 Fluid Mechanics Associated with Atherosclerosis and Stenosis 154

5.3 Pulse Transmission Characteristics at Vascular Branching 157

5.3.1 Impedance Matching and Wave Reflections 157

5.3.2 Area Ratio Concept 160

5.3.3 Minimum Local Reflections at Vascular Branching Junctions 164

5.4 Optimization Aspects Applicable to Vascular Branching 166

5.4.1 Optimizing Vessel Radius and the Cube Law 166

5.4.2 Optimizing Branching Radii and Angles 170

6 The Venous System

6.1 The Reservoir Properties and Venous Return 172

6.1.1 Venous Compliance and Reservoir Characteristics 172

6.1.2 Structural Properties of Veins 174

6.1.3 Venous Return 175

6.2 Pressure and Flow Waveforms in Vein 176

6.2.1 The Normal Pressure and Flow Waveforms in Veins 176

6.2.2 Respiration Effects on Venous Pressure and Flow Waveforms 178

6.2.3 Abnormal Venous Pressure and Flow Waveforms 180

6.3 Modeling and Collapsible Vessel Properties 182

6.3.1 Steady Flow in Collapsible Tubes 182

6.3.2 Flow Limitation and Model Experiments 184

6.3.3 Pulse Wave Transmission Characteristics in Veins 188

7 The Microcirculation

7.1 Structure of the Microcirculation 192

7.1.1 Functional Organization of the Microvasculature 192

7.1.2 The Capillary Circulation 196

7.2 Pressure-Flow Relation and Microcirculatory Mechanics 200

7.2.1 Flow-Related Mechanical Characteristics of the Microcirculation 200

7.2.2 Some Pressure-Related Mechanical Characteristics 202

7.3 Pulse Transmission and Modeling Aspects 206

7.3.1 Pressure and Flow Waveforms in Arterioles and Capillaries 206

7.3.2 Pulse Transmission Characteristics in the Microcirculation 208

7.3.3 Modeling Aspects of the Microcirculation 210

8 Hemodynamic Measurements and Dynamics of the Assisted Circulation

8.1 Pressure, Flow and Dimension Measurements 214

8.1.1 Invasive Blood Pressure Measurements 214

8.1.1.1 The Needle-Pressure Transducer System 214

8.1.1.2 The Catheter-Pressure Transducer Systems 217

8.1.2 Noninvasive Blood Pressure Measurements 222

8.1.2.1 Auscultatory Measurement of Blood Pressure 222

8.1.2.2 Blood Pressure Measurement with the Oscillometric Method 224

8.1.2.3 Noninvasive Blood Pressure Monitoring with Tonometer 225

8.1.3 Blood Flow Measurement 226

8.1.3.1 Electromagnetic Flowmeter 226

8.1.3.2 Ultrasound Doppler Velocimeters 227

8.1.3.3 Indicator Dilution Methods and Thermodilution 229

8.1.4 Measurement of Vascular Dimensions 233

8.2 The Assisted Circulation and the Intra-Aortic Balloon Pump 234

8.2.1 Mechanical Assist Devices and the Assisted Circulation 234.

Notes:

Includes bibliographical references (pages [245]-252) and index.

ISBN:

9810249071

OCLC:

55139658