Dynamics of the Vascular System

by Li, John K.-J.

• ISBN13: 9789810249076
• ISBN10: 9810249071
• Edition: 1st
• Format: Hardcover
• Copyright: 2004-04-01
• Publisher: World Scientific Pub Co Inc

Summary

First volume in a new series, text presents the recent advances in vascular biology and vascular engineering. Explores the new ways for examining the interaction of different parts of the vascular system, including measurement techniques and quantitative methods.

Author Biography

John K-J. Li received his Ph.D. in bioengineering in 1978 from the University of Pennsylvania

Table of Contents

Preface	vii
1. Historical Backgrounds and Book Contents
1.1 Discoveries of the Circulation	1	(6)
1.2 Importance of the Vascular System	7	(1)
1.3 Modern Concepts	8	(1)
1.4 Book Contents	9	(5)
2. Vascular Biology, Structure and Function
2.1 Anatomical Organization of the Vasculature	14	(6)
2.1.1 The Circulatory System	14	(1)
2.1.2 The Heart	14	(4)
2.1.3 The Arteries	18	(1)
2.1.4 The Veins	18	(1)
2.1.5 The Microvasculature	19	(1)
2.2 Mechanical Properties of Blood Vessels	20	(10)
2.2.1 Some Geometric Aspects of Blood Vessels	20	(5)
2.2.2 Vascular Stiffness and Elastic Properties	25	(5)
2.3 Functional Properties of Blood	30	(5)
2.3.1 Blood Plasma and Blood Gas	30	(1)
2.3.2 Oxygen Saturation Curves and Hemoglobin	31	(2)
2.3.3 Red Blood Cells, Hematocrit and Blood Volume	33	(2)
2.4 Control Aspects of the Vascular System	35	(6)
2.4.1 Control of the Central Cardiovascular System	36	(1)
2.4.2 Functions of the Baroreceptors	37	(2)
2.4.3 Arterial Chemoreceptors	39	(2)
3. Physical Concepts and Basic Fluid Mechanics
3.1 Basic Mechanics and Dimensional Analysis	41	(13)
3.1.1 Mass, Length and Time System and the Pi-Theorem of Buckingham	41	(2)
3.1.2 Dimensional Matrix	43	(1)
3.1.3 Dynamic Similitude in Vascular Biology	44	(2)
3.1.4 Elastic and Viscoelastic Properties of Blood Vessels	46	(8)
3.2 Frequency Domain and Fourier Analysis	54	(9)
3.2.1 Periodic Functions	54	(1)
3.2.2 Trigonometric Fourier Series	55	(3)
3.2.3 Complex Form of Fourier Series	58	(2)
3.2.4 Other Aspects of Frequency Domain Analysis	60	(3)
3.2.4.1 Dirichlet Conditions	60	(1)
3.2.4.2 Line Spectrum and Nyquist Criterion	61	(1)
3.2.4.3 Correlation, Coherence and Power Spectrum	61	(2)
3.3 Fluid Mechanics and Rheology	63	(13)
3.3.1 Steady Flow and Poiseuille Equation	63	(4)
3.3.2 Bernoulli's Equation and Narrowing Vessel Lumen	67	(1)
3.3.3 Orifice Flow and Torricelli's Equation	68	(1)
3.3.4 The Gorlin Equation	69	(1)
3.3.5 Flow and Flow Acceleration	69	(3)
3.3.6 Newtonian Fluid, No-Slip, Boundary Conditions and Entry Length	72	(4)
3.3.6.1 Newtonian Fluid	72	(1)
3.3.6.2 No-Slip Boundary Conditions	73	(1)
3.3.6.3 Laminar and Turbulent Flow	73	(2)
3.3.6.4 Entry Length	75	(1)
4. Hemodynamics of Large Arteries
4.1 Ventricular Outflow and the Aorta	76	(13)
4.1.1 Ventricular Ejection	76	(2)
4.1.2 Cardiac Muscle Contraction and Force-Length-Velocity Relation	78	(3)
4.1.3 The Pressure-Volume Curve and Contractility of the Heart	81	(1)
4.1.4 Ejection Fraction, Cardiac Performance, Preload and Afterload	82	(1)
4.1.5 Coupling of the Ventricle and the Arterial System	83	(4)
4.1.6 Dynamic of Heart-Arterial System Interactions	87	(2)
4.2 Pressure-Flow Relations and Vascular Impedance	89	(10)
4.2.1 Pressure and Flow Waveforms in Large and Small Arteries	89	(5)
4.2.2 Vascular Impedance to Blood Flow	94	(5)
4.3 Wave Propagation Phenomena	99	(11)
4.3.1 The Propagation Constant	99	(1)
4.3.2 Foot-to-Foot Velocity	100	(3)
4.3.3 Apparent Propagation Constant and Transfer Function	103	(4)
4.3.4 Determination of the Propagation Constant	107	(3)
4.4 Wave Reflection Phenomena	110	(10)
4.4.1 Influence of Wave Reflections on Pressure and Flow Waveforms	110	(6)
4.4.2 The Reflection Coefficients	116	(2)
4.4.3 Augmentation Index	118	(1)
4.4.4 Wave Reflection Sites	119	(1)
4.5 Modeling Aspects of the Arterial System	120	(22)
4.5.1 Mathematical Formulations	120	(4)
4.5.2 Linear Theories of Oscillatory Blood Flow in Arteries	124	(6)
4.5.3 The Lumped Model of the Arterial System: The Windkessel	130	(6)
4.5.4 Nonlinear Aspects and Pressure-Dependent Arterial Compliance	136	(6)
5. Vascular Branching
5.1 Branching Geometry	142	(6)
5.1.1 Complexity of Vascular Branching	142	(2)
5.1.2 Nonuniform Branching and 3-D Branching Structure	144	(2)
5.1.3 Space-Filling Properties and Modeling	146	(2)
5.2 Fluid Mechanics of Vascular Branching	148	(9)
5.2.1 Branching Geometry and Fluid Dynamic Considerations	148	(6)
5.2.2 Fluid Mechanics Associated with Atherosclerosis and Stenosis	154	(3)
5.3 Pulse Transmission Characteristics at Vascular Branching	157	(9)
5.3.1 Impedance Matching and Wave Reflections	157	(3)
5.3.2 Area Ratio Concept	160	(4)
5.3.3 Minimum Local Reflections at Vascular Branching Junctions	164	(2)
5.4 Optimization Aspects Applicable to Vascular Branching	166	(6)
5.4.1 Optimizing Vessel Radius and the Cube Law	166	(4)
5.4.2 Optimizing Branching Radii and Angles	170	(2)
6. The Venous System
6.1 The Reservoir Properties and Venous Return	172	(4)
6.1.1 Venous Compliance and Reservoir Characteristics	172	(2)
6.1.2 Structural Properties of Veins	174	(1)
6.1.3 Venous Return	175	(1)
6.2 Pressure and Flow Waveforms in Vein	176	(6)
6.2.1 The Normal Pressure and Flow Waveforms in Veins	176	(2)
6.2.2 Respiration Effects on Venous Pressure and Flow Waveforms	178	(2)
6.2.3 Abnormal Venous Pressure and Flow Waveforms	180	(2)
6.3 Modeling and Collapsible Vessel Properties	182	(10)
6.3.1 Steady Flow in Collapsible Tubes	182	(2)
6.3.2 Flow Limitation and Model Experiments	184	(4)
6.3.3 Pulse Wave Transmission Characteristics in Veins	188	(4)
7. The Microcirculation
7.1 Structure of the Microcirculation	192	(8)
7.1.1 Functional Organization of the Microvasculature	192	(4)
7.1.2 The Capillary Circulation	196	(4)
7.2 Pressure-Flow Relation and Microcirculatory Mechanics	200	(6)
7.2.1 Flow-Related Mechanical Characteristics of the Microcirculation	200	(2)
7.2.2 Some Pressure-Related Mechanical Characteristics	202	(4)
7.3 Pulse Transmission and Modeling Aspects	206	(8)
7.3.1 Pressure and Flow Waveforms in Arterioles and Capillaries	206	(2)
7.3.2 Pulse Transmission Characteristics in the Microcirculation	208	(2)
7.3.3 Modeling Aspects of the Microcirculation	210	(4)
8. Hemodynamic Measurements and Dynamics of the Assisted Circulation
8.1 Pressure, Flow and Dimension Measurements	214	(20)
8.1.1 Invasive Blood Pressure Measurements	214	(8)
8.1.1.1 The Needle-Pressure Transducer System	214	(3)
8.1.1.2 The Catheter-Pressure Transducer Systems	217	(5)
8.1.2 Noninvasive Blood Pressure Measurements	222	(4)
8.1.2.1 Auscultatory Measurement of Blood Pressure	222	(2)
8.1.2.2 Blood Pressure Measurement with the Oscillometric Method	224	(1)
8.1.2.3 Noninvasive Blood Pressure Monitoring with Tonometer	225	(1)
8.1.3 Blood Flow Measurement	226	(7)
8.1.3.1 Electromagnetic Flowmeter	226	(1)
8.1.3.2 Ultrasound Doppler Velocimeters	227	(2)
8.1.3.3 Indicator Dilution Methods and Thermodilution	229	(4)
8.1.4 Measurement of Vascular Dimensions	233	(1)
8.2 The Assisted Circulation and the Intra-Aortic Balloon Pump	234	(11)
8.2.1 Mechanical Assist Devices and the Assisted Circulation	234	(11)
Bibliography	245	(8)
Index	253