xi
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
4.5.4 Nonlinear Aspects and Pressure-Dependent Arterial
4.5.3 The Lumped Model of the Arterial System: The Windkessel
........
130
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
5.2.1 Branching Geometry and Fluid Dynamic Considerations
.............
148
5.2 Fluid Mechanics
of
Vascular Branching
.................................................
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
