X
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
3.2.3 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
3.2.2 Trigonometric Fourier Series
...........................................................
55
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
