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Hemodynamics Bioengineering 6000 CV Physiology
Hemodynamics
Bioengineering 6000 CV PhysiologyHemodynamics
Overview and Terminology
Arterioles
• Parameters– Pressure– Velocity– Flow
• laminar vs. turbulent
– Resistance– Viscosity – Energy– Area– Volume
Bioengineering 6000 CV PhysiologyIntro to Circulation
• "The problem of treating the pulsatile flow of blood through the cardiovascular system in precise mathematical terms is insuperable" (Berne and Levy) – Blood is not Newtonian (viscosity is not constant)– Flow is not steady but pulsatile– Vessels are elastic, multibranched conduits of constantly
changing diameter and shape.– Use equations qualitatively
• Local control of blood flow
Bioengineering 6000 CV PhysiologyHemodynamics
Laminar Flow and Turbulence
• Laminar flow– Parabolic profile
• Pulsatile laminar flow– Velocity changes– May reverse direction
• Turbulent flow– Nonaligned movement– Noisy (BP cuff)– Reynolds number
• > 1000 = turbulence• > 200 = eddies possible
– Rarely occurs in healthy vessels
Velo
city
Pro
files
R =�P
�Q̇
C =�V
�P
L =�P
�Q̇/�t
Q̇ = (P1 � P2)⇡r4
8⌘l
R =8⌘l
⇡r4(I =
V
R)
Bioengineering 6000 CV PhysiologyHemodynamics
Hemodynamic Parameters
• Resistance
• Compliance
• Inertance
• Poiseuille's Law– laminar flow– Newtonian fluid– rigid tube– works for small
arteries and veins
Q = flow.
P = pressure η = viscosityV = volume
R =�P
�Q̇
C =�V
�P
L =�P
�Q̇/�t
Q̇ = (P1 � P2)⇡r4
8⌘l
R =8⌘l
⇡r4(I =
V
R)
Bioengineering 6000 CV PhysiologyHemodynamics
Hemodynamic Parameters
• Resistance
• Compliance
• Inductance
• Poiseuille's Law– laminar flow– Newtonian fluid– rigid tube– works for small
arteries and veins
Q = flow.
P = pressure η = viscosityV = volume
Bioengineering 6000 CV PhysiologyHemodynamics
Resistance and Compliance
• Veins vs. arteries– have 24 times the
compliance of arteries– carry 65% of the blood– have even higher blood
storage capacity• Autonomic control
– alters resistance but not compliance (slopes of curves)
– acts to shift blood volume
Sympathetic inhibition
0 100 200Arterial Pressure [mm Hg]
Blo
od F
low
Norm
al
Sympathetic stimulation
0 70 140
Pressure [mm Hg]
Blo
od V
olum
e
Arterial
Venous C =�V
�P
R =�P
�Q̇
⌘ =⌧
du/dy=
F/A
U/Y=
Shear stressShear rate
Bioengineering 6000 CV PhysiologyHemodynamics
ViscosityF
U
uy Y
A
Definition for homogenous Newtonian fluid
• Viscosity increases with– increased hematocrit– constrictions in vessels