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 PhysiologyHemodynamics
Vessels of the Circulatory System
Endothelium
Elastic tissue
Smooth Muscle
Fibrous Tissue
Arteriole30 µm
Capillary8 µm
Venule20 µm
6 µm 0.5 µm 1 µm
Diameter
Wall thickness
Aorta25 mm
Artery4 mm
Vein5 mm
Vena Cava30 mm
2 mm 1 mm 0.5 mm 1.5 mm
Bioengineering 6000 CV PhysiologyHemodynamics
Blood Distribution• Velocities/Flows
– Aorta: 30-50 cm/s– Capillaries: 0-1 cm/s
or 5.5 hours/mm3 • Blood mass: 8% of
body mass• Volumes (percent
of total blood volume)– Systemic: 83%
• Arteries: 11%• Capillaries: 5%• Veins: 67%
– Pulmonary: 12%– Heart: 5%
Aorta Arteries Arterioles Capillaries Venules Veins Venae Cava
VelocityCross-sectional area
Pressure
Percent of blood volume
Velocity
Cross-sectional area
Pressure
Percent of blood volume
Bioengineering 6000 CV PhysiologyHemodynamics
Hemodynamics Basics
• "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
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
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
• Viscosity decreases with– increased flow velocity– vessel diameter below 300 µm
Poor formula for viscosity in small vessels
Hematocrit [%]
Visc
osity
(wat
er=1
)
10
2
20 30 40 50 60 70
4
6
8
10
Water
Plasma
Blood
Bioengineering 6000 CV PhysiologyHemodynamics
Factors that Affect Viscosity• Flow rate: as flow decreases, viscosity increases up to
10-fold. Mechanism: RBCs adhering to each other, and the vessel walls.
• RBCs stick at constrictions, increase viscosity.• Concentration, distribution, shape, and rigidity of the
suspended particles (e.g., RBCs drift to the center so velocity profile flattens from ideal parabolic)
• Fahraeus-Lindqvist effect: reduced η when RBCs line up in small vessels (< 300 µm).
• In very small vessels (< 20 µm), η increases as RBCs fill the capillaries, “tractor tread” motion
• Temperature, blood pressure, presence of anticoagulants,• Measurement conditions: higher in vitro than in vivo.• History (pulsatile flow)
Q̇ = Q̇o
v = vo
Ptot
= Po
= Pdo
+ Plo
Pd
=12⇢v2
o
= Pdo
Pl
= Plo
Bioengineering 6000 CV PhysiologyHemodynamics
Velocity and Pressure
• Example: Aortic stenosis– increased velocity– decreased lateral
pressure– reduced coronary
flow– coronary ischemia
Q̇ = Q̇o
v = vo
Ptot
= Po
Pd
= Pdo
Pl
= Plo
Q̇ = Q̇o
v = kvo
Ptot
= Po
= Pd
+ Pl
Pd
=12⇢(kv
o
)2
= k2Pdo
Pl
= Ptot
� Pd
< Plo
Bioengineering 6000 CV PhysiologyHemodynamics
Aortic Stenosis
Left ventricle
Coronary artery
Coronary artery
Pv
Pavo
Pao (lower than normal)
• Pressure losses– kinetic energy
conversion– energy loss (friction)
Bioengineering 6000 CV PhysiologyHemodynamics
Resistance of the Circulatory System
• Resistance high where pressure drops
• Arterioles have highest resistance
• Paradox?– arterioles have more total
area than arteries– vessels with larger area
have smaller resistance– but arterioles have larger
resistance than arteries?Aorta Arteries Arterioles Capillaries Venules Veins Venae
Cava
VelocityCross-sectional areaPressurePercent of blood volume
VelocityCross-sectional area
Pressure
An, rn, Rn
Rt
Rt = 4Rw!
Aw = 4An
rw = 2rn
1Rt
=4X
1=1
1Rn
=4
Rn
Rw =k
r4w
=k
(2rn)4=
k
16r4n
=14⇤ k
4r4n
=Rt
4
Bioengineering 6000 CV PhysiologyHemodynamics
Resistance-Area Paradox
• Net flow must be constant
• One vessel splitting to four increases total resistance!
Aw, rw, Rw
R =8⌘l
⇡r4=
k
r4
Rt =Rn
4=
k
4r4n
Rw = Rt
At = 16An = 4Aw
Bioengineering 6000 CV PhysiologyHemodynamics
Resistance Break Even Point
• Break-even point at 16 to 1 (for Rw=Rt).
• Capillaries have more than 16:1 ratio
Aw, rw, Rw
An, rn, Rn
Rt
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 vesselsVe
loci
ty P
rofil
es