hemodynamics of the vasculature. objectives: distribution of blood volume, flow, pressure, vessel...
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Hemodynamics of the Vasculature
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OBJECTIVES:
• Distribution of blood volume, flow, pressure, vessel resistance throughout the circulatory system.
• Discuss Poiseuille's Law and the effects of radius, length, viscosity and resistance on blood flow.
• Limitations of applying classical hemodynamics to blood.
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Flow = Pressure Difference Resistance
(Ohm’s Law)
HEMODYNAMICS
The Physical properties of blood, blood vessels and the heart and their interactions
Consists of : Pressure = Mean Arterial Pressure (MAP) Flow = Cardiac Output (CO) Resistance = Total peripheral resistance (TPR)
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Effect of Pressure Difference on Blood Flow
Flow ╡ P
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Q= 10 ml/s Q= 5 ml/s
Flow is inversely proportional to vessel length (L)
Q ╡ 1/L
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Flow is dependent
on 4th power of the
radius (r4)
Q= 10 ml/sQ= 160 ml/s
Q ╡ r4
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Effect of Radius on Flow
Q ╡ r4
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Flow is Inversely Proportional to Viscosity
Q ╡ ή
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Poiseuille’s Law
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Poiseuille’s Law - Assumptions
• Flow is steady (constant)– The pump (heart) is pulsatile
– Arterial vessels dampen changes, but not steady
• Flow is laminar– Generally true except at bifurcations
• Fluid is Newtonian– Newtonian fluid is homogeneous, fixed viscosity
– Is suspension, non-homogeneous
– Viscosity increases with increasing hematocrit
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Poiseuille’s Law
R = 8 ή L π r4
Q = ΔP/R
R = ΔP/Q
Q = ΔP π r4
ή L 8
Where:R = Resistanceή = Viscosity of BloodL = length of blood vesselR4 = radius of blood vessel raised to the 4th power
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Effect of the diameter of the blood vessel on the velocity of blood flow .
Downloaded from: StudentConsult (on 9 March 2007 10:18 PM)
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Cardiovascular Dynamics
Simulation based on 3D noninvasive imaging
Based on contrast-enhanced magnetic resonance angiogram of the abdominal aorta
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Coarctation of the Aorta
Significant morbidity (hypertension, aneurysms, stroke) may be attributed to abnormal hemodynamics in the aorta and its branches
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Laminar Flow
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Parabolic velocity profile
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Comparison of laminar flow to turbulent blood flow..
LaminarFlow
TurbulentFlow
Parabolic velocity profile
Axial and Radial Flow
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Laminar Flow- – all points in fluid move parallel to walls of tube– Each layer of blood stays at same distance from
wall– Blood cells forces to center of vessel
Turbulent Flow- – At bifurcations of blood vessels– Pressure drop greater than with laminar (square)– Makes heart work harder– Blood clots and thrombi much more likely to
develop
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Effect of turbulence on pressure-flow relationship
Turbulence decreases flow
at any given perfusion pressure
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Pressure-Flow Relationship
Reynolds's Number
Dimensionless number,
relates inertial forces to
viscous forcesReynolds number above 2000 associated with turbulent flow
Reynold’s Number = density * diameter * mean velocity
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Figure 4-4 Effect of the diameter of the blood vessel on the velocity of blood flow.
Downloaded from: StudentConsult (on 9 March 2007 10:18 PM)
© 2005 Elsevier
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Systemic Circulation-
Comprised of Parallel and
Series Circuits
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Parallel and Series Circuits
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Arrangements of blood vessels in series and in parallel.
Arrows show direction of blood flow. R=Resistance
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Figure 4-9 Systemic arterial pressure during the cardiac cycle. Systolic pressure is the highest pressure measured during systole. Diastolic pressure is the lowest pressure measured during diastole. Pulse pressure is the difference between systolic pressure and diastolic pressure. (See the text for a discussion of mean arterial pressure.)
Downloaded from: StudentConsult (on 9 March 2007 10:18 PM)
© 2005 Elsevier
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Figure 4-1 A schematic diagram showing the circuitry of the cardiovascular system. The arrows show the direction of blood flow. Percentages represent the percent (%) of cardiac output. See the text for an explanation of the circled numbers.
Downloaded from: StudentConsult (on 9 March 2007 10:18 PM)
© 2005 Elsevier
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Law of LaPlace
Vessels are “built to withstand the wall tensions they normally “see”
If intravascular pressure increases will increase vessel wall tension (T)
In response, vascular smooth muscle contracts and T returns to normal
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Law of LaPlace
T = (∆P*r) / µm
Where T = tension in the vessel wall ∆P = Transmural pressure r = radius of the vessel
µm = wall thickness
May explain critical closing pressure
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Law of LaPlace
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Law of LaPlace- Relevance• For given BP, increasing the radius of the vessel leads to
a increase in tension. • Arteries must have thicker walls than veins because they
carry much higher BP. • Capillaries also carry significant BP, but unlike arteries,
capillary walls are thin. Small size leads to reduced level of tension so thick walls not needed.
• Conclusions: Properties of this relationship helps us understand the variable thickness of arteries, veins, and capillaries.
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LaPlace’s Law Explains …
• Aneurysms
• Blood vessel distensibility
• Effects of ventricular dilatation on contraction
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End of lecture