Hemodynamics of the Vasculature

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.

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)

Effect of Pressure Difference on Blood Flow

Flow ╡ P

Q= 10 ml/s Q= 5 ml/s

Flow is inversely proportional to vessel length (L)

Q ╡ 1/L

Flow is dependent

on 4th power of the

radius (r4)

Q= 10 ml/sQ= 160 ml/s

Q ╡ r4

Effect of Radius on Flow

Q ╡ r4

Flow is Inversely Proportional to Viscosity

Q ╡ ή

Poiseuille’s Law

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

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

Effect of the diameter of the blood vessel on the velocity of blood flow .

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Cardiovascular Dynamics

Simulation based on 3D noninvasive imaging

Based on contrast-enhanced magnetic resonance angiogram of the abdominal aorta

Coarctation of the Aorta

Significant morbidity (hypertension, aneurysms, stroke) may be attributed to abnormal hemodynamics in the aorta and its branches

Laminar Flow

Parabolic velocity profile

Comparison of laminar flow to turbulent blood flow..

LaminarFlow

TurbulentFlow

Parabolic velocity profile

Axial and Radial Flow

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

Effect of turbulence on pressure-flow relationship

Turbulence decreases flow

at any given perfusion pressure

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

Figure 4-4 Effect of the diameter of the blood vessel on the velocity of blood flow.

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© 2005 Elsevier

Systemic Circulation-

Comprised of Parallel and

Series Circuits

Parallel and Series Circuits

Arrangements of blood vessels in series and in parallel.

Arrows show direction of blood flow. R=Resistance

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.)

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© 2005 Elsevier

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.

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© 2005 Elsevier

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

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

Law of LaPlace

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.

LaPlace’s Law Explains …

• Aneurysms

• Blood vessel distensibility

• Effects of ventricular dilatation on contraction

End of lecture