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.

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) Flow = Pressure Difference Resistance (Ohm’s Law)

Effect of Pressure Difference on Blood Flow Flow ╡ P

Flow is inversely proportional to vessel length (L) Q= 10 ml/s Q= 5 ml/s Q ╡ 1/L

Flow is dependent on 4th power of the radius (r4) Q= 10 ml/s Q= 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

R = 8 ή L π r4 Poiseuille’s Law Q = ΔP π r4 ή L 8 Q = ΔP/R R = ΔP/Q Where: R = Resistance ή = Viscosity of Blood L = length of blood vessel R4 = radius of blood vessel raised to the 4th power R = ΔP/Q

Effect of the diameter of the blood vessel on the velocity of blood flow. Downloaded from: StudentConsult (on 9 March 2007 10:18 PM)

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.. Parabolic velocity profile Axial and Radial Flow Turbulent Flow The length of the arrows shows the approximate velocity of blood flow. Laminar blood flow has a parabolic profile, with velocity lowest at the vessel wall and highest in the center of the stream Comparison of laminar flow to turbulent blood flow..

Laminar Flow- Turbulent 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 forces Reynolds 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. Downloaded from: StudentConsult (on 9 March 2007 10:18 PM) © 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 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

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

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