1. Hemodynamics of the Vasculature

2. 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.

3. 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)

4. Effect of Pressure Difference on Blood Flow
Flow ╡ P

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

6. Flow is dependent on 4th power of the radius (r4)
Q= 10 ml/s
Q= 160 ml/s
Q ╡ r4

7. Effect of Radius on Flow
Q ╡ r4

9. Flow is Inversely Proportional
to Viscosity
Q ╡ ή

10. Poiseuille’s Law

11. 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

12. 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

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

14. Cardiovascular Dynamics Simulation based on 3D noninvasive imaging
Based on contrast-enhanced magnetic resonance angiogram of the abdominal aorta

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

16. Laminar Flow

17. Parabolic velocity profile

18. 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..

19. 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

20. Effect of turbulence on pressure-flow relationship
Turbulence decreases flow at any given perfusion pressure

21. 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

22. Figure 4-4 Effect of the diameter of the blood vessel on the velocity of blood flow.
Downloaded from: StudentConsult (on 9 March :18 PM)
© 2005 Elsevier

23. Systemic Circulation- Comprised of Parallel and Series Circuits

24. Parallel and Series Circuits

25. Arrangements of blood vessels in series and in parallel.
Arrows show direction of blood flow. R=Resistance

26. 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 :18 PM)
© 2005 Elsevier

27. 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 :18 PM)
© 2005 Elsevier

28. 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

29. 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

30. Law of LaPlace

31. 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.

32. LaPlace’s Law Explains …
Aneurysms
Blood vessel distensibility
Effects of ventricular dilatation on contraction

34. End of lecture