Turbulent Arterial Flows

1. Turbulent Arterial Flows Mike Fortin

2. Definitions and Nomenclature Pulsatile Flow Stenosis Throat Systole Diastole

3. Scale Diameter of an Artery Aorta ~ 25 mm Capillary ~ 8 µm Velocity in an Artery Aorta ~ 0.3-0.5 m/s Capillary ~ 0.00-0.01 m/s Reynolds Numbers 1-4000

4. Specific Arteries Abdominal Aortic Reynolds Number ~ 600 in a normal healthy individual. Can increase to ~ 6000 in the same individual during exercise conditions.

5. What is in Blood? Proteins, lipoproteins, ions, and cells. Red blood cells Red blood cells makeup approximately 40% of blood by volume. Semisolid particles. Increase blood viscosity Cause non-Newtonian behavior in small blood vessels.

6. Turbulence Modeling What model works the best? Many have been tested. Large Eddy Simulation? Time-averaged Navier-Stokes? Computationally intensive. Not Practical.

7. Problems with Modeling Blood is a non-Newtonian fluid in small vessels. In larger vessels, this can be neglected. Arteries are somewhat elastic. Diameter is not constant. Arteries dilate to accommodate for increases in flow. Contraction occurs to control systemic vascular resistance or venous pooling. Many physical attempts at modeling use rigid tubes.

8. Model Validation X-ray contrast angiography Requires injection of radioactive substance Tells percent stenosis, but nothing of flow rate Doppler ultrasound Require an acoustic or optical window Tell velocities within 90% Magnetic resonance imaging Turbulence in a stenosis causes signal loss

9. Arteries, but not Veins? Pulsatile flow exists in arteries. Veins exhibit a fairly constant flow. Blood flow in arteries is coming from the heart. Blood flow in veins is going to the heart. By the time blood gets to the veins, losses have created a fairly steady flow.

10. Turbulence at a Bifurcation Carotid artery bifurcation Flow is mostly laminar entering the division Separation occurs and turbulence develops

11. Stenosis Flow separation occurs at low Reynolds Numbers With a 70% stenosis, critical upstream Reynolds Number is only 300.

12. Stenosis Effects on Flow Diameter of the vessel decreases Typically given in a percent reduction in diameter. Velocity increase is not linear with percent decrease of diameter. It increases as the square. Causes flow separation. Turbulence downstream causes significant flow resistance.

13. Is This Bad? “Most flows are turbulent. Laminar flow is the exception.” The body likes laminar flow. Turbulent flow reduces pressure and causes head loss.

14. How Bad is Bad? Aneurysms Abdominal Aortic ~ 15,000 deaths per year in the US. Stroke Heart Attack Lower-Limb Ischemia Replacement of Blood Vessels Must be the same size

15. Conclusions Medical community Not engineers. Not necessarily content, but have sufficient knowledge to know turbulence is not a good thing. Engineering community One more area that needs to be advanced to the point where a model is reliable enough to predict the laminar-turbulent transition and the turbulent blood flow regime.

16. References Ku, David N. “Blood Flow in Arteries.” Annual Review of Fluid Mechanics. 1997. 29:399-434. Taylor, C.A., Hughes, T.J.R., Zarins, C.K. “Finite Element Modeling of Three Dimensional Pulsatile Flow in the Abdominal Aorta: Relevance to Atherosclerosis. Annals of Biomedical Engineering, 1998. 26:975-987. Yellin, E.L., “Laminar-Turbulent Transition Process in Pulsatile Flow.” Circulation Research, 1966. XIX:791-804. Younis, B.A., Berger, S.A. “ A Turbulence Model for Pulsatile Arterial Flows.” ASME. 2004. 126:578-584.