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1. Turbulent Arterial Flows Mike Fortin
2. Definitions and Nomenclature Pulsatile Flow
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.
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?
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
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.
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.
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.