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Turbulent Arterial Flows

Definitions and Nomenclature. Pulsatile FlowStenosisThroatSystoleDiastole. Scale. Diameter of an ArteryAorta ~ 25 mmCapillary ~ 8

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Turbulent Arterial Flows

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Turbulent arterial flows l.jpg

Turbulent Arterial Flows

Mike Fortin

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Definitions and Nomenclature

  • Pulsatile Flow

  • Stenosis

  • Throat

  • Systole

  • Diastole

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  • 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

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Specific Arteries

  • Abdominal Aortic

    • Reynolds Number ~ 600 in a normal healthy individual.

    • Can increase to ~ 6000 in the same individual during exercise conditions.

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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.

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Turbulence Modeling

  • What model works the best?

    • Many have been tested.

      • Large Eddy Simulation?

      • Time-averaged Navier-Stokes?

        • Computationally intensive. Not Practical.

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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.

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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

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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.

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Turbulence at a Bifurcation

  • Carotid artery bifurcation

    • Flow is mostly laminar entering the division

    • Separation occurs and turbulence develops

* American Heart Association

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  • Flow separation occurs at low Reynolds Numbers

  • With a 70% stenosis, critical upstream Reynolds Number is only 300.

* Churchill Livingstone INC

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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.

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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.

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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

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  • 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.

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  • 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.