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Turbulent Arterial Flows. Mike Fortin. Definitions and Nomenclature. Pulsatile Flow Stenosis Throat Systole Diastole. 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.

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definitions and nomenclature
Definitions and Nomenclature
  • Pulsatile Flow
  • Stenosis
  • Throat
  • Systole
  • Diastole
  • 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
specific arteries
Specific Arteries
  • Abdominal Aortic
    • Reynolds Number ~ 600 in a normal healthy individual.
    • Can increase to ~ 6000 in the same individual during exercise conditions.
what is in blood
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.
turbulence modeling
Turbulence Modeling
  • What model works the best?
    • Many have been tested.
      • Large Eddy Simulation?
      • Time-averaged Navier-Stokes?
        • Computationally intensive. Not Practical.
problems with modeling
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.
model validation
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
arteries but not veins
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.
turbulence at a bifurcation
Turbulence at a Bifurcation
  • Carotid artery bifurcation
    • Flow is mostly laminar entering the division
    • Separation occurs and turbulence develops

* American Heart Association

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

* Churchill Livingstone INC

stenosis effects on flow
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.
is this bad
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.
how bad is bad
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
  • 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.
  • 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.