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Models of Flow-Induced Loading on Blood Cells in Laminar and Turbulent Flow, with Application to Cardiovascular Device Flow

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Abstract

Viscous shear stress and Reynolds stress are often used to predict hemolysis and thrombosis due to flow-induced stress on blood elements in cardiovascular devices. These macroscopic stresses are distinct from the true stress on an individual cell, which is determined by the local microscale flow field. In this paper the flow-induced stress on blood cells is calculated for laminar and turbulent flow, using simplified models for cells and for turbulent eddies. The model is applied to estimate shear stress on red blood cells in flow through a prosthetic heart valve, using the energy spectral density measured by Liu et al. [J. Biomech. Eng. 122:118–124, 2000]. Results show that in laminar flow, the maximum stress on a cell is approximately equal to the macroscopic viscous shear stress. In turbulent flow through a prosthetic heart valve, the estimated root mean square of flow-induced stress on a cell is at least an order of magnitude less than the Reynolds stress. The results support the hypothesis that smaller turbulent eddies cause higher stress on cells. However, the stress due to an eddy depends on the velocity scale of the eddy as well as its length scale. For the heart valve flow investigated, turbulence contributes to flow-induced stress on cells almost equally across a broad range of the frequency spectrum. The model suggests that Reynolds stress alone is not an adequate predictor of cell damage in turbulent flow, and highlights the importance of the energy spectral density.

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Abbreviations

A,B :

functions of f

a :

cell radius

E :

energy spectral density

f :

frequency

K :

ratio of stress oscillation amplitude to velocity oscillation amplitude

L :

length scale

m :

mass

p :

pressure

r :

radial coordinate

Re :

Reynolds number

t :

time

u :

fluid velocity

\({\bar{u}}\) :

mean fluid velocity

u′:

fluid velocity fluctuation

v :

cell velocity

v′:

cell velocity relative to freestream

x i :

Cartesian coordinate

α:

phase angle

\({\dot{\gamma}}\) :

shear rate

η:

Kolmogorov length scale

θ:

azimuthal coordinate

μ:

dynamic viscosity

ρ:

density

σ:

stress

φ:

polar coordinate

0:

oscillation amplitude or characteristic scale

c:

cell

p:

plasma

rms:

root mean square

R:

Reynolds (stress)

v:

viscous (stress)

∞:

freestream

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Acknowledgments

Patrick N. Dooley gratefully acknowledges the support of the Irish Research Council for Science, Engineering and Technology, funded by the National Development Plan.

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Authors and Affiliations

  1. National Centre for Biomedical Engineering Science and Department of Mechanical and Biomedical Engineering, National University of Ireland, Galway, Ireland

    Nathan J. Quinlan & Patrick N. Dooley

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  1. Nathan J. Quinlan
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Correspondence to Nathan J. Quinlan.

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Quinlan, N.J., Dooley, P.N. Models of Flow-Induced Loading on Blood Cells in Laminar and Turbulent Flow, with Application to Cardiovascular Device Flow. Ann Biomed Eng 35, 1347–1356 (2007). https://doi.org/10.1007/s10439-007-9308-8

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