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Fluid-Wall Modelling of Mass Transfer in an Axisymmetric Stenosis: Effects of Shear-Dependent Transport Properties

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Abstract

Mechanical forces, such as low wall shear stress (WSS), are implicated in endothelial dysfunction and atherogenesis. The accumulation of low density lipoprotein (LDL) and hypoxia are also considered as main contributing factors in the development of atherosclerosis. The objective of this study was to investigate the influences of WSS on arterial mass transport by modelling the flow of blood and solute transport in the lumen and arterial wall. The Navier-Stokes equations and Darcy’s Law were used to describe the fluid dynamics of the blood in the lumen and wall respectively. Convection-diffusion-reaction equations were used to model LDL and oxygen transport. The coupling of fluid dynamics and solute dynamics at the endothelium was achieved by the Kedem-Katchalsky equations. A shear-dependent hydraulic conductivity relation extracted from experimental data in the literature was employed for the transport of LDL and a shear-dependent permeability was used for oxygen. The integrated fluid-wall model was implemented in Comsol Multiphysics 3.2 and applied to an axisymmetric stenosis. The results showed elevated LDL concentration and reduced oxygen concentration in the subendothelial layer of the arterial wall in areas where WSS is low, suggesting that low WSS might be responsible for lipid accumulation and hypoxia in the arterial wall.

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Abbreviations

c :

concentration, mol m−3

D :

diffiusivity, m2 s−1

J s :

solute flux across the endothelium, mol s−1 m−2

J v :

transmural velocity across the endothelium, m s−1

K :

solute lag coefficient

L p :

hydraulic conductivity of the endothelium, m s−1 Pa−1

p :

pressure, Pa

P :

permeability, m s−1

u :

velocity of blood flow, m s−1

κ:

Dacian permeability, m2

μ:

Pa s

ρ:

density, kg m−3

σ d :

osmotic reflection cofficient

σ f :

solvent reflection coefficient

τ w :

wall shear stress, Pa

l :

blood lumen

w :

arterial wall

LDL :

low density lipoprotein

oxy :

oxygen

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ACKNOWLEDGMENTS

This work was supported by the Leverhulme Trust (F07 058/AA).

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Authors and Affiliations

  1. Department of Chemical Engineering, Imperial College London, South Kensington Campus, London, SW7 2AZ, United Kingdom

    Nanfeng Sun, Nigel B. Wood & X. Yun Xu

  2. National Heart and Lung Institute, International Centre for Circulatory Health, Imperial College London, 59-61 North Wharf Road, Paddington, London, W2 1LA, United Kingdom

    Alun D. Hughes & Simon A. M. Thom

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  1. Nanfeng Sun
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Correspondence to X. Yun Xu.

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Sun, N., Wood, N.B., Hughes, A.D. et al. Fluid-Wall Modelling of Mass Transfer in an Axisymmetric Stenosis: Effects of Shear-Dependent Transport Properties. Ann Biomed Eng 34, 1119–1128 (2006). https://doi.org/10.1007/s10439-006-9144-2

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