Annals of Biomedical Engineering

, Volume 34, Issue 7, pp 1119–1128 | Cite as

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

  • Nanfeng Sun
  • Nigel B. Wood
  • Alun D. Hughes
  • Simon A. M. Thom
  • X. Yun Xu


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.


LDL transport Oxygen transport Lipid accumulation Hypoxia Atherosclerosis Wall stress stress 


Principal symbols


concentration, mol m−3


diffiusivity, m2 s−1


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


transmural velocity across the endothelium, m s−1


solute lag coefficient


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


pressure, Pa


permeability, m s−1


velocity of blood flow, m s−1


Dacian permeability, m2


Pa s


density, kg m−3


osmotic reflection cofficient


solvent reflection coefficient


wall shear stress, Pa



blood lumen


arterial wall


low density lipoprotein





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


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Copyright information

© Biomedical Engineering Society 2006

Authors and Affiliations

  • Nanfeng Sun
    • 1
  • Nigel B. Wood
    • 1
  • Alun D. Hughes
    • 2
  • Simon A. M. Thom
    • 2
  • X. Yun Xu
    • 1
  1. 1.Department of Chemical EngineeringImperial College LondonLondonUnited Kingdom
  2. 2.National Heart and Lung Institute, International Centre for Circulatory HealthImperial College LondonLondonUnited Kingdom

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