Change in Properties of the Glycocalyx Affects the Shear Rate and Stress Distribution on Endothelial Cells

[+] Author and Article Information
Wen Wang

Medical Engineering Division, School of Engineering and Materials Science, Queen Mary,  University of London, London E1 4NS, United Kingdomwen.wang@qmul.ac.uk

J Biomech Eng 129(3), 324-329 (Nov 04, 2006) (6 pages) doi:10.1115/1.2720909 History: Received May 04, 2006; Revised November 04, 2006

The endothelial glycocalyx mediates interactions between the blood flow and the endothelium. This study aims to evaluate, quantitatively, effects of structural change of the glycocalyx on stress distribution and shear rate on endothelial cells. In the study, the endothelial glycocalyx is modeled as a surface layer of fiber matrix and when exposed to laminar shear flow, the matrix deforms. Fluid velocity and stress distribution inside the matrix and on cell membranes are studied based on a binary mixture theory. Parameters, such as the height and porosity of the matrix and the drag coefficient between fluid and matrix fibrils, are based on available data and estimation from experiments. Simple theoretical solutions are achieved for fluid velocity and stress distribution in the surface matrix. Degradation of the matrix, e.g., by enzyme digestion, is represented by reductions in the volume fraction of fibrils, height, and drag coefficient. From a force balance, total stress on endothelial surface remains constant regardless of structural alteration of the glycocalyx. However, the stress that is transmitted to endothelial cells by direct “pulling” of fiber branches of the glycocalyx is reduced significantly. Fluid shear rate at the cell membrane, on the other hand, increases. The study gives quantitative insight into the effect of the structural change of the glycocalyx on the shear rate and pulling stress on the endothelium. Results can be used to interpret experiments on effects of the glycocalyx in shear induced endothelial responses.

Copyright © 2007 by American Society of Mechanical Engineers
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Figure 5

Changes in τ∕τ0 and γ̇∕γ̇0 as the surface matrix is gradually degraded. The x-axis represents increasing degradation state of the surface layer. Solid lines represent the case that degradation results in an increasingly thinner matrix, but the height of the surface layer remains unchanged, ε=0.1R. Dashed lines represent the added effect of reduction in the height of the surface layer, where ε decreases linearly from 0.1R to 0.01R as ϕ increases from 0.5 to 0.9.

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Figure 1

Schematic representation of steady laminar flow in a cylindrical tube lined by a thin fiber matrix surface layer. x‐o‐r is the cylindrical coordinates and x is the distance in the flow direction. R is the radius to the interface of the surface layer. ε is the height of the surface layer. V(r) is the fluid velocity in the cylinder. For the thin surface layer, local Cartesian coordinates are used, where y is in the—r direction. y=0 is the surface of the endothelium and y=ε is the interface between the fluid and glycocalyx.

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Figure 2

Fluid velocity in a vessel lined by a thin surface matrix layer: (a) Velocity profile when ε=0.1R, ϕ=0.9 and α=3.0. The two dashed lines represent limiting cases when ϕ=0 (solid layer) and ϕ=1 (fluid layer). (b) Fluid velocity in the matrix layer. Curves 1, 2, and 3 represent the effect of fluid porosity ϕ, where ε=0.1R, α=3.0, and ϕ increases from 0.5 (curve 1) to 0.7 (curve 2) and 0.9 (curve 3). Curve 4 represents a single change of α from 3.0 to 2.0 in comparison to curve 3. Curve 5 considers a reduction in the height of the matrix layer from ε=0.1R to 0.05R in comparison to curve 4.

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Figure 3

Pulling stress on endothelial surface transmitted by glycocalyx, τ∕τ0 under different values of α and ϕ. During degradation of glycocalyx, α decreases and ϕ increases. For each ϕ value, there are three curves representing three different cases where the change in α is caused by change in the drag coefficient k only (dashed line), change in k and ε with equal contributions (solid line), and change in the height of the glycocalyx ε only (dashed-dotted line).

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Figure 4

Shear rate on endothelial surface γ̇∕γ̇0 under different values of α and ϕ. Degradation of glycocalyx results in decrease in α and increase in ϕ. For each ϕ value, there are three curves representing three different cases where the change in α is due to change in the drag coefficient k only (dashed line), change in k and ε with equal contributions (solid line), and change in the height of the glycocalyx ε only (dashed-dotted line).




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