The effect of the endothelial-cell glycocalyx on the motion of red blood cells through capillaries

Abstract

The analysis of the rheology of the blood/capillary system presented here details the complex fluid-structure interactions that arise among blood cells, plasma, and the endothelial-cell glycocalyx. The capillary is modeled as a rigid cylindrical tube lined with a biphasic poroelastic wall layer which approximates the glycocalyx. The blood is approximated as a fluid suspension of tightly fitting deformable cells driven through the tube under a pressure gradient. Using mixture theory, the wall layer is modeled as interacting fluid and solid constituents in which the fluid is assumed to be linearly viscous and the solid is assumed to be linearly elastic. Axisymmetric lubrication theory is applied to the fluid in the gap between the red cell and the glycocalyx. The analysis details the fluid-phase velocity field throughout the wall and lubrication layers and provides the Reynolds equation for the pressure gradient along the length of the cell. The shell equations of equilibrium are employed to describe the mechanics governing the axisymmetric deformation of the red-cell membrane, where it is assumed that shear stress on the surface of the cell is balanced solely by isotropic membrane tension. Making use of the analytic expressions for the Reynolds equation and shear stress distribution on the cell surface, the pressure profile, membrane tension, and red-cell shape are obtained through numerical solution of a reduced system of coupled, nonlinear, ordinary differential equations. Rheological quantities including apparent viscosity and capillary tube hematocrit are presented and compared with in vitro and in vivo experimental data. The analysis predicts that the presence of a 1/2-microm-thick glycocalyx in a 5-microm capillary results in a threefold increase in resistance and a reduction in capillary tube hematocrit of more than 30% compared with the corresponding values in a 5-microm smooth-walled tube. Results are qualitatively consistent with in vivo observations of blood flow in microvascular networks.