Motion of red blood cells near microvessel walls: effects of a porous wall layer

Abstract

A two-dimensional model is used to simulate the motion and deformation of a single mammalian red blood cell (RBC) flowing close to the wall of a microvessel, taking into account the effects of a porous endothelial surface layer (ESL) lining the vessel wall. Migration of RBCs away from the wall leads to the formation of a cell-depleted layer near the wall, which has a large effect on the resistance to blood flow in microvessels. The objective is to examine the mechanical factors causing this migration, including the effects of the ESL. The vessel is represented as a straight parallel-sided channel. The RBC is represented as a set of interconnected viscoelastic elements, suspended in plasma, a Newtonian fluid. The ESL is represented as a porous medium, and plasma flow in the layer is computed using the Brinkman approximation. It is shown that an initially circular cell positioned close to the ESL in a shear flow is deformed into an asymmetric shape. This breaking of symmetry leads to migration away from the wall. With increasing hydraulic resistivity of the layer, the rate of lateral migration increases. It is concluded that mechanical interactions of RBCs flowing in microvessels with a porous wall layer may reduce the rate of lateral migration and hence reduce the width of the cell-depleted zone external to the ESL, relative to the cell-depleted zone that would be formed if the interface between the ESL and free-flowing plasma were replaced by an impermeable boundary.