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.

Red blood cell phase separation in symmetric and asymmetric microchannel networks: effect of capillary dilation and inflow velocity

“…Furthermore, the endothelial surface layer (ESL i.e. macromolecular layer lining the endothelial surface) was found to play an important role on blood flow resistance and its dependence to the flow rates515253. In our microvascular models we were not able to model the ESL, however some promising results have been recently shown using single brush-coated micro-channels as in vitro ESL model54.…”

Blood viscosity in microvessels: Experiment and theory

“…In such cases, the forces driving cells away from the wall may be highly sensitive to the shape of the RBC in regions where it is closest to the wall. The theory for generation of lift forces on deformable particles close to solid boundaries according to lubrication theory [53] may be helpful in obtaining insight into the relationship between the deformation of RBCs that approach the walls and the resulting generation of lift forces [20]. …”

“…Beaucourt et al [3] modeled the interactions of rigid and deformable vesicles with a compressible but impermeable wall substrate, representing the ESL. Conversely, Hariprasad and Secomb [20] considered the layer to be permeable but of fixed width, and showed that the rate of lateral migration of two-dimensional model RBCs decreased with increasing permeability of the layer.…”

Lateral migration of a spherical capsule near a plane wall in Stokes flow

“…Doddi and Bagchi [13] examined the lateral migration of a capsule in a Poiseuille flow with parallel plate geometry, but again, the effects of two walls in addition to the shear gradient could not be examined separately. Hariprasad and Secomb [14] explored the motion of a two-dimensional viscoelastic particle resembling a capsule in a microchannel with a porous layer representing the glycocalyx. Most recently, Singh et al [15] investigated * yimai@pfsl.mech.tohoku.ac.jp the lateral migration of a capsule near a wall in a parallel-plate Couette flow at small Reynolds number using a front-tracking method.…”