Forces on a wall-bound leukocyte due to flowing red blood cells

As part of the inflammation response, white blood cells (leukocytes) bind nearly statically to blood vessel walls before they transmigrate through the endothelium and exit the vessel. The inter-cellular interactions between the wall-adhered leukocyte and flowing red blood cells (erythrocytes) play a critical role in this process. We present a quantitative investigation of the forces exerted on a leukocyte at this stationary stage. The simulation tool is based on a fast O(NlogN) boundary integral formulation, which permits the red cells to be realistically flexible and to approach to small separation distances. The red blood cells are modeled as elastic shell membranes enclosing Newtonian fluid with a larger viscosity than the Newtonian plasma outside of them. Membrane inertia is taken to be negligible, so motion matches fluid velocity. They allow for a finite deformation with strong resistance to surface dilatation and relatively small but finite resistance to bending. The no-slip condition is applied both on the leukocyte and the vessel walls. The tube diameters for all cases are less than 20 microns. We will show that at these scales the cellular character of blood significantly affects the forces that the leukocyte experiences. For a tube hematocrit of 25% and a spherical protrusion with a diameter 0.75 that of the tube, the average forces are increased by about 40%, and the local forces by more than two folds relative to forces from an effective-viscosity-homogenized blood. For constant pressure gradients along the tube, the wall-bound leukocyte could cause blockage in that vessel; this cannot be addressed with a homogeneous model. Different contact angles for the leukocyte as well as different mechanical properties for the erythrocytes are examined. The effects of flow conditions as well as the vessel geometry is also considered. It is found that at the scales comparable to the size of the cells, a homogeneous model of blood will result in large errors when calculating the forces on a wall-bound leukocyte. Also, stiffer models for red cells such as rigid or rubber discs, overpredict these forces