Microvascular Cell Depletion Model

Abstract

Blood flow in arterioles is dominated by the behaviour of red blood cells (RBCs) carried by plasma through repeatedly bifurcating networks. A cell depletion model is presented that closely couples the distribution of haematocrit, shear rate and non-Newtonian viscosity to account for the migration and aggregation of RBCs. A transport equation is solved for the haematocrit, and the Quemada model is used to evaluate the viscosity, such that the viscosity tends to the plasma viscosity as the haematocrit tends to zero. This model is applied to a set of single arteriole bifurcations, and the distribution of haematocrit, H, and the associated cell depletion layer thickness, δ , are determined for a range of side branch diameters and angles. Variation in the diameter is found to have a very significant effect on H and δ , whilst the angle has a negligible effect. As the side branch diameter varies between 100 and 20% of the main branch diameter, the cell depletion layer thickness at the outlet increases from approximately 25% to almost 100% of the vessel radius. Effectively, at small side branch diameters, relatively few RBCs are drawn into the side branch. In the main branch, the haematocrit distribution maintains a very blunt profile with a relatively thin cell depletion layer that varies little with changes to the geometry of the side branch.