Numerical simulation of sickle cell blood flow in the transverse arteriole-capillary microvasculature

A numerical simulation of normal and sickle cell blood flow through the transverse arteriolecapillary microcirculation has been formulated and used to understand some of the dominant mechanisms involved in the onset of vascular stasis resulting from sickle cell disease. The transverse arteriole - capillary network is described by the Strahler's method of network branching and the oxygen and blood transport is modeled in the capillaries by a Krogh cylinder analysis utilizing Lighthill's lubrication theory as developed by Berger and King. In the arterioles, Poiseuille's law is used to represent blood flow characteristics. By applying this flow model and utilizing volumetric blood flow continuity at each network bifurcation, a nonlinear system of equations is developed. This system of equations is solved iteratively using a steepest descent algorithm coupled with a Newton solver. Ten different networks are generated and flow results are calculated under three different blood types and conditions, normal blood, sickle cell blood without precapillary oxygen loss, and sickle cell blood with precapillary oxygen loss. Total volumetric blood flow through the network is greater in the two sickle cell blood simulations than in the normal blood simulations. Conversely, due to the anemia related to sickle cell disease, the actual red blood cell flux is greater in the normal blood case even though the red blood cell velocity is smaller. Differences are observed in all cases when blood flow is compared to what would be expected if simple Poiseuille flow was the dominant mechanism. Finally the percentage of capillary blockage in the network is shown to increase dramatically with decreasing pressure drop across the network in the two sickle cell cases while there is no blockage when normal blood flows through the simulated networks. In the case of sickle cell disease, it is concluded that without any vasomotor dilation response to decreasing oxygen concentrations in the blood, capillary blockage will occur in the microvasculature even at normal pressure drops across the transverse arteriole - capillary networks.