A hemodynamic analysis for determining critical hematocrit in transfusions for sickle cell patients

Because of complicated rheological issues related with sickle cell blood, there exists a practical need to rationally determine critical hematocrit in transfusions for sickle cell patients. In this research, two major effects, i.e. oxygen concentration and hematocrit, are considered in a theoretical hydrodynamic model incorporating oxygen transport and lubrication theory. The pressure drop depends on the compliance of red blood cells, which changes with oxygen concentration in sickle red cells. Under the assumption that after transfusion, the upper limit of the local resistance of a capillary should not surpass that in the same capillary of normal blood flow, critical hematocrit values with different exchange percentage rates are determined. The current clinical ceiling value of 35 percent for total hematocrit after the transfusion, for the first time, finds its analytical reasoning through mathematical modeling. Plots of critical hematocrit values versus the transfusion exchange percentage are provided in the paper.