Diffusion and convection in the capillaries in sickle-cell disease.

A model has been developed which couples the transport of oxygen in the capillaries to the motion of sickle cells. A Krogh model is used to model the oxygen transport, while the motion of the HbSS red cells is assumed to be determined by lubrication theory. Reversibly sickled cells are considered, with an assumed dependence of their compliance, or deformability, on the PO2 level. The model predicts that when the pressure gradient driving the cells in the capillary has normal values the cells move faster than normal cells and exit the capillary at relatively high PO2 levels, higher than for normal cells under the same conditions. This is due primarily to the much lower hematocrit typical of sickle-cell disease. Under conditions of reduced driving pressure gradient the situation changes, the cell velocity falls proportionally by an even greater amount, as do the PO2 levels, conditions conducive to the development of the deleterious effects associated with sickling. These results suggest that whereas the compensatory mechanisms in sickle-cell disease are adequate under normal conditions, they may fail under conditions which reduce the pressure gradient across the capillaries, such as vasoconstriction of the arterioles.