Mathematical model of erythrocytes as point-like sources.

A new approach to investigate the effect of pericapillary gradients, caused by the particulate nature of blood, on oxygen partial pressure (pO2) in tissue is presented. The blood erythrocytes are modeled as point-like sources, which makes the system independent of the geometry of the erythrocytes. This model is semi-analytical and is developed to estimate the pO2 far from the erythrocytes. It does so through calculation of the extraction pressure, which accounts for the capillary oxygen drop as compared to homogeneous blood. It is particularly useful to estimate pO2 in regions where the oxygen concentration is low. Simulations have been performed for a cylindrical tissue geometry and parameters are chosen for rat heart muscle. In accordance with the literature, for a fixed total oxygen supply low hematocrit values result in a lower pO2 at the border of the tissue cylinder than high values do. Also a decrease in hematocrit results in higher values for the extraction pressure. Finally, it was found that the effect of the particulate nature of blood is most distinct at low hematocrit values.