Parametric analysis of the relationship between end-capillary and mean tissue PO₂ as predicted by a mathematical model

An increase of the partial pressure of oxygen in venules towards larger vessels has been observed experimentally, but the mechanism of this phenomenon has not been established. The present study considers a simple mathematical model of oxygen transport from a capillary to the surrounding tissue cylinder and analyses the conditions under which the end-capillary partial pressure of oxygen is lower that the mean tissue pressure. Under these conditions oxygen would diffuse into the venules since they are surrounded by the tissue with a higher partial pressure of oxygen. Cerebral circulation is chosen for these calculations and conditions of normoxia, hypoxic hypoxia, carbon monoxide hypoxia, anemia, and polycythemia are simulated. The tissue metabolic rate is also varied. It is found that under most conditions the relationship between the end-capillary and mean tissue partial pressures of oxygen can be reversed when one of the parameters is varied within its physiological range, i.e. the difference between these variables could be either positive or negative depending on the value of the parameters. Therefore, under many realistic conditions this mechanism would contribute to an increase of the partial pressure of oxygen in the venules. This conclusion should hold for a more realistic geometrical model of capillary network, but the relationships between the end-capillary and mean tissue partial pressures of oxygen, in addition to their dependence on the parameters considered in this study, would likely be dependent on the spatial location within the network.