The rate of oxygen release and its effect on capillary O2 tension: a mathematical analysis

Abstract

The time required by the red blood cells (RBC) to release the O2 needed by the tissues may be rate-limiting under conditions of reduced O2 supply (DO2). A time-dependent mathematical model of capillary O2 transport is developed to explore the effect of RBC deoxygenation kinetics on the intracapillary plasma PO2. The tissue capillaries are represented by a series of perfectly mixed compartments. In each compartment O2 is removed by the tissues as a chemical reaction takes place between O2 and oxyhemoglobin (HbO2). A system of differential equations is formulated to monitor changes in the intracapillary concentration of HbO2 and plasma O2. These equations allow for changes in blood flow, arterial oxygenation, capillary transit time, rate of O2 uptake, hemoglobin concentration and the position of the oxyhemoglobin dissociation curve. The predicted capillary PO2 for conditions of normal O2 supply is less than the PO2 calculated assuming an instantaneous rate of RBC deoxygenation. This difference in plasma PO2 is not present in the venous end of the capillary, since at this point oxyhemoglobin and plasma O2 have sufficient time to re-establish equilibrium. The discrepancy in PO2 profiles is magnified by anemia, [( Hemoglobin] = 5 g/dl), and hypoxemia, (PaO2 = 25 Torr). For these conditions of severe DO2 reduction, the end-capillary PO2 is significantly less than the venous PO2. These results suggest that (1) the kinetics of RBC deoxygenation can play an important role in the delivery of O2 to the tissues, and (2) the venous PO2 is not always an accurate measure of the end capillary PO2.