Nonequilibrium kinetics; Molecular diffusion; Facilitated diffusion; Chemical kinetics; Metabolic consumption
A mathematical model has been formulated to analyze the effect of nonequilibrium kinetics on oxygen delivery to tissue. The model takes into account molecular diffusion, facilitated diffusion in the capillary blood, convection, chemical kinetics of O2 with hemoglobin, and the rate of metabolic consumption. A line iterative technique is described to solve numerically the resulting coupled system of nonlinear partial differential equations with physiologically relevant boundary and entrance conditions. With nonequilibrium kinetics the end-capillary PO2 is found to be lower than that in the venous blood. The effect is more pronounced during hypoxia and anemia.
It is found that the tissue PO2 at the lethal corner decreases with the decrease in blood velocity, arterial PO2, hemoglobin concentration, P50, and increase in COHb concentration or metabolic rate, while the difference between end-capillary PO2 and venous PO2 increases, which reflects the effect of nonequilibrium kinetics on the delivery of O2 to tissue. Thus, the consideration of venous PO2 as an indicator of tissue PO2 in clinical and experimental studies may be questionable.