An analytical model for oxygen transport in tissue capillaries in a hyperbaric environment with first order metabolic consumption

A mathematical model for oxygen transport in the systemic capillary and the surrounding tissue is described. The model takes into account the molecular diffusion in both axial and radial directions in the capillary and tissue, the convective effect of the blood, and the saturation of haemoglobin with oxygen in the blood. The first order metabolic consumption rate of O2 in the tissue is considered. The nonlinear O2 dissociation curve (ODC) is approximated by a linear function to simulate the conditions of hyperbaric environment. Its slope is determined by evaluating the derivative of ODC at the arterial PO2. The resulting system of partial differential equations is solved analytically by the method of eigenfunction expansion. It is shown that O2 is transported in the first one-fifth part of the tissue by diffusion (radial and axial), while, in the remaining part of the tissue, radial diffusion is stabilized. The accumulation of O2 in the tissue is found to be larger with the first order metabolic rate in comparison to the zero order metabolic rate.