Modelling of oxygen transport in systemic circulation in a hyperbaric environment.

A mathematical model is developed for analysing the transport of oxygen in the systemic capillaries and surrounding tissue in a hyperbaric environment. The governing equation in the capillary describes the transport due to molecular diffusion (radial as well as axial) and the convective effect of the blood. The non-linear oxygen dissociation curve is represented by a linear function simulating the conditions of a hyperbaric environment. The corresponding equation in the tissue region is based on the transport of oxygen due to radial as well as axial diffusion and the zero order metabolic consumption rate. The equations in both the regions are connected through the interface conditions. An analytical solution of the resulting system of elliptic partial differential equations with the physiologically relevant boundary conditions is obtained by the method of eigenfunction expansion. It is found that the amount of oxygen decreases from the core of the capillary to the periphery of the tissue. It is shown that significant radial diffusion of oxygen takes place in the initial part of the tissue close to the arterial end. The accumulation of oxygen in the tissue has been examined in terms of various non-dimensional parameters. The physiological relevance of these parameters in determining the degree of accumulation of O2 in the tissue in a hyperbaric environment is discussed in the light of previous experimental studies.