Finite-element analysis of oxygen transport in the systemic capillaries.

A mathematical model is formulated for the transport of O2 in the systemic capillaries and surrounding tissue. The model takes into account molecular diffusion, the convective effect of the blood, the nonlinear effects of oxyhaemoglobin, and the consumption of O2 in the metabolic process. A finite-element formulation for solving the equations governing the mass transfer in the capillary is described. A fixed-point iterative technique is used to deal with the nonlinearities in the model. The concentration of O2 is found to decrease from the axis of the capillary to the periphery of the tissue. It is shown that, owing to the nonlinear effects of oxyhaemoglobin, the partial pressure of oxygen (PO2) in the capillary and tissue increases. It is also shown that the tissue PO2 increases as (i) the arterial blood PO2 increases, (ii) the Péclet number increases, and (iii) the diffusive flux of O2 from the capillary decreases.