A two-layer model for studying the effect of plasma layer on the delivery of oxygen to tissue using a finite element method

Abstract A mathematical model is described for the transport of oxygen in the systemic capillaries and the surrounding tissue. The model takes into account the molecular diffusion, the convective effect of the blood, the nonlinear effects of oxyhaemoglobin, and the consumption of oxygen in the metabolic process. A two-layer model for the blood consisting of a core of erythrocytes surrounded by a cell-free plasma layer has been considered. A finite element formulation has been given to solve the resulting nonlinear convective-diffusion equations with the physiologically relevant boundary conditions. A fixed point iterative technique is used for the nonlinear terms. It is found that PO 2 (partial pressure of oxygen) in the tissue increases as the core-to-capillary diameter ratio increases. The tissue PO 2 is found to be lower with a heterogeneous model in comparison with a homogeneous model, and thus the analysis shows that the plasma layer obstructs the transport of oxygen from the blood to the tissue. The effect of capillary diameters and core radii on the delivery of oxygen to tissue has also been examined.