A two-layer model for studying the effect of plasma layer on the delivery of oxygen to tissue using a finite element method
The authors present a mathematical model for the transport of oxygen in the system capillaries and in the surrounding tissue. The model can find applications when one studies 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 is proposed. The resulting nonlinear convective diffusion equations with the physiologically relevant boundary conditions are solved by a finite element methods, and a fixed point iterative technique is used to tackle the nonlinear terms. The authors report that partial pressure of oxygen in the tissue increases when the core-to-capillary diameter ratio increases. This conclusion follows from the fact that the plasma layer obstructs the transport of oxygen from the blood to the tissue. The effects of capillary diameters and core radii on the delivery of oxygen to tissue are also examined.
nonlinear convective diffusion equations
scientific article; zbMATH DE number 1062739