A simple model for prediction of oxygen transport rates by flowing blood in large capillaries

A simple model has been developed for simulation of oxygen transport to and from blood flowing in conduits of the diameter of arterioles and larger (greater than or equal to 20 microns). The basis is the large capillary model (LCAP) of P.K. Nair, et al. 1989 which has been validated experimentally. Detailed calculations of the oxygen concentration distribution reveal that the dominant resistance to oxygen transport is distributed in the plasma. Relatively little resistance is present within or in the immediate vicinity of the red cells. On the basis of these findings, LCAP was simplified from four simultaneous nonlinear partial differential equations (PDEs) to one PDE by (1) assuming chemical equilibrium within the red blood cells, (2) neglecting intracellular and extracellular boundary layer resistances, and (3) incorporating transport in the cell-free region adjacent to the capillary wall into the boundary conditions. The simplified model is much easier to apply mathematically to new situations. A comparison between LCAP and the simpler model shows that they give virtually the same predictions, and the predictions agree well with experimental measurements. The model is predictive in that all the parameters are determined from the literature or from independent measurements. Thus it should be useful in studies of physiological significance, as well as in design and analysis of extracorporeal blood oxygenators.