Oxygen delivery from red cells

This paper deals with the theoretical analysis of the unloading of oxygen from a red cell. A scale analysis of the governing transport equations shows that the solutions have a boundary layer structure near the red-cell membrane. The boundary layer is a region of chemical nonequilibrium, and it owes its existence to the fact that the kinetic time scales are shorter than the diffusion time scales in the red cell. The presence of the boundary layer allows an analytical solution to be obtained by the method of matched asymptotic expansions. A very useful result from the analysis is a simple, lumped-parameter description of the oxygen delivery from a red cell. The accuracy of the lumped-parameter description has been verified by comparing its predictions with results obtained by numerical integration of the full equations for a one-dimensional slab. As an application, we calculate minimum oxygen unloading times for red cells.