Numerical study of oxygen uptake by layers of hemoglobin solution.

Numerical solutions have been obtained for the equations describing 02 uptake by layers of concentrated hemoglobin solution 0.25, 0.5, 1, 1.6, 2, 3.6, 5, 10, and 20 p thick. The results indicate that the diffusion of oxyhemoglobin has almost no effect on the rate of oxygenation of the 0.25 p layer, but its influence increases with increasing layer thickness, so that it shortens the time required to reach 50 % saturation in the 1.6 p layer by 23 % and in the 5~ layer by 34 %. For the 1.6 ,u layer, which might be considered a model red blood cell, the results suggest that the rate at which 0~ reacts with hemoglobin is of primary importance early in the uptake process, but that later the diffusion of 0~ into the deeper parts of the layer becomes rate-limiting. Facilitated diffusion Oxygen diffusion Hemoglobin Oxyhemoglobin The partial differential equations that describe the diffusion and chemical reaction of O2 in Hb solution are nonlinear and thus not solvable by analytical methods. For this reason much of the theoretical work done in this area has involved approximate solutions to the diffusion equations or solutions to approximations of the diffusion equations (see ROUGHTON (1959) for a thorough review). Most of this work is due to Roughton, Forster, and their associates, who have been extremely inventive in wresting important insights from seemingly intractable equations. The electronic digital computer has made it practical to solve the diffusion equations numerically. The advantages of this approach are that it can deal with the nonlinearities present in the equations and theoretically solutions may be had with whatever accuracy is desired. Accepted for publication 20 May 1970. 1 Reprint requests: McCollum-Pratt Institute, The Johns Hopkins University, Baltimore, Maryland 21218, U.S.A.