A Polygonal Approximation for Unsteady State Diffusion of Oxygen into Hemoglobin Solutions

Abstract

Several authors have grappled with the problem of developing methods for conveniently calculating the rate of oxygen transfer into a film of whole blood. The problem is very difficult because blood is a heterogeneous fluid and also the hemoglobin-oxygen reaction is so complex. In order to obtain manageable analytical equations one is forced to assume that blood is a homogeneous fluid and that the saturation of hemoglobin is determined by equilibrium with the local dissolved oxygen concentration. One might question whether the latter assumption is valid, especially in situations where the blood film is exposed to a new gas environment for very short periods of time as in the disc oxygenator. Even if changes in oxygen concentration are occurring slowly enough so that one might assume that hemoglobin is in chemical equilibrium with the local oxygen concentration, there is still a problem of obtaining an approximation for the nonlinear oxygen hemoglobin saturation curve that can be used to generate valid analytical expressions for the unsteady state oxygenation process.