A Simplified Model of the Oxygen Supply Function of Capillary Blood Flow

Abstract

An analytic model of the role of capillary blood flow in supplying oxygen to tissue has been developed. This model is less complicated than previously used models, yet may be more realistic. The fundamental point of departure here is that consideration of the radial concentration gradients in the capillary is avoided by assuming the capillary to be “well-stirred”. The source-sink role of the erythrocyte with respect to oxygen is retained in a distributed sense. The inhomogeneity of blood on the scale of the capillary as well as the phenomenon of bolus flow justify this approximation. A closed form solution to the resulting equations is readily obtained and compares favorably with the results of computer based computations of axial oxygen pressure profiles. This model is therefore expected to be of significant value in further work.