An analytical model for axial diffusion in the Krogh cylinder.

Abstract

The tissue level distribution of oxygen (O2) in the hemoglobinless perfused heart has been measured under controlled conditions with Whalen PO2 microelectrodes (Schubert, Whalen, and Nair, 19 78). In an attempt to understand tissue level details of O2 transport we compared that PO2 distribution to those predicted by mathmatical models. Models incorporating only radial transport in the tissue compared poorly with the measured histograms. Blum’s (1960) model with radial and axial diffusion was found to be in error (Schubert, 1976), and a correct solution had not been published. A unique analytic model was derived by modifying the radial transport phenomena so that the axial diffusional transport could be included. This model displays trends seen in the experimental data. Unfortunately the best match was obtained by increasing the value of the axial diffusion coefficient, D, considerably beyond the value accepted in the literature. This led to questions about the appropriateness of the radial transport assumptions which could be answered only be seeking the correct solution to the problem originally posed by Blum.