Axial Oxygen Diffusion in the Krogh Model

Abstract

The cylindrical steady-state model developed by Krogh with Erlang has served as the basis of understanding oxygen supply in living tissue for over eighty years. Due to its simplicity and agreement with some observations, it has been extensively used and successfully extended to new fields, especially for situations such as drug diffusion, water transport, and ice formation in tissues. However, the applicability of the model to make even a qualitative prediction of the oxygen level of specific volumes of the tissue is still controversial. We recently have developed an approximate analytical solution of a steady-state diffusion equation for a Krogh cylinder, including oxygen concentration in the capillary. This model was used to explain our previous experimental data on myocardial pO₂ in isolated perfused rat hearts measured by EPR oximetry. An acceptable agreement with the experimental data was obtained by assuming that a known limitation of the existing EPR methods—a tendency to over-weight low pO₂ values—had resulted in an under-estimate of the pO₂. These results are consistent with recent results of others, which stress the importance of taking into account the details of what is measured by various methods.