A theoretical analysis of the relationship between venous blood and mean tissue oxygen pressures

Starting with the Krogh-Erlang equation, and the assumptions necessary for that simple model, an equation for mean tissue oxygen pressure is derived and solved for a number of plausible conditions in order to examine the degree to which venous blood P O 2 approximates the calculated mean tissue value. For normal resting conditions there is a remarkably close agreement between the two values, but there are significant deviations when capillary density, metabolic rate, hemoglobin concentration and cardiac output are altered. The purpose of the analysis is not to defend quantitatively the Krogh tissue model, which is admittedly crude, nor to propose that the mean tissue P O 2 has any unique physiological significance, but to make a first approximation of tissue oxygenation, and to define the usefulness of venous blood as an index of mean tissue P O 2 applicable to the Krogh model. Insights are provided concerning optimal modes of response to hypoxic stress and the. problems of tissue oxygenation in physiological and patho-physiological states.