On the theory of blood-tissue exchanges: I. Fundamental equations

A mathematical analysis of the absorption of an inert gas by a heterogeneous system ofn phases, e.g., a limb consisting ofn tissues, is presented. The total uptake of gas, ϕ(t), up to timet is given in terms of arterial concentration, cardiac delivery, blood volume, and the volume, permeability, and partition coefficient of each tissue. The theory predicts how the uptake curve should change in shape under a variety of physiological conditions, and how from the numerical values of the constants the values of certain tissue constants, e.g. permeabilities, may be obtained. The material in this article should be construed only as the personal opinion of the writers and not as representing the opinion of the Navy Department officially.