A formula for the oxygen uptake of thin tissue slice in terms of its surface oxygen tension

An analytical solution to the oxygen diffusion equation with a sink term representing the oxygen consumption rate is obtained for thin tissue slice. The model of the oxygen consumption rate used depends on the oxygen tension and is known as zero- to first-order kinetics model (Michaelis–Menten-like kinetics model). The solution reflecting the conditions in Warburg-type experiments yields a formula for the oxygen uptake of a tissue slice as a function of the oxygen tension at its boundary. This formula is a useful tool at identification of the local tissue respiration parameters involved — the maximum oxygen consumption rate and the critical oxygen tension. Two applications of the formula are shown. The first one uses data for slices of skeletal muscle tissue taken from Kawashiro and Scheid [T. Kawashiro, P. Scheid, Dependence of O2 uptake on tissue PO2: experiments in intact excised rat skeletal muscle, in: D.W. Lübbers, H. Acker, E. Leninger-Follert, T.K. Goldstick (Eds.), Oxygen Transport to Tissue-V, in: Adv. Exper. Med. Biol., vol. 169, 1984, pp. 497–505]. In the second case, by use of the effective thickness concept, the formula is applied to data from an experiment with tissue pieces of other geometry [P.R.B. Caldwell, B.A. Wittenberg, The oxygen dependency of mammalian tissues, Am. J. Med. 57 (1974) 447–452]; the parameters of six albino-rat tissues (kidney, heart, liver, brain, diaphragm, and lung) are estimated.