Diffusion in tissue slices with metabolism obeying Michaelis-Menten kinetics

Kawashiro, Nüsse & Scheid (1975) proposed a "diffusion method" of measurement of the metabolic rate in slices of tissue, and derived a mathematical relationship between the parameters which could be measured experimentally without penetration into the tissue, and the metabolic rate; the latter was assumed to obey zero-order chemical kinetics. In the present paper, we present a mathematical description of the steady-state diffusion in tissue slices with metabolism obeying an uptake kinetics of the Michaelis-Menten type, and demonstrate that the "diffusion method" is suitable for determination of the parameters of the Michaelis-Menten kinetics. It is analyzed how to choose the thickness of the tissue slice in order to achieve the maximum resolution of the method.