A theoretical analysis of the rate of resting metabolism of isolated papillary muscle

A mathematical model of simple oxygen diffusion into a homogeneous cylindrical muscle is developed. The model incorporates a variable sigmoidal relationship between oxygen consumption and oxygen concentration. For any given consumption-concentration relationship, the simulated mean basal metabolic rate (averaged over the radial extent of the muscle) is computed. This calculation is repeated for a range of muscle diameters, yielding the basal metabolic rate-muscle size relationship. This theoretical relationship, which is specific for the underlying oxygen consumption-concentration relationship, is then compared to observed resting heat production-muscle size data reported in the literature. Simulated results fail to explain observed data unless the underlying oxygen consumption-concentration relationship is of a highly improbable form. It is suggested that agreement between theoretical results, based on realistic oxygen consumption-concentration relationships, and experimental observations might be achieved if the mathematical model were extended to include a contribution by myoglobin-facilitated oxygen diffusion to the total oxygen flux.