Radius-dependent decline of performance in isolated cardiac muscle does not reflect inadequacy of diffusive oxygen supply.

The study of cardiac energetics commonly involves the use of isolated muscle preparations (papillary muscles or trabeculae carneae). Their contractile performance has been observed to vary inversely with thickness. This inverse dependence has been attributed, almost without exception, to inadequate diffusion of oxygen into the centers of muscles of large diameter. It is thus commonly hypothesized that the radius-dependent diminution of performance reflects the development of an anoxic core. We tested this hypothesis theoretically by solving a modification of the diffusion equation, in which the rate of oxygen consumption is a sigmoidal function of the partial pressure of oxygen. The model demonstrates that sufficiently thick muscles, operating at sufficiently high rates of oxygen demand or sufficiently low ambient partial pressures of oxygen, will indeed show diminished energetic performance, whether indirectly indexed as stress (force per cross-sectional area) development or as the rate of heat production. However, such simulated behavior requires the adoption of extreme parameter values, often differing by an order of magnitude from their experimental equivalents. We thus conclude that the radius-dependent diminution of muscle performance in vitro cannot be attributed entirely to an insufficient supply of oxygen via diffusion.