Modelling diffusive O₂ supply to isolated preparations of mammalian skeletal and cardiac muscle

Abstract

The purpose of this study was to use A. V. Hill’s equation describing diffusion of O₂ into cylindrical muscles to assess the adequacy of O₂ supply for commonly used isolated preparations of mammalian cardiac and skeletal muscles. The diffusion equation was solved numerically to give the maximum, steady state O₂ diffusion distances (i.e. the distance from the surface of the muscle to the radial location where ${P}_{{\rm O}_{2}}$ is 0) for both resting and contracting muscles and for a range of temperatures. Non-steady state solutions for the rest-to-work transition were also determined to estimate how long contractile activity could be continued before anoxia develops at the muscle centre. The influence on muscle oxygenation of myoglobin-facilitated O₂ diffusion was also assessed. The analysis was performed for typical sized, whole muscles from adult rats and mice, for frog sartorius muscle and for a range of temperatures. Muscle O₂ consumption rates were taken from the literature. The results indicated that (1) diffusive O₂ supply would be adequate to support resting metabolism of soleus and EDL muscles of rat and mouse but may not be adequate to support the transient high resting metabolic rate of papillary muscles shortly after dissection, (2) during steady contractile activity of soleus and EDL muscles, particularly those from the rat, over a reasonable range of duty cycles, adequate O₂ supply could only be ensured if the radii of preparations was substantially smaller than those of whole muscles and (3) for cardiac muscles, diffusive O₂ supply could only support steady-state metabolism at twitch frequencies <1 Hz for whole papillary muscles from rat and <3 Hz for those from mouse. Reducing experimental temperature markedly enhances O₂ supply to skeletal, but not cardiac, muscle. O₂ supply from myoglobin had only minimal effects on oxygenation under typical isolated muscle conditions.