Role of geometry and anisotropic diffusion for modelling PO2 profiles in working red muscle

A 3-dimensional analytical model of O2 diffusion in heavily working muscle is proposed which considers anisotropic, myoglobin (Mb)-facilitated O2 diffusion inside the muscle fiber and a carrier-free layer separating erythrocytes and fiber. The model is used to study the effects of some commonly applied simplifying assumptions (reduced dimensionality, neglected anisotropy) on the resulting PO2 distributions: (1) In order not to underestimate PO2 drops near erythrocytes, modelling O2 transport in 3 dimensions is important. (2) For a capillary-to-fiber ratio of 1, the results from the 2-dimensional version of the present model and from a Krogh-type model which incorporates a carrier-free layer agree well. (3) This is not true if the capillary-to-fiber ratio is 2. (4) In neither case, a Hill-type model furnishes a good description of the PO2 distributions. (5) Anisotropic diffusion may become important under critical O2 supply conditions. For a capillary-to-fiber ratio of 1, a Krogh-type model in which the O2 fluxes within the carrier-free layer are adapted according to Hellums (Microvasc. Res. 13: 131, 1977) yields almost identical PO2 distributions as the present 3-dimensional model.