Facilitated diffusion in a tissue cylinder with an anoxic region

When the diffusion of oxygen is facilitated by myoglobin this diffusional transport can adequately supply oxygen required by tissue metabolism over greatly increased distances. Earlier analyses of this phenomenon have considered the rate of reaction between oxygen and myoglobin as infinitely fast. A first-order correction which takes into account the finite rate of reaction involves a reaction boundary layer at the surface where the oxygen enters the tissue, and a second reaction boundary layer around an anoxic region in the tissue when such a region is present. These corrections are calculated for a tissue cylinder and the results obtained are compared with results neglecting the finiteness of the reaction rate. The maximum distance over which facilitated diffusion can supply oxygen is less when the corrections are taken into account. For physiologically relevant parameter values the size of an anoxic region is predicted to be larger by about 15% of the radius of the tissue cylinder.