On facilitated oxygen diffusion in muscle tissues.

The role of myoglobin in facilitated diffusion of oxygen in muscle in examined in a tissue model that utilizes a central supplying capillary and a tissue cylinder concentric with the central capillary, and that includes the nonlinear characteristics of the oxygen-hemoglobin dissociation reaction. In contrast to previous work, this model exhibits the effect of blood flow and a realistic, though ideal, tissue-capillary geometry. Solutions of the model equations are obtained by a singular-perturbation technique, and numerical results are discussed for model parameters of physiologic interest. In contrast to the findings of Murray, Rubinow, Taylor, and others, fractional order perturbation terms obtained for the "boundary-layer" regions near the supplying capillaries are quite significant in the overall interpretation of the modeling results. Some closed solutions are found for special cases, and these are contrasted with the full singular-perturbation solution. Interpretations are given for parameters of physiologic interest.