A versatile model of steady state O2 supply to tissue. Application to skeletal muscle.

A model of combined convective and diffusive O2 transport to tissue is suggested which allows for the calculation of PO2 distributions in a cuboid tissue region with arbitrary microvascular geometries and blood flows. Carrier-facilitated O2 diffusion in the erythrocytes and in the tissue and red blood cell reaction kinetics are considered. The model is based on analytical descriptions of the PO2 fields of single erythrocytes surrounded by carrier-free layers in an infinite three-dimensional space containing an O2 carrier such as myoglobin. These PO2 fields are overlaid to obtain a solution of the differential equation of diffusion in respiring tissue. The model has been applied to a situation in heavily working skeletal muscle. Resulting PO2 profiles exhibit steep peri-capillary PO2 gradients. Further into the fiber, the profiles are essentially flat at low PO2 levels in good agreement with experimental findings (Gayeski and Honig. 1986. Am. J. Physiol. 251:H789-H799). PO2 dependence of facilitation of O2 transport produces a "layer deficient of functional carrier" which extends into the muscle fiber and which represents a reserve of O2 conductance automatically recruited in exercise. Furthermore, it results in a homogenization of red blood cell O2 fluxes which accounts for the absence of PO2 gradients along the muscle fiber axis (cf. Gayeski and Honig. 1988. Am. J. Physiol. 254: H1179-H1186).