Calculation of oxygen pressures in tissue with anisotropic capillary orientation. I. Two-dimensional analytical solution for arbitrary capillary characteristics

In tissue with a distinct orientation of the oxygen supplying structures, the capillaries, a mathematical description of oxygen transport is feasible in terms of two-dimensional diffusion in a plane perpendicular to the capillaries. Muscle tissue is an example of a highly anisotropic tissue. With some additional simplifying assumptions, a solution can be constructed in terms of capillary sources for arbitrary capillary characteristics, in particular, capillary locations. The solution includes facilitated diffusion by myoglobin in the tissue. For homogeneous tissue, the solution becomes explicit allowing direct calculation of tissue oxygen pressure at any location in a field of simple geometry (circular, rectangular). Also, the size of the area into which each capillary distributes its oxygen, the oxygen supply area, is readily calculated.