Substrate Diffusion and Consumption in Rectangular Capillary-Tissue Bed

Abstract A diffusion equation can be used to estimate the oxygen concentration profiles for a highly-regular capillary bed of skeletal muscle. In reality, the capillaries may be arranged more or less randomly in normal tissues. The oxygen concentration, along with its time-wise distribution, may be uneven. Heterogeneity in the tissue bed is much more commonly considered. This article presents a mathematical analysis of the capillary-tissue exchange of substrate in microcirculation in rectangular regions where multiple capillaries are embedded with arbitrary characteristics. A matching technique is used to help solve the associated governing equations.