Substrate diffusion from an array of capillaries with co-current and counter-current flow

A method is presented for analyzing the exchange of substrates from a two-dimensional array of parallel capillaries arranged in a manner characteristic of skeletal muscle. In general, the tissue is nonuniformly perfused by these capillaries, and large scale diffusion occurs from the regions that are richly perfused to the regions that are poorly perfused. The method developed leads to a coupled system of nonlinear ordinary differential equations for the substrate concentration within the capillaries, and is easy to apply even for vascular beds containing a large number of capillaries. Interaction among the capillaries is examined for the case when the flow in all the capillaries is in the same direction, co-current flow, and when some of the capillaries are flowing in the opposite direction, counter-current flow.