A model for capillary exchange

Abstract

A mathema-tical model based on previous experimental work for material exchange across capillary walls is developed for the case where both capillary flow and transcapillary exchange are taken into account. Solutions are given for very early times and for later times for which an asymptotic solution was obtained. These solutions give intracapillary concentration profiles as well as the concentration in the extracellular space as a function of time. The asymptotic solutions indicate that the rate constant for the tissue buildup is Q/V(I - exp - PA/Q) when Q is the per-fusion rate, V the tissue volume, P the permeability coefficient, and A is the capillary area. The early time solutions predict that there will be appearance of transported substance in the capillary at points beyond the convected material because of an extracellular space shunt due to the rapid extracellular diffusion postulated in the model. In the discussion criticisms are given of other models concerned with the quantification of transcapillary exchange.