A Convection—Diffusion Model of Capillary Permeability with Reference to Single-injection Experiments

Abstract

A theoretical model of the transport of neutral molecules across the capillary wall has been developed. The model is applicable to single-injection experiments. The mutual coupling between the diffusion and convection of solute molecules in extracellular pores under the influence of restriction has been considered as responsible for the capillary permeability. The extraction, which is experimentally measurable, and solute flows across the capillary membrane, have been calculated with the continuity equation in the steady state as well as in the case of relaxation phenomena in the membrane-concentration profile due to non-steady-state properties. Explicit equations of the steady-state extraction, suitable for experimental application, are presented, showing the effect of the convection in increasing the capillary permeability and thus in opposing the restriction caused by the solute-membrane interaction. Non-steady-state computations were performed on an analog computer and showed that back transport from the membrane compartment to the blood stream may be partly responsible for the regain of solute molecules which have earlier passed into the capillary wall.