A Steady-State Filtration Model for Transluminal Water Movement in Small and Large Blood Vessels

Abstract

It is now generally accepted that the intercellular cleft between adjacent endothelial cells is the primary pathway for the transluminal movement of water and small ions in the vasculature. A steady-state theoretical model has been developed to show quantitatively how the geometry of the intercellular cleft between adjacent endothelial cells is related to both the water movement and pressure distribution in the subendothelial space and to examine how the existence of a subendothelial interaction layer affects the hydraulic resistance of the media of vessels of varying wall thickness. The velocity and pressure fields in the media are described using porous matrix theory based on Darcy’s law and a lubrication-type analysis is used to describe the flow in a variable geometry intercellular cleft. These two equations are solved simultaneously to determine the unknown pressure distribution beneath the endothelium and the flow in the arterial media. Application of this model shows that, when the tight junction in the cleft is 26 Å or less, more than half of the total hydraulic resistance of the wall occurs across the endothelial cell monolayer, for a vessel whose wall thickness is less than 0.02 cm. This finding is in good agreement with the experimental findings of Vargas, et al. (1978) for rabbit aorta. Contrary to previous belief, the model shows that the filtration resistance of an arterial wall with intact endothelium does not scale linearly with wall thickness due to the highly nonlinear resistance of the endothelial interaction layer.