A theoretical model to study the effect of convection and leaky junctions on macromolecule transport in artery walls.

A mathematical model is presented herein to determine the effect of convection on macromolecular transport across an artery wall due to transmural or osmotic pressure differences. The model is based on an extension of the leaky junction-cell turnover model of Weinbaum et al. (1985) to take into account a combined transport mechanism of convection and diffusion and also to provide the leaky junctions in the model with a finite resistance, thus allowing the results to be extended to intercellular clefts with a retarding extracellular matrix or to macromolecules whose dimensions are nearly the same as the junctional width. The results from this improved model show that the effect of pressure on transarterial macromolecular transport is important especially for cell turnover rates greater than 1% and that significant changes in the equilibrium balance of the cholesterol carrying LDL molecules in the arterial wall can occur due to a very small fraction of leaky junctions. At very high turnover rates (large fraction of leaky junctions) the effect of convection on macromolecular transport becomes dramatic and explains the very large increases in uptake observed experimentally after artificially inducing extensive endothelial damage.

Effect of cell turnover and leaky junctions on arterial macromolecular transport.

A new quantitative model is presented to explore the changes in vascular permeability that would result if the intercellular clefts around widely scattered endothelial cells were to become leaky to macromolecules in the range of roughly 4-10 nm during normal cell turnover. Although these open junctions occupy less than 10(-5) of the en face area of the endothelial surface, it is shown that the endothelial permeability can increase by 50-100% due to the experimentally observed regional variations in turnover in the larger arteries, whereas in the thinner walled veins and smaller arteries the subendothelial concentration is not significantly elevated. These results provide a very plausible explanation for the observed focal differences in the uptake of 125I-albumin and 131I-fibrinogen in blue and white areas and the nonselectivity of the local enhancement in uptake for these two molecules as a function of molecular size. The model has important implications for the localization of atherogenesis and the importance of endothelial cell turnover on the transport of proteins in vessels of all sizes.

A steady-state filtration model for transluminal water movement in small and large blood vessels.

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 A 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.