A fiber matrix model for the filtration through fenestral pores in a compressible arterial intima.

We advance a new hypothesis to explain the changes in hydraulic conductivity of an intact artery wall with transmural pressure previously observed by Tedgui and Lever [Am. J. Physiol. 247 (Heart Circ. Physiol. 16): H784-H791, 1984] and Baldwin and Wilson [Am. J. Physiol. 264 (Heart Circ. Physiol. 33): H26-H32, 1993]. This hypothesis suggests that compaction due to pressure loading of the proteoglycan matrix in the arterial intima near fenestral pores of the internal elastic lamina (IEL) leads to a narrowing of the pore entrance area and a large decrease in local intrinsic Darcy permeability of the matrix. To quantitatively assess the feasibility of this mechanism, a local two-dimensional model is proposed to study filtration flow in the vicinity of fenestral pores in a compressible intima. Using a heterogenous fiber matrix theory, we first predict the change in Darcy permeability with intimal thickness (Li). The model then calculates local velocity profiles and pressure distributions in the intima and media. The results show a marked nonlinear steepening of intimal pressure profiles near fenestral pores when the intima thins at higher luminal pressures. The predicted relative change in resistances of the IEL (with intima, R(I)) and of the media (Rm) shows a steep increase in R(I)/Rm when Li is <20% of its unstressed value. Numerical results also suggest that intimal compression has a limiting behavior in which the much stiffer collagen fibrils inhibit further compaction at high pressures after the proteoglycan matrix is maximally compressed. Predictions are also presented to show how different transmural pressures alter growth of an intimal horseradish peroxidase spot that derives from a localized (a single cell's boundary) endothelial leakage. Such a prediction is amenable to experimental verification.