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

Abstract

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.

Transport in rat vessel walls. I. Hydraulic conductivities of the aorta, pulmonary artery, and inferior vena cava with intact and denuded endothelia

“…Of primary importance is whether transmural convection is very different and, thereby, transports different amounts of macromolecules into the walls of the PA and the IVC than into the aorta. The detailed measurements of L p for the aorta will complete a consistent set of data, all taken from the rat, for the model of Huang et al (16). It will also demonstrate whether the behavior of L p with pressure and endothelial denudation in rabbit aorta, attributed to intimal compression, also occurs in rat aorta.…”

“…Kim and Tarbell (22) attempted to explain the trend with a wall compaction hypothesis that invoked a variation of void fraction with distance into the wall. Huang et al (16) constructed a theory based on a large observed disparity in matrix structure and void volume between the intima (ϳ90% void for albumin) and media (a few percent void for albumin) (37). Their theory suggested that the intima easily compresses under pressure until its stiff collagen matrix carries the load and allows no further compression, but the dense media is nearly incompressible at these pressures.…”

“…More likely, the smaller value of L p(e ϩ i) for the aorta may reflect the fact that its measurement by difference means it includes not only the conductance/resistance of the endothelium but also contributions from the intima. Whereas the sparse intima normally contributes negligible resistance to water flow, Huang et al (16) suggest that intimal compaction by ⌬P loading can force the endothelium to block IEL fenestrae, thereby drastically increasing wall resistance to water flow and causing the measured L p(e ϩ i) to be significantly smaller than L p of the endothelium alone [L p(e) ]. Because the aorta has a complete and thick IEL, this effect would be strongest in the aorta.…”

“…To explain the behavior of rabbit aortic L p with ⌬P and with endothelial denudation, Kim and Tarbell (22) developed a theory based on whole wall compaction, whereas Huang et al (16) proposed a new mathematical model that invoked the ultra-high intimal porosity to restrict pressure compaction to the intima. They predicted that rising pressure compressed the intima, thereby decreasing its void space and slightly increasing its resistance; the compressed endothelium could block IEL fenestrae, altering the water flow and increasing its resistance much more significantly.…”

A theory for water and macromolecular transport in the pulmonary artery wall with a detailed comparison to the aorta

“…The PA intima pressure P SI lies above the aorta P SI . This indicates that the flow resistance due to the endothelium plus SI, including effects of SI compression and IEL fenestral blockage (22,24), contribute a smaller fraction of the total wall resistance in the PA than the aorta. [The statement of Shou et al (45) * are remarkably similar near the cleft, despite the vessels' very different ⌬P* and total wall L pt * .…”