Macromolecular transport across the vessel wall, apparently the earliest pre-atherosclerotic event, is known to occur due to advection by transmural (i.e., across the vessel wall) pressure-driven plasma (water and solutes) transport through leaky junctions around rare endothelial cells that are temporarily widened and leaky, some because they are either dying or dividing. A wall parameter, the hydraulic conductivity (Lp), defined as the ratio of the transmural water flux to (hydrostatic-oncotic, the latter universally taken as zero in large artery walls) pressure difference, is central to the understanding of this transmural water transport in detail. On one hand, it advects macromolecules like low-density lipoprotein (LDL) into the arterial subendothelial intima (SI) through these leaks and spreads it there, thereby giving it the chance to bind to extracellular matrix and possibly to trigger the start of atherosclerotic lesion formation. On the other hand, the overall water flow across the normal (non-leaky) endothelium dilutes the local SI LDL concentration, thereby likely slowing binding kinetics, and washing not-yet-bound lipid further into the wall.
Our group’s discovery of the presence of Aquaporin-1 (AQP) in rat aortic endothelial cells suggests a new possibility of water transport across the endothelial cell, alongside the generally accepted paracellular route. Interestingly, we found that chemically blocking AQPs changes rat aortic wall Lp in a strongly pressure dependent manner. We then proposed a new theory that agrees well with this otherwise perplexing experimentally-observed pressure-dependence. It suggests that AQPs contribute about 30% to the phenomenological endothelial Lp at low transmural pressures. However, since the lumen is isotonic, an AQP-mediated, transendothelial cell, pure water flow into the arterial SI should set up an oncotic pressure gradient ΔΠ that opposes and quickly halts the ΔP-driven flow through the cell. How then could trans-AQP flow persist for many hours, as our chemical blocking of AQP experiments show? We have developed a filtration and advection-diffusion model for water and the transport of the small, oncotically-active solute albumin across the glycocalyx layer, across endothelial interface and through the entire vessel wall. The filtration flow and the mass transfer problem are intimately coupled: The flow advects tracer while albumin differences across the endothelium set up a ΔΠ that sucks fluid across the endothelium. And it is nonlinear: the advective term is the product of two dependent variables, velocity and (the gradient of) the concentration. We simultaneously solve the combined steady state problem as the long-time solution of an unsteady problem that we attack with finite difference methods. We use parameters taken from the literature, mostly from experiment.
Our results show that, since the media retardation coefficient ~ 0.3, the media acts to strongly filter the transport of the solute albumin relative to the water solvent, causing a build-up of albumin in the media that backs up into the SI by the time steady state is achieved. In contrast to our naïve suggestion above, this increased albumin concentration results in higher osmotic pressures in the SI than in the glycocalyx, which drives the water flow into the SI from the luminal side of the EC, and not the other way around. Thus, even though oncotic gradients are normally assumed negligible across the walls of large arteries, we find that they indeed play a role within those vessel walls. We show to what extent these oncotic gradients mask the true wall and layer hydraulic conductivities. We look at the effects of vesicular albumin transport and of varying the junctional boundary conditions on these results. Given AQP’s presence in the high-pressure cardiac endocardium, heart, lung and renal epithelia, resolving and understanding how mass-transfer-induced osmotic gradients interact with the flows that advect those solutes may have far broader and illuminating implications.