Pre-atherosclerotic flow and oncotically active solute transport across the arterial endothelium

Highlights

• Blood pressure drives water & oncotically-acive solutes like albumin into artery walls that can affect early cholesterol buildup/atherogenesis.

• Blood pressure compresses the arterial subendothelial intima to inhibit this flow; endothelial cell aquaporin-1 controls this compression.

• Surprisingly, oncotic are comparable to hydrostatic forces at low pressures until intima compression; increased aquaporins delays compression.

• One expects oncotic forces due to aquaporin to stop flow into the wall, but media filtration raises intima albumin to reverse their direction.

• Theory predicts raising endothelial aquaporin levels would decompress the intima at physiologic pressures, increase flow & slow atherogenesis.

Abstract

Atherosclerosis starts with transmural (transwall) pressure-driven advective transport of blood-borne low-density lipoprotein (LDL) cholesterol across rare endothelial cell (EC) monolayer leaks into the arterial subendothelial intima (SI) wall layer where they can spread, bind to extracellular matrix and seed lesions. The local SI LDL concentration, which governs LDL’s binding kinetics, depends on the overall diluting transmural liquid flow. Transmural pressures typically compress the SI at physiological pressures, which keeps this flow low. Nguyen et al. (2015) showed that aortic ECs express the water channel protein aquaporin-1 (AQP1) and the transEC (δP) portion of the transmural (ΔP) pressure difference drives, in parallel, water across AQP1s and plasma across interEC junctions. Since the lumen is isotonic, selective AQP1-mediated water flow should quickly render the ECs’ lumen side hypertonic and the SI hypotonic; resulting transEC oncotic pressure differences, δπ, should oppose δP and quickly halt transEC flow. Yet Nguyen et al.’s (2015) transAQP1 flows persist for hours. To resolve this paradox, we extend our fluid filtration theory Joshi et al. (2015) to include mass transfer for oncotically active solutes like albumin. This addition nonlinearly couples mass transfer, fluid flow and wall mechanics. We simultaneously solve these problems at steady state. Surprisingly it finds that media layer filtration causes steady SI to exceed EC glycocalyx albumin concentration. Thus δπ reinforces rather than opposes δP, i.e., it sucks water from, rather than pushing water into the lumen from the SI. Endothelial AQP1s raise the overall driving force for flow across the EC above δP, most significantly at pressures too low to compress the SI, and they increase the ΔP needed for SI compression. This suggests the intriguing possibility that increasing EC AQP1 expression can raise this requisite compression pressure to physiological values. That is, increasing EC AQP1 may decompress the SI at physiological pressures, which would significantly increase SI thickness, flow and subsequently SI LDL dilution. This could retard LDL binding and delay preatherosclerotic lesion onset. The model also predicts that glycocalyx-degrading enzymes decrease overall transEC driving forces and thus lower, not raise, transmural water flux.

Introduction

Atherosclerosis is a disease of large, high-pressure arteries (Ross, 1986, Wilson, Wilson, 1991, Tarbell, 2003). For decades numerous experimental and theoretical studies have investigated how blood-borne low density lipoprotein (LDL) cholesterol crosses the arterial endothelium and binds to extracellular matrix just below it; these are recognized as the critical earliest events leading to foam cells, preatherosclerotic lesions and eventually atherosclerotic plaques (Nielsen, 1996, Tarbell, 2003, Tedgui, Lever, 1984, Yang, Vafai, 2008). Specifically, blood-borne monocytes transmigrate into the artery wall in regions of accumulated subendothelial lipid, mature to macrophages and scavenge accumulated lipid. When overwhelmed they turn into necrotic foam cells that, along with lipid, constitute the earliest lesions, which can evolve into plaques that thicken and harden the wall. Artery wall plaque can eventually compromise the flow cross-section and/or lead to plaque rupture whose debris can suddenly block smaller downstream vessels (Vander et al., 1998).

The artery wall is a layered structure (schematic in Fig. 1). A monolayer of endothelial cells (EC) connected by tight junctions and with a glycocalyx (GX) mesh on its lumen side separates the blood from a very thin (~ 250 μ in rat) subendothelial intima (SI), a very porous extracellular matrix (ECM) layer. An internal elastic laminar (IEL) separates the SI from the thick and dense media that comprises the bulk of the wall and consists of alternating layers of elastin and smooth muscle cells (SMCs) with ECM, followed by the adventitia, a loose connective tissue layer. The earliest mathematical models assumed one-dimensional (depending only on the endothelium-normal direction) LDL diffusion into the artery wall, consistent with early theories postulating that free vesicles ferried LDL across the endothelium (Palade, 1960). However double-tracer (Chien et al., 1982) and serial section electron microscopy studies showed far too few free vesicles to support such transport. In contrast, short-time large-molecular tracer (e.g., horseradish peroxidase (HRP) (Chuang et al., 1990), Evans Blue albumin (EBA) conjugate (Stemerman et al., 1986), Lucifer Yellow LDL (Lin et al., 1989)) studies showed macromolecular entry into the artery wall to be anything but uniform; these macromolecules transmigrated via rare localized endothelial leakage sites to form subendothelial tracer spots that grew very rapidly with time after tracer injection. Endothelial regions around intercostal branches showed roughly twice the leakage site density as non-branch areas (Chuang, Cheng, Lin, Jan, Lee, Chien, 1990, Wu, Chi, Jerng, Lin, Jan, Wang, Chien, 1990) and spontaneous hypertensive rat (SHR) aortas have roughly triple the leakage frequency of their normotensive cousins; these branch regions and SHR arteries are precisely those that exhibit increased early lesions (Packham, Rowsell, Jørgensen, Mustard, 1967, Bell, Adamson, Schwartz, 1974, Bell, Gallus, Schwartz, 1974, Schwenke, Carew, 1989). Finally, macromolecular leakage across small mm² tissue samples was  ~ 50 times that of control regions showing no leakage sites, meaning that background macromolecular wall entry is far smaller than via localized leaks (Stemerman et al., 1986). Chien and coworkers showed that 99% of endothelial cells in M-phase leak EBA (Lin et al., 1988), 80% leak albumin (Lin et al., 1989), together comprising  ~  30% of all EBA and 45% of LY-LDL leaks, whereas IgG-stained dying cells (Lin, 1990) and those with stigmata (Chuang et al., 1990) account for most of the remaining leaks that number  ~ 1 in 2000–5000 cells in rat aorta. Much smaller water molecules (2.8 Å) easily pass through all junctions. Refs. Weinbaum et al. (1985), Chien et al. (1988) expand on the leaky junction hypothesis for macromolecular transport in the artery wall. These data make it clear that any one-dimensional model (variation only normal to the endothelium, e.g., Yang, Vafai, 2008, Sun, Wood, Hughes, Thom, Xu, 2007, Khakpour, Vafai, 2008, Jesionek, Kostur, 2015, Jesionek, Slapik, Kostur, 2016) or higher dimensional model (e.g., Chung, Vafai, 2013, Ai, Vafai, 2006, Yang, Vafai, 2006) that assumes the endothelium has uniform properties cannot explain the behavior near an isolated leak, but rather averages over much larger regions that miss regional leakage variation. As we shall see, such models also miss other physiologically-relevant issues.

Meanwhile, some early one-dimensional theories included transmural-pressure-dependent advection in parallel with diffusion, but treated the subendothelial structure as a uniform medium (Tzeghai et al., 1986). These theories could not explain Fry’s studies of minipig aorta (Fry et al., 1986) and Smith and Staples’ postmortem studies of human arteries (Smith and Staples, 1982), both of which showed SI cholesterol concentrations exceeding those in the lumen. To remedy this deficiency, Fry, 1985, Fry, 1987 first suggested treating the wall as a four-layer medium (endothelium, SI, IEL and media), where the IEL with its fenestral holes could act as a molecular sieve and thereby increase SI LDL above its lumen value. Despite this evidence models that treat the subendothelial space as a uniform porous medium, but the endothelium as having normal and leaky junctions and vesicles persist (Olgac et al., 2008).

Even early two-dimensional (in the directions z into the wall and radially r from the center of a leaky cell, assuming axisymmetry in the region near the leaky cell), steady state, diffusion-only models showed that an en face leaky area of ${10}^{-6}$ of the endothelial surface - i.e., amounting to leaks through the junctions around only a few cells per ten thousand - was enough to account for the observed increase in macromolecular permeability (Weinbaum et al., 1985). However, time-dependent tracer studies of HRP radial spot size growth (Chuang, Cheng, Lin, Jan, Lee, Chien, 1990, Stemerman, Morrel, Burke, Colton, Smith, Lees, 1986) showed growth far too fast for any reasonable diffusivity. This necessitated the inclusion of pressure-driven macromolecular advection, not simply in z, but through localized endothelial leaks and then in r as well as in z subendothelially. Data (Campbell, Roach, 1981, Song, Roach, 1983) indicating that fenetral diameters were order 1μ and likely accounting for only 0.1–2% of the IEL area suggested that fluid and advected macromolecules entering the SI via a leaky junction flowed radially parallel to the endothelium in the SI to find a fenestral path into the media, again necessitating a two- or three-dimensional model; asumed axisymmetry about a single leak allows a two dimensional model. Flux and concentration continuity and far different cross-sectional void fractions of the IEL and surrounding tissue revealed large velocity discontinuities.

Yuan et al. (1991) proposed the first two-dimensional advection-diffusion model for artery wall transport. They used Fry’s four-layer wall and a leaky junction hydraulic conductivity (L_P), the ratio of fluid flux to total (hydrostatic and osmotic) pressure difference, two orders of magnitude higher than for normal endothelium. They found significant radial SI pressure-driven flow and tracer advection from the leak, but still produced tracer spots far smaller than observed. Since direct measurement of SI (with a thickness of less than 1% of the media thickness) transport parameters was impossible, Yuan et al. (1991) assumed identical SI and media transport parameters. Huang et al. (1994) objected to this assumption due to Lark et al. (1988)’s, Wight and Hascall (1983) immunology finding that, whereas the SI contains large amounts of chondroitin-sulfate proteoglycans and collagen, media smooth muscle cells produce far more of the dense dermatin-sulfate proteoglycan. Moreover, Truskey et al.’s autoradiography using ¹²⁵I-LDL found SI LDL concentrations near the leaky junction 0.6 that of the lumen value (Truskey et al., 1992), which would be impossible if the SI had the same LDL space as the media (< 0.1 Tedgui and Lever, 1987). Finally, recent ultra-rapid freezing/rotary shadow etchings by Frank and Fogelman (1989) and Nievelstein et al. (1991) had overcome the problem of ECM collapse upon chemical fixation for electron microscopy to show clear images of intact SI ECM fibers and spacings. Huang et al. (1994) used these values with fiber matrix theory (Curry, Michel, 1980, Curry, 1984, Curry, 1986, Levick, 1987) to calculate an SI void space of over 95% and, consequently SI transport parameters up to two orders of magnitude higher than medial values. The theory with these parameters predicted far faster radial SI advection that for the first time easily explained both observed SI LDL concentrations and tracer spot size growth. In their model, leaky junctions accounted for less than 1/20 of 1% of the endothelial area.

Due to computing power limitations at the time, Huang et al. (1994) facilitated calculation by simplifying both SI (essentially a boundary-layer type assumption that SI variables did not vary across its thickness) and media (nearly one-dimensional) transport. These simplifications turned out to introduce significant inaccuracies, especially near and below the leaky junction, the most critical region where large tracers entered the wall. Zeng et al. (2012) eliminated these assumptions and inaccuracies, realigned the experimental and theoretical definitions of the Peclet number, and corrected (Huang et al., 1994’s) guessed values of parameters that were measured years after (Huang et al., 1994), e.g., the fractional IEL fenestral area in rat aorta (0.043, not 0.002) and normal junction hydraulic conductivity (6.50 vs $1.14\times {10}^{-8}$ cm/s/mmHg). They developed a similar theory for water and macromolecular transport in the pulmonary artery and connected their different structures to different transport outcomes (Shou et al., 2007), e.g., very different tracer spot size growth rates, very well. Predictions made with independently-determined parameters (see below) agreed very well with experiment.

All of these theories rely on numerous parameters, most culled from literature measurements and others, e.g., SI parameters, calculated from fiber matrix theory using observed fiber sizes and spacings. The most consequential parameters for advection-dominated transport are the regional, especially the SI, hydraulic conductivities. Artery wall layer hydraulic conductivity measurements usually assumes no internal osmotic/oncotic differences. Artery wall filtration properties exhibit a strong transmural pressure (ΔP)-dependence (Baldwin, Wilson, Simon, 1992, Baldwin, Wilson, 1993, Lever, 1987, Tedgui, Lever, 1984, Tedgui, Lever, 1987, Joshi, Jan, Rumschitzki, 2015), even without considering endothelial-derived chemical mediators (Baldwin and Wilson, 1993). Tedgui and Lever (1984) found a high value of intact rabbit aorta $L_{P_t}$ that dropped  ~ 1/3 from 70 to 180 mmHg; endothelial denudation rendered it pressure-independent at roughly double its intact high-pressure value. Lever (1987) showed that this drop takes place by 100 mmHg and then remains unchanged at higher pressures. Baldwin et al. (1992), Baldwin and Wilson (1993) modified the measurement technique to conduct all measurements on the same rabbit vessels and found qualitatively similar results uniformly a factor of two higher. Shou et al. (2007) adapted these techniques to the far smaller rat aorta and found results quantitatively consistent with Tedgui and Lever (1984) values. To explain the observed $L_{P_t}$ drop with pressure, Kim and Tarbell (1994) theorized that pressure compacts the media, which implies a spatial variation of media fiber sizes. In contrast, Tedgui and Lever (1987) found no change in aortic sucrose space from 70 to 180 mmHg.

Based on their discovery (Huang et al., 1994) of extreme SI sparseness, Huang et al. (1997) proposed that, rather than pressure compressing the dense media (~ 42% void space Tedgui and Lever, 1987), it compresses the SI until  ~ 100 mmHg where sturdy collagen fibers (estimated from Frank and Fogelman (1989) as  ~ 5% of SI volume) support the load to resist further compression. SI compression decreases SI ECM fiber spacing and thus fiber-matrix-derived SI transport parameters. More importantly, it juxtaposes the endothelium and IEL fenestrae to partially block fluid fenestral entry. They (Huang et al., 1998) captured fenestral blockage in aortic sections fixed at 100 mmHg. Endothelial denudation removes a critical resistance layer, so L_{P_{m+I}} is double $L_{P_t}$, and it eliminates SI compression and fenestral blockage, and thus renders $L_{P_t}$ pressure independendent. Their local filtration theory calculates $L_{P_t}$ with only normal junctions, the vast majority of the endothelium. They solve incompressible Darcy flow from the lumen through the normal junctions around a single, perfectly circular EC, in the SI parallel to the endothelium towards and through a circular IEL fenestral hole ideally aligned concentric with the EC, and into and through the media. They assume impermeability of the EC outside of its junctions and of the IEL outside of its fenestrae and that the SI compresses as a Hookean spring to calculate the pressure and flow fields in the wall for different levels of SI compression. Integrating the velocity across any cross section gives the volumetric flow rate. The difference (δP) between the lumen pressure and integral of the SI pressure field over the SI side of the EC gives the net pressure difference or force/area on the cell. This allows calculation of the $L_{P_t}$ of the entire artery wall and the effective $L_{P_{e+i}}$ of the endothelium plus SI, an input the above global wall models require. Finally by comparing the calculated $L_{P_{e+i}}$s for different SI compressions with the corresponding $L_{P_{e+i}}$’s extracted from various groups’ measurements (Tedgui, Lever, 1984, Tedgui, Lever, 1987, Baldwin, Wilson, Simon, 1992, Baldwin, Wilson, 1993, both in rabbit aorta available at the time, and later rat aorta values Shou, Jan, Rumschitzki, 2007, Nguyen, Toussaint, Xue, Raval, Cancel, Russell, Shou, Sedes, Sun, Yakobov, et al., 2015), they find compression level for each ΔP up to maximal compression. From L_i(ΔP) one finds the corresponding SI spring constant that predicts compression levels and $L_{P_{e+i}}$ for any transmural pressure. This theory predicted a factor of 5 SI compression with increasing ΔP. Subsequent measurements showed excellent agreement, evincing an average factor of 6 SI compression (Huang et al., 1998). Both Dabagh et al. (2009) in a model with a very different idealized geometry and Jesionek et al. (2016) in a one-dimensional model used these results for SI thickness vs ΔP to introduce ΔP-parameter and SI thickness dependence into whole wall models to study how hypertension affects LDL transport. Jesionek et al. (2016) fit their $L_{P_e}$ from steady wall LDL concentration vs ΔP measurements rather than from available direct flow measurements.

In 1988, Peter Agre and coworkers discovered the membrane protein aquaporin-1 (AQP1) that acts as a hydrophilic channel in an otherwise hydrophobic membrane (Denker et al., 1988). They showed it to be the long-sought-after, highly-specific, ubiquitous water pore that is key to the kidney’s ability to filter huge volumes of water (Hara-Chikuma, Verkman, 2006, Verkman, 2005) and, along with other members of the aquaporin family, to water transport across nearly all physiological membranes (Nielsen et al., 1993). In response to an osmotic difference, AQP1 can transport  ~ 3 × 10⁹ water molecules/sec at no ATP cost (Murata et al., 2000). AQP1 was detected in human and rat coronary arteries (Shanahan et al., 1999), mouse aorta (Saadoun et al., 2005) and many other tissues (Gao, Tang, Li, Huan, 2012, Hasegawa, Lian, Finkbeiner, Verkman, 1994, Nielsen, Smith, Christensen, Agre, 1993). Using specific antibodies against AQP1, Nguyen et al. (2015) showed avid AQP1 expression in bovine and rat aortic endothelial cells (AECs) in vitro and in rat AECs in whole aortas ex vivo. Although Shanahan et al. (1999) had detected AQP1 in AECs, Nguyen et al. (2015) revealed at least one of their functions in AECs: Chemical blocking using non-toxic levels of HgCl₂ or siRNA knockdown (Xue, 2011) of AEC AQP1 reduced aortic hydraulic conductivity (blocking numbers) by 32 ± 4% at 60 mmHg, but hardly changed it at 100 mmHg (11 ± 2%) and 140 mmHg (5 ± 3%). This for the first time showed that a hydrostatic, and not just an osmotic, pressure difference can drive water across the endothelium. In order to explain the pressure-dependence of this drop, Nguyen et al. (2015) suggested that, just as a sail with no holes supports a larger fraction of a pressure drop across it than a sail with holes, so too an endothelium with absent or inoperative AQP1s takes up a larger fraction of the transmural pressure drop, ΔP. It therefore achieves the critical trans-endothelial force/area for SI compression at a lower ΔP than an endothelium with normal functioning AQP1s. This motivated Joshi et al. (2015) to extend Huang et al. (1997)’s theory to include trans-endothelial AQP1 flow and to show that indeed increasing/ decreasing AEC AQP1 increases/ decreases the critical transmural pressure at which the SI compresses to a point where ECs block IEL fenestrae and vessel wall $L_{P_t}$ drops sharply. Complementing this work, subsequent experiments in Toussaint et al. (2017) and Raval et al. (2019) indeed show that an AEC AQP1 increase raises this critical ΔP. This ability is potentially significant since, under normal physiological pressure the SI is compressed. Understanding how manipulating EC AQP1 expression affects wall $L_{P_t}$ holds out the possibility of decompressing the SI to dramatically increase transmural flow by increasing the critical ΔP to normal physiological ΔPs. As we discuss below, a higher transAQP flow would dilute SI LDL concentrations, thereby significantly slowing its kinetics of binding to SI ECM, the putative triggering step leading to plaque formation and eventually to atherosclerosis.

Yet one dare not ignore osmotic/oncotic effects. AQP1’s water specificity presents an oncotic paradox. Pure transAQP water flow into the SI should both raise the small solutes’ (e.g. albumin, most responsible for oncotic pressure) concentration on the lumen side and lower it on the SI side of the EC. The resulting transendothelial oncotic pressure difference, δπ, should act against δP to rapidly halt this flow, in contrast to, e.g., Nguyen et al. (2015) experiments that evince steady transAQP1 water flow over many hours. Moreover, the EC surface glycocalyx (GX) layer may be the primary molecular filter for oncotically-active solutes (Hu and Weinbaum, 1999); it may help determine (Hu, Adamson, Liu, Curry, Weinbaum, 2000, Adamson, Lenz, Zhang, Adamson, Weinbaum, Curry, 2004, Zhang, Adamson, Curry, Weinbaum, 2006) the actual transendothelial - rather than global - oncotic and total Starling forces driving water across the capillary endothelium. The GX layer may play a similar role in large arteries. This paper develops a nonlinearly coupled (flows advects tracer and tracer differences cause oncotic differences across membranes) water and small solute transport theory across all aortic wall layers, including the GX, to resolve this paradox. It turns out to be useful to solve for steady solutions as long-time limits of a fictitious unsteady problem. By understanding the detailed role that EC AQP1 plays in controlling the oncotic pressures, fluid flows and the detailed force distribution in the vessel wall, we can see if/how manipulating EC AQP1 distributions may allow SI decompression at physiological pressures to potentially retard early atherosclerosis.

One factor potentially mitigating the oncotic paradox is that, although pure water enters the SI through EC AQP1s, isotonic fluid crossing the EC junction flows parallel to the endothelium in the ultra-thin, sparse SI until it finds an IEL fenestra to access the dense media. Typical SI radial fluid velocities (~  10${}^{-5}$-10${}^{-7}$ cm/s Huang et al., 1997) and the EC radius (~  10–15 µm) indicate this fluid spends  > 100 s in the SI. Diffusive mixing normal to the endothelium in the SI occurs in  ~ ms (for diffusivities $\sim {10}^{-7}$ cm²/s) and thus elevates the albumin concentration adjacent to the abluminal EC membrane. Model solutions below for the pressure, velocities and concentrations in all wall layers and oncotic pressure differences across all boundaries and thus across the EC will reveal if /how important this effect is. It will show why the transcellular flow does not halt due to oncotic buildup. It will calculate the actual driving forces per unit area, $\delta P-\sigma \delta \pi ,$ σ the solute osmotic reflection coefficient, acting across the endothelium vs ΔP and thus the true endothelial hydraulic conductivity $L_{P_e},$ in contrast to what has until now come from ignoring δπ. It will thus explain the dominant mechanisms that control the variation in the phenomenological intact vessel $L_{P_t}$ with ΔP. That will facilitate examining how effective AQP1 upregulation is in changing the critical ΔP for SI decompression and $L_{P_t}$ increase to potentially slow preatherosclerosis. We examine the effects of enzymatic GX degradation and pathologies such as abnormal blood albumin concentrations.