There is considerable evidence that lipoprotein cholesterol, after crossing the arterial endothelium and entering the intima from the vascular lumen, lodges in extracellular lipid packets (labeled "liposomes") bound to the extracellular matrix. These liposomes appear to form by occasional attachment of a low-density lipoprotein (LDL) to the intimal matrix and to grow in place mainly by appending available free LDL. The liposome size distributions observed in chronically hypercholesteremic (WHHL) and in short-term cholesterol-fed rabbits are quite different. We propose a hierarchy of simple nucleation-polymerization models to describe liposome formation and growth. Even the simplest of these (with only one adjustable parameter) agrees extremely well with the WHHL data. In contrast, the cholesterol-fed rabbit data seem to result from the short-term nonuniform intimal history of LDL supply, which is a consequence of the focal nature of the transendothelial LDL flow through isolated transient leakyjunctions. The same models used for the WHHL data, together with this intimal nonuniformity, superimposed on a slow uniform transendothelial seepage also account very well for this cholesterol-fed rabbit data.
The present study aims to experimentally elucidate subtle structural features of the rat valve leaflet and the related nature of macromolecular transport across its endothelium and in its subendothelial space, information necessary to construct a rational theoretical model that can explain observation. After intravenous injection of horseradish peroxidase (HRP), we perfusion-fixed the aortic valve of normal Sprague-Dawley rats and found under light microscopy that HRP leaked through the leaflet's endothelium at very few localized brown spots, rather than uniformly. These spots grew nearly as rapidly with HRP circulation time before euthanasia as aortic spots, particularly when the time axis only included the time the valve was closed. These results suggest that macromolecular transport in heart valves depends not only on the direction normal to, but also parallel to, the endothelial surface and that convection, as well as molecular diffusion, plays an important role in macromolecular transport in heart valves. Transmission electron microscopy of traverse leaflet sections after 4-min HRP circulation showed a very thin ( approximately 150 nm), sparse layer immediately beneath the endothelium where the HRP concentration was much higher than that in the matrix below it. Nievelstein-Post et al.'s (Nievelstein-Post P, Mottino G, Fogelman A, Frank J. Arterioscler Thromb 14: 1151-1161, 1994) ultrarapid freezing/rotary shadow etching of the normal rabbit valve's subendothelial space supports the existence of this very thin, very sparse "valvular subendothelial intima," in analogy to the vascular subendothelial intima.
This paper proposes a new, two-dimensional convection-diffusion model for macromolecular transport in heart valves based on horseradish peroxidase (HRP) experiments on rats presented in the first of the papers in this series (Part I; Zeng Z, Yin Y, Huang AL, Jan KM, Rumschitzki DS. Am J Physiol Heart Circ Physiol 292: H2664-H2670, 2007). Experiments require two valvular intimae, one underneath each endothelium. Tompkins et al. (Tompkins RG, Schnitzer JJ, Yarmush ML. Circ Res 64: 1213-1223, 1989) found large variations in shape and magnitude in transvalvular (125)I-labeled low-density lipoprotein (LDL) profiles from identical experiments on four squirrel monkeys. Their one-dimensional, uniform-medium diffusion-only model fit three parameters independently for each profile; data variability resulted in large parameter spreads. Our theory aims to explain their data with one parameter set. It uses measured parameters and some aortic values but fits the endothelial mass transfer coefficient (k(a)=k(v)=1.63 x 10(-8) cm/s, where subscripts a and v indicate aortic aspect and ventricular aspect, respectively) and middle layer permeability (K(p(2))=2.28 x 10(-16)cm(2)) and LDL diffusion coefficient [D(2)(LDL)=5.93 x 10(-9) cm(2)/s], using one of Tompkins et al.'s profiles, and fixes them throughout. It accurately predicts Part I's rapid localized HRP leakage spot growth rate in rat leaflets that results from the intima's much sparser structure, dictating its far larger transport parameters [K(p(1))= 1.10 x 10(-12)cm(2), D(1)(LDL/HRP)=1.02/4.09 x 10(-7)cm(2)/s] than the middle layer. This contrasts with large arteries with similarly large HRP spots, since the valve has no internal elastic lamina. The model quantitatively explains all of Tompkins et al.'s monkey profiles with these same parameters. Different numbers and locations of isolated macromolecular leaks on both aspects and different section-leak(s) distances yield all profiles.
The heart valve leaflets of 29-day cholesterol-fed rabbits were examined by ultrarapid freezing without conventional chemical fixation/processing, followed by rotary shadow freeze-etching. This procedure images the leaflets' subendothelial extracellular matrix in extraordinary detail, and extracellular lipid liposomes, from 23 to 220 nm in diameter, clearly appear there. These liposomes are linked to matrix filaments and appear in clusters. Their size distribution shows 60.7% with diameters 23-69 nm, 31.7% between 70 and 119 nm, 7.3% between 120 and 169 nm, and 0.3% between 170 and 220 nm (superlarge) and suggests that smaller liposomes can fuse into larger ones. We couple our model from Part II of this series (Zeng Z, Yin Y, Jan KM, Rumschitzki DS. Am J Physiol Heart Circ Physiol 292: H2671-H2686, 2007) for lipid transport into the leaflet to the nucleation-polymerization model hierarchy for liposome formation proposed originally for aortic liposomes to predict liposome formation/growth in heart valves. Simulations show that the simplest such model cannot account for the observed size distribution. However, modifying this model by including liposome fusing/merging, using parameters determined from aortic liposomes, leads to predicted size distributions in excellent agreement with our valve data. Evolutions of both the liposome size distribution and total liposome mass suggest that fusing becomes significant only after 2 wk of high lumen cholesterol. Inclusion of phagocytosis by macrophages limits the otherwise monotonically increasing total liposome mass, while keeping the excellent fit of the liposome size distribution to the data.
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