Experimental determination and mathematical model of the transient incorporation of cholesterol in the arterial wall

Modeling cholesterol metabolism and atherosclerosis

Atherosclerotic cardiovascular disease (ASCVD) is the leading cause of morbidity and mortality among Western populations. Many risk factors have been identified for ASCVD; however, elevated low-density lipoprotein cholesterol (LDL-C) remains the gold standard. Cholesterol metabolism at the cellular and whole-body level is maintained by an array of interacting components. These regulatory mechanisms have complex behavior. Likewise, the mechanisms which underpin atherogenesis are nontrivial and multifaceted. To help overcome the challenge of investigating these processes mathematical modeling, which is a core constituent of the systems biology paradigm has played a pivotal role in deciphering their dynamics. In so doing models have revealed new insights about the key drivers of ASCVD. The aim of this review is fourfold; to provide an overview of cholesterol metabolism and atherosclerosis, to briefly introduce mathematical approaches used in this field, to critically discuss models of cholesterol metabolism and atherosclerosis, and to highlight areas where mathematical modeling could help to investigate in the future. This article is categorized under: Cardiovascular Diseases > Computational Models.

Cholesterol Homeostasis: An In Silico Investigation into How Aging Disrupts Its Key Hepatic Regulatory Mechanisms

The dysregulation of intracellular cholesterol homeostasis is associated with several age-related diseases, most notably cardiovascular disease (CVD). Research in this area has benefitted from using computational modelling to study the inherent complexity associated with the regulation of this system. In addition to facilitating hypothesis exploration, the utility of modelling lies in its ability to represent an array of rate limiting enzymatic reactions, together with multiple feedback loops, which collectively define the dynamics of cholesterol homeostasis. However, to date no model has specifically investigated the effects aging has on this system. This work addresses this shortcoming by explicitly focusing on the impact of aging on hepatic intracellular cholesterol homeostasis. The model was used to investigate the experimental findings that reactive oxygen species induce the total activation of 3-hydroxy-3-methylglutaryl-coenzyme A (HMG-CoA) reductase (HMGCR). Moreover, the model explored the impact of an age-related decrease in hepatic acetyl-CoA acetyltransferase 2 (ACAT2). The model suggested that an increase in the activity of HMGCR does not have as significant an impact on cholesterol homeostasis as a decrease in hepatic ACAT2 activity. According to the model, a decrease in the activity of hepatic ACAT2 raises free cholesterol (FC) and decreases low-density lipoprotein cholesterol (LDL-C) levels. Increased acetyl CoA synthesis resulted in a reduction in the number of hepatic low-density lipoprotein receptors, and increased LDL-C, FC, and cholesterol esters. The rise in LDL-C was restricted by elevated hepatic FC accumulation. Taken together these findings have important implications for healthspan. This is because emerging clinical data suggest hepatic FC accumulation is relevant to the pathogenesis of non-alcoholic fatty liver disease (NAFLD), which is associated with an increased risk of CVD. These pathophysiological changes could, in part, help to explain the phenomenon of increased mortality associated with low levels of LDL-C which have been observed in certain studies involving the oldest old (≥85 years).

Asymptotic analysis of a mathematical model of the atherosclerosis development

A mathematical model, which takes into account new experimental results about diverse roles of macrophages in the atherosclerosis development, is proposed. Using technic of upper and lower solutions, the existence and uniqueness of its positive solution are justified. After the nondimensionalization, small parameters are found and the multiscale analysis of the corresponding perturbed problem is performed when those parameters tend to zero. In particular, the limit two-dimensional problem, which is a coupled system of reaction–diffusion equations and ordinary differential equations, is derived; the asymptotic approximation is constructed; the uniform pointwise estimate for the difference between the solution of the original problem and the solution of the limit problem as well as the respective [Formula: see text]-estimates for the fluxes are proved.

Computational analysis of coupled blood-wall arterial LDL transport

The transport of macromolecules, such as low density lipoproteins (LDLs), across the artery wall and their accumulation in the wall is a key step in atherogenesis. Our objective was to model fluid flow within both the lumen and wall of a constricted, axisymmetric tube simulating a stenosed artery, and to then use this flow pattern to study LDL mass transport from the blood to the artery wall. Coupled analysis of lumenal blood flow and transmural fluid flow was achieved through the solution of Brinkman's model, which is an extension of the Navier-Stokes equations for porous media. This coupled approach offers advantages over traditional analyses of this problem, which have used possibly unrealistic boundary conditions at the blood-wall interface; instead, we prescribe a more natural pressure boundary condition at the adventitial vasa vasorum, and allow variations in wall permeability due to the occurrence of plaque. Numerical complications due to the convection dominated mass transport process (low LDL diffusivity) are handled by the streamline upwind/Petrov-Galerkin (SUPG) finite element method. This new fluid-plus-porous-wall method was implemented for conditions typical of LDL transport in a stenosed artery with a 75 percent area reduction (Peclet number=2 x 10(8)). The results show an elevated LDL concentration at the downstream side of the stenosis. For the higher Darcian wall permeability thought to occur in regions containing atheromatous lesions, this leads to an increased transendothelial LDL flux downstream of the stenosis. Increased transmural filtration in such regions, when coupled with a concentration-dependent endothelial permeability to LDL, could be an important contributor to LDL infiltration into the arterial wall. Experimental work is needed to confirm these results.

Effect of endothelial integrity, transmural pressure, and time on the intimal-medial uptake of serum 125I-albumin and 125I-LDL in an in vitro porcine arterial organ-support system

This report describes a new in vitro, metabolically supported, Sinclair Research Farm minipig aortic preparation in which the intimal-medial uptakes (M, mg.cm-2 of intimal surface) of porcine 125I-albumin and normocholesterolemic (nonoxidized) porcine 125I-low density lipoprotein (LDL) from a stirred, autogenous serum (containing a 125I-protein concentration of c0, mg.cm-3 at 37 degrees C and pH 7.4) were studied as functions of transmural pressure (0 < or = P < or = 150 mm Hg), time (30 < or = t < or = 120 minutes), and endothelial integrity. The following new observations were made: 1) The normalized transendothelial uptakes (M/c0, cm) of both albumin and LDL across normal intact aortic endothelial surfaces were insensitive to P. This indicated that these macromolecular solutes were not readily convected across the normal aortic endothelial surface despite increasing P. 2) However, the associated transendothelial M/c0 versus t relations for the normal intact surfaces were shown to increase monotonically with t in a manner consistent with a simple diffusive transport across a large surface barrier into the subjacent media, either with (Cases 2A and 2B) or without (Case 1) an associated transmural water convection. 3) The shapes of these temporal M/c0 curves of albumin and LDL were virtually the same; however, the magnitude of the albumin M/c0 curve was about sevenfold greater than that of LDL. 4) The M/c0 across the injured endothelial surface (Case 2C) not only increased monotonically with t but also increased significantly with P, indicating that in the absence of a normal endothelial surface, a very large convective component was added to the transport processes across the exposed aortic endothelial basement membrane and internal elastica. We conclude that: 1) the normal porcine aortic endothelial surface can provide a virtually complete barrier to the transendothelial convective transport of both albumin and LDL, 2) the diffusive barrier of the normal endothelial surface to LDL was sevenfold greater than that to albumin, 3) loss of the endothelial cell layer was associated with a threefold increase in the (P = 0) diffusive intimal-medial uptake of serum albumin in contrast to an eightfold increase in the pressurized (P = 150 mm Hg) combined diffusive-convective intimal-medial albumin uptake in the same vessel.