Theoretical models for transport of low-density lipoproteins 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.

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.

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

Experimental data of the radial incorporation of labeled cholesterol [14C-4] into the artery wall is regressed against a mathematical model that predicts macromolecular transport in this biological system. Data is obtained using excised canine carotid arteries that are perfused in vitro under pulsatile hemodynamic conditions for 2 hr. Vessels are exposed to either normotensive hemodynamics, hypertensive hemodynamics, or simulations in which the rate of flow or vessel compliance is deliberately altered. Several arteries are studied under normotensive conditions following balloon catheter deendothelialization. Transmural concentration profiles of [14C-4] activity are determined by microcryotomy of longitudinal sections of perfused vessels. Nonlinear Marquardt regression on 12 experimental cases yields parameter estimates of effective diffusivity, D and solute filtration velocity, V. Results of this experimental investigation support our hypothesis that hemodynamics and the endothelial lining influence wall flux in intact vessels. Exposure to altered (vs normotensive) hemodynamics is associated with increased incorporation of labeled cholesterol. A similar observation is made for deendothelialized vessels (e.g. a greater accumulation of label and a rise in convective flux). Based upon our companion measurements of vessel wall forces and endothelial cellular morphology accompanying hemodynamic simulations, we suggest that hemodynamically induced alterations to endothelial structures lead to the increased permeability, convection and incorporation that we observe in this work.