Abstract
Atherosclerosis is a chronic disease which involves the build up of cholesterol and fatty deposits within the inner lining of the artery. It is associated with a progressive thickening and hardening of the arterial wall that result in narrowing of the vessel lumen and restriction of blood flow to vital organs. These events may cause heart attack or stroke, the commonest causes of death worldwide. In this paper we study the early stages of atherosclerosis via a mathematical model of partial differential equations of reaction-diffusion type. The model includes several key species and identifies endothelial hyperpermeability, believed to be a precursor on the onset of atherosclerosis. For simplicity, we reduce the system to a monotone system and provide a biological interpretation for the stability analysis according to endothelial functionality. We investigate as well the existence of solutions of traveling waves type along with numerical simulations. The obtained results are in good agreement with current biological knowledge. Likewise, they confirm and generalize results of mathematical models previously performed in literature. Then, we study the non monotone reduced model and prove the existence of perturbed solutions and perturbed waves, particularly in the bistable case. Finally, we extend the study by considering the complete model proposed initially, perform numerical simulations and provide more specific results. We study the consistency between the reduced and complete model analysis for a certain range of parameters, we elaborate bifurcation diagrams showing the evolution of inflammation upon endothelial permeability and LDL accumulation and we consider the effect of anti-inflammatory process on the system behavior. In this model, the regulation of atherosclerosis progression is mediated by anti-inflammatory responses that, up to certain extent, lead to plaque regression.
Highlights
Some other factors have emerged as key regulators of many endothelial cell functions, including barrier function, which are deregulated during atherogenesis, such as high-density lipoproteins (HDLs) [55] and nitric oxide (NO) [54]
This work is devoted to the mathematical modeling of atherosclerosis
It provides an initial model that describes the anti and pro-inflammatory processes arising during the atherogenesis through partial differential equations of reaction-diffusion type
Summary
Atherosclerosis is a chronic cardiovascular disease of the arterial wall that involves immunoinflammatory mechanisms as a response to abnormal cholesterol deposits in the inner layers of arteries. Atherosclerotic lesions develop in the coronary, cerebral, and peripheral arteries and the aorta and restrict the blood flow to vital organs. The history of atherosclerosis dates back to ancient times when its early description was considered to be the restriction of the transit of blood through thickening of the vessels This conveys to the etymology of the term atherosclerosis derived from the Greek words athero, meaning gruel, or paste, corresponding to the accumulation of fatty material in the central core of the plaque, and the term sclerosis, meaning thickening of the intimal layer of arteries [50]. A deeper understanding of molecular mechanisms of atherosclerosis contributes to explore more effective preventive and therapeutic targets
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