Steady State Solution and Its Stability Analysis of a Reaction-Diffusion Mathematical Model for LDL, Lipoprotein(a), and CRP in Atherosclerosis

Abstract

This study presents a reaction-diffusion mathematical model to investigate the spatiotemporal dynamics of low-density lipoprotein (LDL), lipoprotein(a), and C-reactive protein (CRP) within the arterial wall, key mediators in the pathogenesis of atherosclerosis and related cardiovascular diseases. The model employs a system of partial differential equations to capture both the diffusion of these biomolecules and their biochemical interactions, including LDL oxidation, CRP-mediated inflammatory responses, and plaque initiation. Numerical simulations, implemented using the finite difference method, demonstrate that CRP substantially accelerates LDL oxidation and promotes plaque deposition, particularly in regions of locally elevated lipoprotein concentrations. Furthermore, the results indicate that elevated CRP levels synergistically enhance the pro-atherogenic effects of LDL and lipoprotein(a), highlighting the critical role of inflammation in plaque progression. These findings underscore the potential of anti-inflammatory therapeutic strategies, alongside lipid-lowering interventions, in mitigating atherosclerotic risk. The proposed model provides a robust computational framework for elucidating the interactive effects of lipid metabolism and vascular inflammation in the progression of cardiovascular disease.