Mathematical Modelling of the Effects of Statins on the Growth of Necrotic Core in Atherosclerotic Plaque

Abstract

A large necrotic core increases the risk of atherosclerotic plaque instability. Statins can delay the growth of necrotic core in plaques, but the kinetic mechanism of statins in slowing down the necrotic core has not yet been addressed in detail. In this paper, a mathematical model is governed by a system of advection-diffusion-reaction equations coupling of the porous nature of vessel wall is established and applied to illustrate the plaque growth with lipid-rich necrotic core (LRNC) with and without statins using finite element method. We study the influence of LRNC plaque growth for different drug concentrations at different time intervals. The results showed that the drug use at different time points has a significant impact on the treatment efficacy. Compared with  short-term, low-dose treatment, early statin treatment with high dose showed more pronounced effects on reducing the low-density lipoprotein (LDL) cholesterol, decreasing the volume of necrotic core, changing the characteristics of plaques, and improving the plaque stability. The model is validated by comparing with the clinical data, and may be used to predict the progression of LRNC plaque and the effects of statin therapy.