Mathematical Modeling Of Atherosclerotic Plaque Progression

Observational studies have identified that several important processes are involved in the development of atherosclerotic plaques,including lipid deposition,inflammatory response,angiogenesis,and intraplaque hemorrhage caused by the leaky neovessels.Here we propose the first mathematical model incorporating intraplaque neovascularization and hemodynamic calculation with plaque destabilization for the quantitative evaluation of the role of neoangiogenesis and IPH in the vulnerable atherosclerotic plaque formation.An angiogenic microvasculature is generated by two-dimensional nine-point discretization of endothelial cell proliferation and migration from the vasa vasorum.Three key cells(endothelial cells,macrophages and smooth muscle cells)and three key chemicals(VEGF,MMP,ECM)are involved in the plaque progression model,and described by the reaction-diffusion partial differential equations.The hemodynamic calculation of the microcirculation on the generated microvessel network is carried out by coupling the intravascular,interstitial and transvascular flow.The plasma concentration in the interstitial domain is defined as the description of IPH area according to the diffusion and convection with the interstitial fluid flow,as well as the extravascular movement across the leaky vessel wall.The simulation results demonstrate a series of pathophysiological phenomena during the vulnerable progression of an atherosclerotic plaque,including the expanding necrotic core,the exacerbated inflammation,the high microvessel density(MVD)region at the shoulder areas,the transvascular flow through the capillary wall and the IPH.The important role of IPH in the plaque destabilization is evidenced by simulations with varied model parameters.It is found that the IPH can significantly speed up the plaque vulnerability by increasing necrotic core and thinning fibrous cap.In addition,the decreased MVD and vessel permeability may slow down the process of plaque destabilization by reducing the IPH dramatically.Afterwords,we propose a multiphysical mathematical model by fully coupling lipid deposition,monocytes/macrophages recruitment and angiogenesis to investigate the pathophysiological responses of an atherosclerotic plaque to the dynamic changes in the microenvironment.The time evolutions of cellular and acellular components within the plaque microenvironment are assessed quantitatively and the comparisons of the simulation results with the MRI and histology data show a good consistency.Models with and without angiogenesis are compared to demonstrate the important role of neovasculature in the accumulation of ox-LDL and macrophages in the atherosclerotic lesion,leading to the formation of a lipid core and an inflammatory microenvironment,which eventually results in plaque destabilization.This model can serve as a theoretical platform for the investigation of the pathological mechanisms of plaque progression and may contribute to the optimal design of atherosclerosis treatment strategies,such as lipid-lowering or anti-angiogenetic therapies.