A spatially resolved and quantitative model of early atherosclerosis
In the prevention and medical treatment of atherosclerosis -- a chronic inflammatory vascular disease of the artery wall which could cause a stroke or myocardial infarction, a decisive step is to predict whether early the atherosclerotic plaques continue to grow, stagnate or become regressive. The authors develop a spatially resolved and quantitative mathematical model of key contributors of early atherosclerosis. The stability of atherosclerotic plaques is assessed on some measurable or computable in vivo inputs such as blood cholesterol concentrations or wall shear stresses. The model uses Darcy's law for the transmural flow through vessel walls and the Kedem-Katchalsky equations for endothelial fluxes of lipoproteins and a novel submodel for macrophage recruitment. A broad spectrum of models of various aspects of atherosclerosis has been created over recent decades. A comprehensive overview of the existing models of atherosclerosis is given in the review by \textit{A. Parton}, \textit{V. McGilligan}, \textit{M. O' Kane}, \textit{F. R. Baldrick} and \textit{S. Watterson} [``Computational modelling of atherosclerosis'', Briefings Bioinform. 17, No. 4, 562--575 (2016; \url{doi:10.1093/bib/bbv081})]. The formation of early atherosclerotic plaques is modeled and quantified in a previous work of the present authors [\textit{M. P. Thon} et al., Bull. Math. Biol. 80, No. 1, 175--214 (2018; Zbl 1385.92027)]. In that publication, a parameterized set of ordinary differential equations (ODEs) was developed that predicts key inflammatory and lipid processes of early atherosclerosis. The established ODE model is able to predict the stability of early model plaques based on the recruitment of LDL, HDL and macrophages. The present model is the first to provide a complete predictive parameter set for all those key processes of early atherosclerosis. The structure of this work is as follows: In Section 2, before the spatially resolved model is established, submodels of the recruitment of macrophages as well as of the fluxes of LDL and HDL are developed. Section 3 gives a complete parameter set for the models and all computational results derived from them. The result is critically assessed and discussed in Section 4. Supporting details are given in Appendix A and Appendix B.
scientific article; zbMATH DE number 7135703
scientific article