Mathematical Modeling and Numerical Simulation of Atherosclerosis
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This paper presents a mathematical model and its numerical implementation to analyze the progression of atherosclerosis, a common vascular disease that manifests in abnormal thickening of the artery wall. The model materializes the so-called outside-in paradigm, where the pathology is rooted in the malfunctioning of vasa vasorums, the micro blood vessels responsible for artery wall nourishment. Said malfunction drives an inflammatory response that leads to overgrowth and wall thickening, ultimately resulting in a stenosis that narrows the lumen. The inflammatory response also induces abnormal mechanical stresses in the wall and triggers ordinary growth and remodelling mechanisms toward maintaining tissue stress homeostasis. The balance between inflammation and stress-regulated growth then determines the development of atherosclerosis. This work uses a phase-field approach that describes the propagation of tissue inflammation, strongly coupled to the mechanical description of the problem. The model is based on a fully three-dimensional finite deformation description and accounts for anisotropic tissue growth. AceGen, a symbolic and automatic differentiation tool, supported model development and resulted in a numerical FORTRAN subroutine invoked by ANSYS. Several numerical examples show the versatility and robustness of the description and provide new insights of how atherosclerosis might progress.
