Mechanical and Biochemical Simulations of Atherosclerosis*

Atherosclerosis is a disease considered to be one of the leading causes of death. Understanding the behavior and dynamics of the vessel wall before and after atherosclerosis has been a motivation for many studies.
We investigate this phenomenon as a combination of mechanical deformation of the vessel wall along with the cell and chemical dynamics that happen inside of it.
We consider the vessel wall as a growing hyperelastic material with three layers, each having a different set of mechanical properties. To describe tissue growth we use morphoelasticity as the mathematical framework. To include the stiffening effect of collagen fibers we employ a Holzapfel-Gasser-Ogden anisotropic strain energy function.
In addition, we explore the distribution of oxidized lipids, macrophages, foam cells, oxygen and necrotic cells in the intima at each growth step via a system of PDEs.
All numerical simulations are carried out via the finite element method on the FENICS framework.
Altogether, this allows us to observe intimal thickening as a result of vessel growth along with histological changes within the wall such as the development of necrotic zones. Our simulations show results similar to the images acquired from ultrasounds scans.