Numerical modeling and simulation of arterial walls

Stent surgery and balloon angioplasty are standard treatments for ateriosclerotic arteries. The treatment of arteriosclerosis by a balloon angioplasty and also the placement of a stent involves large deformations of the arterial walls. The numerical simulation of these large deformations is a challenging task which involves many computational state of the art techniques. Numerical methods for anisotropic, almost incompresible nonlinear hyperelastic elasticity models are developed including apropriate finite elment discretizations, robust nonlinear solvers and highly parallizable domain decomposition methods. Joint work with Prof. Dr.-Ing. Jörg Schröder, Institute for Mechanics, Abt. Bauwissenschaften, Fakultät für Ingenieurwissenschaften, Universität Duisburg-Essen, Prof. Dr. Oliver Rheinbach, Institut für Numerische Mathematik und Optimierung, TU Freiberg, and Prof. Dr. med. Raimund Erbel, Westdeutsches Herzzentrum, Universiätsklinik Essen.

_{Stress in an arterial wall. See D. Balzani, D. Böse, D. Brands, R. Erbel, A. Klawonn, O. Rheinbach, J. Schröder Engineering Computations, Vol. 29 No. 8, pp. 888-906 (2012).}