Towards a computational laboratory for the numerical simulation of arterial wall models
mit Prof. Dr. Axel Kawonn, Duisburg-Essen

17 Uhr, Alexander von Humboldt-Haus, Hüfferstraße 61, Münster
www.sfbmobil.de

Cardiovascular diseases are the prime cause of death in the Western World. Arteriosclerotic plaques may lead to an obstruction of the blood flow and can cause heart attacks and strokes. Balloon dilation and stenting are established treatments to dilate the artery and keep it open. Nowadays, the two traditional principles of science, theory and experiment, are complemented by numerical simulations as a third principle. Simulations of the process of balloon dilation may help to gain medical insight. In a current research project in Essen anatomical and physiological data of the arterial wall necessary for such simulations are obtained from ultrasound imaging. The treatment of arteriosclerosis by a ballon angioplasty 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. In this talk, a computational framework for the numerical simulation of large elastic deformations is presented.

The mechanical behavior of arterial walls in the physiological range can be described by nonlinear anisotropic hyperelastic models. Different models are considered and each of them is represented by a polyconvex strain energy function in order to guarantee the existence of minimizers. The discretization of these three dimensional models by the finite element method usually results in a large number of equations with up to several million degrees of freedom. The solution of such large systems requires efficient state of the art solvers which are suitable for parallel computers. Dual-primal FETI methods are among the most severely tested domain decomposition methods for the solution of partial differential equations on parallel computers. A computational framework using a Newton-Krylov-FET approach for the solution of the discretized models will be discussed and applied to different material wall models and geometries. The arterial geometries are obtained by intravascular ultrasound (IVUS) and virtual histology. Material parameters obtained by tension tests are considered.

This presentation is based on joint work with Dr. Oliver Rheinbach, Faculty of Mathematics, University of Duisburg-Essen, Prof. Dr.-Ing. Jörg Schröder, Dipl.-Ing. Dominik Brands, Dipl.-Ing. Sarah Brinkhues, Institute of Mechanics, Division of Civil Engineering, Faculty of Engineering, University of Duisburg-Essen, and Prof. Dr. med. Raimund Erbel, Dr. med. Dirk Böse, West-German Heart Center, Essen, University of Duisburg-Essen. The support by the Deutsche Forschungsgemeinschaft is gratefully acknowledged.