Numerical approximation of reaction-diffusion-mechanics systems and applications in cardiac biomechanics

The Faculty of Informatics is pleased to announce a seminar given by Ricardo Ruiz Baier

DATE: Tuesday, April 28th 2015
PLACE: USI Lugano Campus, room A13, Red building (Via G. Buffi 13)
TIME: 09.30

ABSTRACT:
In this talk we address some aspects of an active-strain model for cardiac electromechanics. The governing equations consist on a finite elasticity problem describing macroscopic tissue contraction, a reaction-diffusion system written on a deformable domain and describing the electrophysiology of the beating heart, and a system of ODEs governing ionic activity and sub-cellular activation mechanisms.

We introduce a set of assumptions and modifications that permit us to derive existence and uniqueness of weak solutions to a linearized version of this coupled system. We continue with the convergence study of a classical finite element scheme and comment on possible extensions to the analysis.

Next we propose a new mixed-primal Galerkin approximation of general elasticity equations coupled with a nonlinear reaction-diffusion system. The formulation has the advantage that the strain is introduced as mixed variable in the equations of elastodynamics, which in turn acts as coupling field needed to update the diffusion of the modified reaction-diffusion system. This allows to approximate the additional field with the desired accuracy. We close with a few insightful numerical tests illustrating some features of the proposed methods, and that indicate how far the linearized problem is from the original nonlinear model.

BIO:

• Since 2014: SNSF senior researcher at Institut des Sciences de la Terre, University of Lausanne
• 2009-2012/2013: Postdoctoral fellow / Lecturer at EPFL
• 2008: PhD in Applied Mathematics, Universidad de Concepción, Chile

HOSTS: Prof. Rolf Krause and Prof. Olaf Schenk