Numerical solution of an active strain formulation for the electromechanical activity in the heart
Wednesday 9th June 2010
Nobile, Fabio; Quarteroni, Alfio; Ruiz Baier, Ricardo
We propose a finite element method for solving a system of equations describing the coupling between cardiac mechanics and electrical signalling. The model is based on a multiplicative decomposition of the deformation tensor into a passive and active part, the latter carrying the information of the electrical potential propagation and anisotropy of the cardiac tissue into the equations of incompressible or nearly incompressible nonlinear elasticity, governing the mechanical response of the biological material. Moreover, by changing from an Eulerian to a Lagrangian configuration, the underlying problem exhibits a nonlinear diffusion term in the equations of the electrical propagation (namely, the bidomain and monodomain equations). Piecewise quadratic finite elements are used to approximate the displacements field, while for pressure, electrical potentials and ionic variables, we use piecewise linear elements. Various test cases show that the proposed method is able to capture some important features of the studied phenomenon, and illustrate the behavior of the global model.