title: A fully implicit finite element method for bidomain models of cardiac electromechanics.
abstract: We propose a novel, monolithic, and unconditionally stable finite element algorithm for the bidomain-based approach to cardiac electromechanics. We introduce the transmembrane potential, the extracellular potential, and the displacement field as independent variables, and extend the common two-field bidomain formulation of electrophysiology to a three-field formulation of electromechanics. The intrinsic coupling arises from both excitation-induced contraction of cardiac cells and the deformation-induced generation of intra-cellular currents. The coupled reaction-diffusion equations of the electrical problem and the momentum balance of the mechanical problem are recast into their weak forms through a conventional isoparametric Galerkin approach. As a novel aspect, we propose a monolithic approach to solve the governing equations of excitation-contraction coupling in a fully coupled, implicit sense. We demonstrate the consistent linearization of the resulting set of non-linear residual equations. To assess the algorithmic performance, we illustrate characteristic features by means of representative three-dimensional initial-boundary value problems. The proposed algorithm may open new avenues to patient specific therapy design by circumventing stability and convergence issues inherent to conventional staggered solution schemes.
authors.affiliation: Department of Mechanical and Process Engineering, ETH Zurich, Zurich, Switzerland ; Institute for Structural Analysis, Technische Universität Dresden, Dresden, Germany ; Institut für Mechanik, (Bauwesen), Lehrstuhl I, Universität Stuttgart, Germany.
authors.forename: Hüsnü
authors.initials: H
authors.lastname: Dal
authors.forename: Serdar
authors.initials: S
authors.lastname: Göktepe
authors.forename: Michael
authors.initials: M
authors.lastname: Kaliske
authors.forename: Ellen
authors.initials: E
authors.lastname: Kuhl