A fully implicit finite element method for bidomain models of cardiac electromechanics


Dal H. , Goektepe S. , Kalıske M., Kuhl E.

COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING, vol.253, pp.323-336, 2013 (Journal Indexed in SCI) identifier identifier identifier

  • Publication Type: Article / Article
  • Volume: 253
  • Publication Date: 2013
  • Doi Number: 10.1016/j.cma.2012.07.004
  • Title of Journal : COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING
  • Page Numbers: pp.323-336
  • Keywords: Electromechanics, Bidomain model, Finite element method, Coupled problems, Monolithic, Cardiac mechanics, REACTION-DIFFUSION SYSTEMS, KRYLOV-SCHWARZ METHOD, MULTIGRID PRECONDITIONER, ACTIVE CONTRACTION, PHYSIOME PROJECT, BEATING HEART, 3 DIMENSIONS, IN-VIVO, ELECTROCARDIOLOGY, EQUATIONS

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. (C) 2012 Elsevier B.V. All rights reserved.