A Numerical Study of Scalable Cardiac Electro-Mechanical Solvers on HPC Architectures

Abstract

We introduce and study some scalable domain decomposition preconditioners for cardiac electro-mechanical 3D simulations on parallel HPC (High Performance Computing) architectures. The electro-mechanical model of the cardiac tissue is composed of four coupled sub-models: (1) the static finite elasticity equations for the transversely isotropic deformation of the cardiac tissue; (2) the active tension model describing the dynamics of the intracellular calcium, cross-bridge binding and myofilament tension; (3) the anisotropic Bidomain model describing the evolution of the intra- and extra-cellular potentials in the deforming cardiac tissue; and (4) the ionic membrane model describing the dynamics of ionic currents, gating variables, ionic concentrations and stretch-activated channels. This strongly coupled electro-mechanical model is discretized in time with a splitting semi-implicit technique and in space with isoparametric finite elements. The resulting scalable parallel solver is based on Multilevel Additive Schwarz preconditioners for the solution of the Bidomain system and on BDDC preconditioned Newton-Krylov solvers for the non-linear finite elasticity system. The results of several 3D parallel simulations show the scalability of both linear and non-linear solvers and their application to the study of both physiological excitation-contraction cardiac dynamics and re-entrant waves in the presence of different mechano-electrical feedbacks.

TheopenCARPSimulation Environment for Cardiac Electrophysiology

“…Preceding initiatives in this vein include openCMISS [12] and Chaste [50], but their success has been mixed so far, as their rate of adoption has been rather marginal. Reasons are multifactorial: For groups developing numerical methods, there is limited demand as they have the capability to build custom tailored frameworks themselves [17,[51][52][53][54][55] that facilitate the implementation of disruptive changes at any time, without the frictional losses involved in community projects where changes have to be agreed upon by various stakeholders. This is in stark contrast to the demands within the applied CEP modeling community.…”

3D-0D closed-loop model for the simulation of cardiac biventricular electromechanics

“…Our 3D-0D model is composed of four core models supplemented by a suitable coupling condition between the 3D and the 0D model. The core models are related to the different interplaying physical processes (at the molecular, cellular, tissue and organ levels) involved in the heart pumping function: cardiac electrophysiology (E ) [17,75,76,77], cardiomyocytes active contraction (A ) [19,78,79,80,81,82], tissue mechanics (M ) [83,84,85,86] and blood circulation (C ) [15,25,28,29,42,43,87]. The coupling condition is established by the volume conservation constraints (V ) [15].…”

Scalable Newton-Krylov-BDDC and FETI-DP Deluxe Solvers for Decoupled Cardiac Reaction-Diffusion Models

“…So far, operator splitting strategies [2,22] or semi-implicit time discretizations [3,25] have been widely preferred to fully implicit ones [15], as the latter are computationally very expensive if the electrical model is coupled with very stiff and high-dimensional non-linear system of ODEs [12,23]. In the same fashion as in previous works of some of the Authors [13,14,21] (where overlapping Schwarz preconditioners were considered) we propose here a solution approach based on the decoupling of the two models: the ODEs system is solved first, then the non-linear problem arising from the implicit time discretization of the Bidomain system is solved and updated.…”

“…Thus far, BDDC algorithms have been applied to semi-implicit time discretizations of the Bidomain model (see e.g. [25]), while Newton-Krylov-BDDC solvers have been developed for the non-linear system arising from the discretization of finite elasticity equations modelling the mechanical contraction and relaxation of the cardiac muscle [3,16].…”