Electro-mechanical modeling and simulation of reentry phenomena in the presence of myocardial infarction

In this work we present a parallel solver for the numerical simulation of the cardiac electro-mechanical activity. We first review the most complete mathematical model of cardiac electro-mechanics, the so-called electro-mechanical coupling (EMC) model, which consists of the following four sub-models, strongly coupled together: the Bidomain model for the electrical activity at tissue scale, constituted by a parabolic system of two reaction-diffusion partial differential equations (PDEs); the finite elasticity system for the mechanical behavior at tissue scale; the membrane model for the bioelectrical activity at cellular scale, consisting of a stiff system of ordinary differential equations (ODEs); the active tension model for the mechanical activity at cellular scale, consisting of a system of ODEs. The discretization of the EMC model is performed by finite elements in space and an operator splitting strategy in time, based on semi-implicit finite differences. As a result of the discretization techniques adopted, the most computational demanding part at each time step is the solution of the non-linear algebraic system, deriving from the discretization of the finite elasticity equations, and of the linear system deriving from the discretization of the Bidomain equations. The former is solved by a Newton-GMRES-BDDC solver, i.e. the Jacobian system at each Newton iteration is solved by GMRES accelerated by the Balancing Domain Decomposition by Constraints (BDDC) preconditioner. The latter is solved by the Conjugate Gradient method, preconditioned by the Multilevel Additive Schwarz preconditioner. The performance of the resulting parallel solver is studied on the simulation of the induction of ventricular tachycardia in an idealized left ventricle affected by an infarct scar. The simulations are run on the Marconi-KNL cluster of the Cineca laboratory.