A monolithic algorithm for the simulation of cardiac electromechanics in the human left ventricle
Monday 16th October 2017
Gerbi, A.; Dede', L.; Quarteroni, A.
In this paper, we propose a monolithic algorithm for the numerical solution of an electromechanics model of the left ventricle in the human heart. We consider the monodomain equation together with the Bueno-Orovio minimal ionic model for the description of the electrophysiology and the Holzapfel-Ogden strain energy function within the active strain framework for the mechanics of the myocardium. For the latter, we use for the first time in the context of electromechanics a transmurally variable active strain formulation. The Finite Element Method is used for the space discretization, while Backward Differentiation Formulas are used for the time discretization. Both implicit and semi-implicit schemes are addressed in this paper: the Newton method is used to solve the nonlinear system arising in the implicit scheme, while the semi-implicit scheme (corresponding to extrapolation of nonlinear terms from previous timesteps) yields a linear problem at each timestep. In the latter case, stability constraints may pose limitations in the timestep size. Much emphasis is laid into on the preconditioning strategy, which is based on the factorization of a block Gauss-Seidel preconditioner combined with the use of parallel preconditioners for each of the single core models composing the full electromechanics model. This monolithic preconditioner can be easily extended to cases where other ionic models are adopted and, besides heart models, to other integrated problems arising in different multiphysics applications in engineering and applied sciences. Several numerical simulations are carried out in a high performance computing framework for both idealized and patient-specific left ventricle geometries. The latter are obtained from medical MRI images through suitable segmentation procedures to generate the computational mesh. Personalized pressure-volume loops are produced by means of the computational procedure and used to synthetically interpret and analyze the outputs of the electromechanics model.