Segregated algorithms for the numerical simulation of cardiac electromechanics in the left human ventricle
Thursday 26th April 2018
Gerbi, A.; Dede', L.; Quarteroni, A.
In this paper, we propose and numerically assess three segregated algorithms for the numerical solution of the coupled electromechanics problem for the left human ventricle. We split the coupled problem into its core mathematical models and we proceed to their numerical approximation. Space and time discretizations of the core problems are carried out by means of the Finite Element Method and Backward Differentiation Formulas, respectively. In our mathematical model, electrophysiology is represented by the monodomain equation while the Holzapfel-Ogden strain energy function is used for the passive characterization of tissue mechanics. A transmurally variable active strain model is used for the active deformation of the fibers of the myocardium to couple the electrophysiology and the mechanics in the framework of the active strain model. In this work we focus on the numerical strategy to deal with the solution of the coupled model, which is based on novel segregated algorithms that we propose. These also allow using different time discretization schemes for the core submodels, thus leading to the formulation of staggered algorithms, a feature that we sistematically exploit to increase the overall efficiency of the computational procedure. We assess the accuracy of these segregated algorithms, measured by means of numerical tests, which exhibit at least first order of accuracy. We take advantage of the efficiency of the segregated schemes to solve, in an High Performance Computing framework, the cardiac electromechanics problem for the human left ventricle, for both idealized and subject-specific configurations.