Impact of Segregation Scheme on Performance of a Strongly Coupled Electromechanical Solver

Abstract

Fully coupled cardiac electromechanics simulations have in the last few years become feasible on a tissue and organ scale. However, free and open-source tools for running these simulations are still limited. Furthermore, due to the high computational expense of coupling electrophysiology (EP) and mechanics, investigations into choice of coupling scheme is warranted. In this study, we investigate the effect of the selected coupling scheme on accuracy and run time, implemented in a freely accessible, open-source software, Simcardems.We used the monodomain model and the ToR-ORd-dynCI model to describe EP on a tissue and cellular scale, respectively. Mechanics was modeled using an active stress approach. To represent passive tissue we used a Holzapfel-Ogden model of a transversely isotropic material, whereas the Land model was used to represent active contraction. The EP and mechanics components were strongly coupled; each subsystem was solved separately and variables interpolated between them at each mechanics time step. This enabled the use of different temporal and spatial resolutions for EP and mechanics, reducing the computational cost considerably.Here, we implemented three different schemes of variable transfer between EP and mechanics, which we denoted Cai -, CaTRPN- and ζ's split. For each scheme, a different set of variables within the Land model were transferred between the EP and mechanics components of the model. We investigated how simulation time and error depended on the chosen scheme, as well as the selected temporal and spatial resolution of the mechanics mesh.The three segregation schemes required similar computation times, although the ζ's split resulted in the smallest computation errors. By increasing the time step and decreasing the mesh resolution for the mechanics system compared to EP, we achieved a major reduction in run time of our simulations: When increasing the mechanics time step from 0.05 to 0.5 ms with the ζ's split, we achieved an 80 % reduction in run time and only 0.35 % error in active tension with respect to the finest time step. On the spatial scale, a change of mechanics mesh resolution from dxmech = 0.25 mm to 0.5 mm resulted in a 90 % reduction in run time and an error of 0.04 % with respect to the finest mesh.We conclude that the ζ's split scheme - with the majority of active contraction parameters solved on the EP side - was the optimal of the investigated segregation schemes. Furthermore, through investigation of key variables and associated errors for various discretization approaches, our study represents an advancement in the development and verification of freely available electromechanical simulators.

Keywords: electro-mechanics, Finite Element Method, Cardiac modeling, Numerical analysis