Published online in Wiley Online Library (wileyonlinelibrary.com). DOI: 10.1002/cnm.2565 SPECIAL ISSUE PAPER- NUMERICAL METHODS AND APPLICATIONS OF MULTI-PHYSICS IN BIOMECHANICAL MODELING Computational modeling of chemo-electro-mechanical coupling:

Computational modeling of the human heart allows us to predict how chemical, electrical, and mechani-cal fields interact throughout a cardiac cycle. Pharmacological treatment of cardiac disease has advanced significantly over the past decades, yet it remains unclear how the local biochemistry of an individual heart cell translates into global cardiac function. Here, we propose a novel, unified strategy to simulate excitable biological systems across three biological scales. To discretize the governing chemical, electrical, and mechanical equations in space, we propose a monolithic finite element scheme. We apply a highly effi-cient and inherently modular global–local split, in which the deformation and the transmembrane potential are introduced globally as nodal degrees of freedom, whereas the chemical state variables are treated locally as internal variables. To ensure unconditional algorithmic stability, we apply an implicit backward Euler finite difference scheme to discretize the resulting system in time. To increase algorithmic robustness and guarantee optimal quadratic convergence, we suggest an incremental iterative Newton–Raphson scheme. The proposed algorithm allows us to simulate the interaction of chemical, electrical, and mechanical field