We propose a novel whole-heart electromechanical model including atrial contraction • Unprecedented match with healthy cardiac physiology • Physiological atrial eight-shaped pressure-volume loops • Fibers-stretch-rate feedback essential to avoid unphysiologically large fluxes • Crucial interplay among accurate mathematical models and stable numerical methods

We propose a mathematical and numerical model for the simulation of the heart function that couples cardiac electrophysiology, active and passive mechanics and hemodynamics, and includes reduced models for cardiac valves and the circulatory system. Our model accounts for the major feedback effects among the different processes that characterize the heart function, including electro‐mechanical and mechano‐electrical feedback as well as force‐strain and force‐velocity relationships. Moreover, it provides a three‐dimensional representation of both the cardiac muscle and the hemodynamics, coupled in a fluid–structure interaction (FSI) model. By leveraging the multiphysics nature of the problem, we discretize it in time with a segregated electrophysiology‐force generation‐FSI approach, allowing for efficiency and flexibility in the numerical solution. We employ a monolithic approach for the numerical discretization of the FSI problem. We use finite elements for the spatial discretization of partial differential equations. We carry out a numerical simulation on a realistic human left heart model, obtaining results that are qualitatively and quantitatively in agreement with physiological ranges and medical images.

We review and compare different fluid-structure interaction (FSI) numerical methods in the context of heart modeling, aiming at assessing their computational efficiency for cardiac numerical simulations and selecting the most appropriate method for heart FSI. Blood dynamics within the human heart is characterized by active muscular action, during both contraction and relaxation phases of the heartbeat. The efficient solution of the FSI problem in this context is challenging, due to the added-mass effect (caused by the comparable densities of fluid and solid, typical of biomechanics) and to the complexity, nonlinearity and anisotropy of cardiac consitutive laws. In this work, we review existing numerical coupling schemes for FSI in the two classes of strongly-coupled partitioned and monolithic schemes. The schemes are compared on numerical tests that mimic the flow regime characterizing the heartbeat in a human ventricle, during both systole and diastole. Active mechanics is treated in both the active stress and active strain frameworks. Computational costs suggest the use of a monolithic method. We employ it to simulate a full heartbeat of a human ventricle, showing how it allows to efficiently obtain physiologically meaningful results.

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