  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 those partial differential equations that contribute
to the model. 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.
