  We propose an integrated electromechanical model of the human heart, with
focus on the left ventricle, wherein biophysically detailed models describe the
different physical phenomena concurring to the cardiac function. We model the
subcellular generation of active force by means of an Artificial Neural
Network, which is trained by a suitable Machine Learning algorithm from a
collection of pre-computed numerical simulations of a biophysically detailed,
yet computational demanding, high-fidelity model. To provide physiologically
meaningful results, we couple the 3D electromechanical model with a closed-loop
0D (lumped parameters) model describing the blood circulation in the whole
cardiovascular network. We prove that the 3D-0D coupling of the two models is
compliant with the principle of energy conservation, which is achieved in
virtue of energy-consistent boundary conditions that account for the
interaction among cardiac chambers within the computational domain, pericardium
and surrounding tissue. We thus derive an overall balance of mechanical energy
for the 3D-0D model. This provides a quantitative insight into the energy
utilization, dissipation and transfer among the different compartments of the
cardiovascular network and during different stages of the heartbeat. In virtue
of this new model and the energy balance, we propose a new validation tool of
heart energy usage against relationships used in the daily clinical practice.
Finally, we provide a mathematical formulation of an inverse problem aimed at
recovering the reference configuration of one or multiple cardiac chambers,
starting from the stressed configuration acquired from medical imaging. This is
fundamental to correctly initialize electromechanical simulations. Numerical
methods and simulations of the 3D-0D model will be detailed in Part II.
