Real-time whole-heart electromechanical simulations using Latent Neural
  Ordinary Differential Equations
Matteo Salvador Marina Strocchi Francesco Regazzoni Luca Dede' Steven Niederer Alfio Quarteroni
Cardiac digital twins provide a physics and physiology informed framework to
deliver predictive and personalized medicine. However, high-fidelity
multi-scale cardiac models remain a barrier to adoption due to their extensive
computational costs and the high number of model evaluations needed for
patient-specific personalization. Artificial Intelligence-based methods can
make the creation of fast and accurate whole-heart digital twins feasible. In
this work, we use Latent Neural Ordinary Differential Equations (LNODEs) to
learn the temporal pressure-volume dynamics of a heart failure patient. Our
surrogate model based on LNODEs is trained from 400 3D-0D whole-heart
closed-loop electromechanical simulations while accounting for 43 model
parameters, describing single cell through to whole organ and cardiovascular
hemodynamics. The trained LNODEs provides a compact and efficient
representation of the 3D-0D model in a latent space by means of a feedforward
fully-connected Artificial Neural Network that retains 3 hidden layers with 13
neurons per layer and allows for 300x real-time numerical simulations of the
cardiac function on a single processor of a standard laptop. This surrogate
model is employed to perform global sensitivity analysis and robust parameter
estimation with uncertainty quantification in 3 hours of computations, still on
a single processor. We match pressure and volume time traces unseen by the
LNODEs during the training phase and we calibrate 4 to 11 model parameters
while also providing their posterior distribution. This paper introduces the
most advanced surrogate model of cardiac function available in the literature
and opens new important venues for parameter calibration in cardiac digital
twins.