A machine learning method for real-time numerical simulations of cardiac electromechanics

Abstract

We propose a machine learning-based method to build a system of differential equations that approximates the dynamics of 3D electromechanical models for the human heart, accounting for the dependence on a set of parameters. Specifically, our method permits to create a reducedorder model (ROM), written as a system of Ordinary Differential Equations (ODEs) wherein the forcing term, given by the right-hand side, consists of an Artificial Neural Network (ANN), that possibly depends on a set of parameters associated with the electromechanical model to be surrogated. This method is non-intrusive, as it only requires a collection of pressure and volume transients obtained from the full-order model (FOM) of cardiac electromechanics. Once trained, the ANN-based ROM can be coupled with hemodynamic models for the blood circulation external to the heart, in the same manner as the original electromechanical model, but at a dramatically lower computational cost. Indeed, our method allows for real-time numerical simulations of the cardiac function. Our results show that the ANN-based ROM is accurate with respect to the FOM (relative error between 10 −3 and 10 −2 for biomarkers of clinical interest), while requiring very small training datasets (30-40 samples). We demonstrate the effectiveness of the proposed method on two relevant contexts in cardiac modeling. First, we employ the ANN-based ROM to perform a global sensitivity analysis on both the electromechanical and hemodynamic models. Second, we perform a Bayesian estimation of two parameters starting from noisy measurements of two scalar outputs. In both these cases, replacing the FOM of cardiac electromechanics with the ANN-based ROM makes it possible to perform in a few hours of computational time all the numerical simulations that would be otherwise unaffordable, because of their overwhelming computational cost, if carried out with the FOM. As a matter of fact, our ANN-based ROM is able to speedup the numerical simulations by more than three orders of magnitude.

How drugs modulate the performance of the human heart

“…Future work therefore also needs to study the sensitivity of inotropic whole body level results (e.g. end-diastolic and -systolic volumes, ventricular and atrial dyssynchrony, tachycardia) on the biophysical details of the underlying cellular models, and whether or not (potentially machine learning-based) reduced order models can speed up these computations [66][67][68][69].…”

Efficient approximation of cardiac mechanics through reduced order modeling with deep learning-based operator approximation

“…Nonetheless, since Deep-HyROMnet computes the whole displacement at each time instance, any additional output, such as, e.g., the wall thickening, the end-systolic pressure or the longitudinal fractional shortening [67,20], can be considered online without the need to rebuild the ROM. This is a distinguishing feature of the proposed reduction technique, compared to recent frameworks addressing NNbased approximation of quantities of interest, without taking into account the approximation of the field variables involved in the output evaluations [68].…”

Agglomeration of Polygonal Grids using Graph Neural Networks with applications to Multigrid solvers

“…In recent years there has been a great development of Machine Learning (ML) algorithms, a framework which allows to extract information automatically from data, to enhance and accelerate numerical methods for scientific computing [43,44,45,46,47,48,49,50,51,52]. In this work, we propose to use ML-based strategies to efficiently handle polygonal mesh agglomeration, in order to fully exploit all of the benefits of the above mentioned numerical methods, such as geometrical flexibility and convergence properties.…”