Learning cardiac activation and repolarization times with operator learning

TL;DR

This paper demonstrates that operator learning methods like Fourier Neural Operators and Kernel Operator Learning can efficiently predict cardiac activation and repolarization times, offering a faster alternative to traditional PDE-based models for cardiac simulations.

Contribution

It introduces the application of FNO and KOL to learn the mapping from applied stimulus to cardiac activation and repolarization times, including a novel approach for the latter without existing PDE models.

Findings

FNO and KOL are robust to hyperparameters.

Methods are computationally efficient compared to traditional models.

Effective on synthetic and realistic heart geometries.

Abstract

Solving partial or ordinary differential equation models in cardiac electrophysiology is a computationally demanding task, particularly when high-resolution meshes are required to capture the complex dynamics of the heart. Moreover, in clinical applications, it is essential to employ computational tools that provide only relevant information, ensuring clarity and ease of interpretation. In this work, we exploit two recently proposed operator learning approaches, namely Fourier Neural Operators (FNO) and Kernel Operator Learning (KOL), to learn the operator mapping the applied stimulus in the physical domain into the activation and repolarization time distributions. These data-driven methods are evaluated on synthetic 2D and 3D domains, as well as on a physiologically realistic left ventricle geometry. Notably, while the learned map between the applied current and activation time has its modelling counterpart in the Eikonal model, no equivalent partial differential equation (PDE) model is known for the map between the applied current and repolarization time. Our results demonstrate that both FNO and KOL approaches are robust to hyperparameter choices and computationally efficient compared to traditional PDE-based Monodomain models. These findings highlight the potential use of these surrogate operators to accelerate cardiac simulations and facilitate their clinical integration.