Learning geometry-dependent lead-field operators for forward ECG modeling

TL;DR

This paper introduces a geometry-aware neural surrogate model for ECG forward modeling that achieves high accuracy, low data requirements, and computational efficiency by encoding torso anatomy into a low-dimensional space.

Contribution

It presents a novel shape-informed surrogate model that replaces full lead-field computations, enabling fast and accurate ECG simulations with minimal anatomical data.

Findings

Achieves mean angular error of 5° in lead-field approximation

Provides ECG simulations with less than 2.5% relative mean squared error

Outperforms pseudo lead-field approximation in accuracy

Abstract

Modern forward electrocardiogram (ECG) computational models rely on an accurate representation of the torso domain. The lead-field method enables fast ECG simulations while preserving full geometric fidelity. Achieving high anatomical accuracy in torso representation is, however, challenging in clinical practice, as imaging protocols are typically focused on the heart and often do not include the entire torso. In addition, the computational cost of the lead-field method scales linearly with the number of electrodes, limiting its applicability in high-density recording settings. To date, no existing approach simultaneously achieves high anatomical fidelity, low data requirements and computational efficiency. In this work, we propose a shape-informed surrogate model of the lead-field operator that serves as a drop-in replacement for the full-order model in forward ECG simulations. The proposed framework consists of two components: a geometry-encoding module that maps anatomical shapes into a low-dimensional latent space, and a geometry-conditioned neural surrogate that predicts lead-field gradients from spatial coordinates, electrode positions and latent codes. The proposed method achieves high accuracy in approximating lead fields both within the torso (mean angular error 5{\deg}) and inside the heart, resulting in highly accurate ECG simulations (relative mean squared error <2.5%. The surrogate consistently outperforms the widely used pseudo lead-field approximation while preserving negligible inference cost. Owing to its compact latent representation, the method does not require a fully detailed torso segmentation and can therefore be deployed in data-limited settings while preserving high-fidelity ECG simulations.