Towards Deep Learning Surrogate for the Forward Problem in Electrocardiology: A Scalable Alternative to Physics-Based Models

TL;DR

This paper introduces a deep learning surrogate model for the cardiac forward problem in electrocardiology, achieving high accuracy and scalability as an efficient alternative to traditional physics-based models.

Contribution

It presents a novel attention-based sequence-to-sequence DL framework with a hybrid loss, demonstrating high accuracy in predicting ECG signals from cardiac simulations.

Findings

Achieved mean R^2 of 0.99 in simulations

Confirmed importance of convolutional encoders and spectral entropy loss

DL model offers a scalable, cost-effective alternative to physics-based models

Abstract

The forward problem in electrocardiology, computing body surface potentials from cardiac electrical activity, is traditionally solved using physics-based models such as the bidomain or monodomain equations. While accurate, these approaches are computationally expensive, limiting their use in real-time and large-scale clinical applications. We propose a proof-of-concept deep learning (DL) framework as an efficient surrogate for forward solvers. The model adopts a time-dependent, attention-based sequence-to-sequence architecture to predict electrocardiogram (ECG) signals from cardiac voltage propagation maps. A hybrid loss combining Huber loss with a spectral entropy term was introduced to preserve both temporal and frequency-domain fidelity. Using 2D tissue simulations incorporating healthy, fibrotic, and gap junction-remodelled conditions, the model achieved high accuracy (mean $R^2 = 0.99 \pm 0.01$). Ablation studies confirmed the contributions of convolutional encoders, time-aware attention, and spectral entropy loss. These findings highlight DL as a scalable, cost-effective alternative to physics-based solvers, with potential for clinical and digital twin applications.