A unified framework for geometry-independent operator learning in cardiac electrophysiology simulations

TL;DR

The paper introduces a geometry-independent neural-operator approach to predict full-field local activation time maps for atrial electrophysiology, addressing the heavy computational burden of high-fidelity FEM simulations. By projecting heterogeneous patient anatomies and conductivities into a unified Universal Atrium Coordinates space and employing a Vision Transformer-based encoder–decoder, the method attains near real-time LAT predictions with high physiological accuracy. It leverages a large GPU-generated dataset (308,700 simulations across 147 anatomies) and demonstrates strong cross-domain generalisation, especially when training on multi-centre data to mitigate domain shift. The framework promises real-time, patient-specific guidance for AF interventions and large-scale population analyses, effectively bridging mechanistic modelling and clinical workflows.

Abstract

Accurate maps of atrial electrical activation are essential for personalised treatment of arrhythmias, yet biophysically detailed simulations remain computationally intensive for real-time clinical use or population-scale analyses. Here we introduce a geometry-independent operator-learning framework that predicts local activation time (LAT) fields across diverse left atrial anatomies with near-instantaneous inference. We generated a dataset of 308,700 simulations using a GPU-accelerated electrophysiology solver, systematically varying multiple pacing sites and physiologically varied conduction properties across 147 patient-specific geometries derived from two independent clinical cohorts. All anatomical and functional data are expressed in a Universal Atrium Coordinate system, providing a consistent representation that decouples electrophysiological patterns from mesh topology. Within this coordinate space, we designed a neural operator with a vision-transformer backbone to learn the mapping from structural and electrophysiological inputs to LAT fields. With a mean prediction error of 5.1 ms over a 455 ms maximum simulation time, the model outperforms established operator-learning approaches and performs inference in 0.12 ms per sample. Our framework establishes a general strategy for learning domain-invariant biophysical mappings across variable anatomical domains and enables integration of computational electrophysiology into real-time and large-scale clinical workflows.

Figures (5)

• Figure 1: Construction and characterisation of large-scale electrophysiology datasets generated from biophysically detailed simulations.a, Example local activation time (LAT) map from a 3D left atrium (LA) electrophysiology simulation with coronary sinus pacing, together with its projection onto the standardised Universal Atrial Coordinate (UAC) domain. b, UMAP embedding of all UAC-projected LAT maps from Datasets A and B, showing seven pacing-site clusters per cohort and systematic displacement between corresponding clusters, indicating a pronounced domain shift between the two datasets. c, Distribution of maximum LAT across pacing locations in Dataset A, demonstrating linear dependence on LA surface area and sensitivity to conductivity. d, Corresponding analysis for Dataset B, showing the same physiological trends despite cohort-level differences.
• Figure 2: Comprehensive evaluation of model performance for LAT map prediction.a, Our model performance from feature sensitivity tests on Dataset A, demonstrating the contribution of each input feature. b, Evaluation of the impact of two regularisation terms, namely total variance (TV) and Laplacian, on LAT map prediction on Dataset A. c, Performance comparison between our proposed model and established deep learning architectures, including DeepONet, Fourier Neural Operator (FNO), Wavelet Neural Operator (WNO), U-Net, and ResNet on Dataset A. d, Spatial distribution of the averaged LAT prediction error (in ms) across five test cases in a representative validation fold. White circles highlight regions with the highest prediction errors, and adjacent numbers show the average error within those specific regions. e, Performance comparison between Single Pacing Location Models and a Unified Model across seven pacing sites. f, Cross-domain performance comparison on two distinct datasets. The notation $X \rightarrow Y$ indicates that the model was trained on source dataset $X$ and evaluated on target dataset $Y$.
• Figure 3: The overview of our proposed computational framework for operator learning for electrophysiology (EP) simulations. a, Preparation of left atrium (LA) mesh, mapping the 3D vertex coordinates defining the mesh to a 2D grid by Universal Atrial Coordinates (UAC), and identifying the pacing locations. b, The application of our GPU-based FEM solver to produce a large amount of simulated local activation time (LAT) maps, which are also projected to 2D grids by UAC. c, The training of neural operators using the structured simulation data.
• Figure 4: Marking pacing sites on an LA.a, Anterior and posterior views of an LA mesh where the seven pacing locations have been marked. b, Spatial distribution of these pacing sites in UAC coordinates. The blue regions indicate the anatomical openings (pulmonary veins and mitral valve).
• Figure 5: Model architecture.a, The construction of the input and output for neural operator learning, where patient-specific anatomical and physiological parameters are projected onto a structured grid via the Universal Atrial Coordinate system. The pacing location is converted from a point cloud representation into a spatial distribution on the same grid, enabling consistent integration with other input modalities. b, A neural network module that maps a point cloud of shape $(N, 2)$, representing spatial input features such as pacing sites or anatomical landmarks, into a structured 2D grid of shape $(1, 50, 50)$. Here, $N$ refers to the number of vertices where stimulus (pacing) is applied. c, The Vision Transformer block used in (d), which is the original ViT model proposed in vit. d, Our full encoder-decoder architecture, which uses convolutional patch embedding and a Vision Transformer encoder to process the input grid, and then upsamples the latent features using a transposed convolution and projects them into the final LAT map using a convolutional output layer.