Numerical Differentiation-based Electrophysiology-Aware Adaptive ResNet for Inverse ECG Modeling

Electrocardiographic imaging aims to noninvasively reconstruct the electrical dynamic patterns on the heart surface from body-surface ECG measurements, aiding the mechanistic study of cardiac function. At the core of ECGI lies the inverse ECG problem, a mathematically ill-conditioned challenge where small body measurement errors or noise can lead to significant inaccuracies in the reconstructed heart-surface potentials. %Leveraging a well-developed electrophysiological (EP) model, our previous study developed an EP-informed deep learning framework, demonstrating promising effectiveness in improving cardiac map predictions. To improve the accuracy of ECGI and ensure that cardiac predictions adhere to established physical principles, recent advances have incorporated well-established electrophysiology (EP) laws into their model formulations. However, traditional EP-informed models encounter significant challenges, including overfitting to EP constraints, limitations in network scalability, and suboptimal initialization. These issues compromise prediction accuracy and stability, hindering their effectiveness in practical applications. This highlights the need for an advanced data analytic and predictive tool to achieve reliable cardiac electrodynamic restoration. Here, we present a Numerical Differentiation-based Electrophysiology-Aware Adaptive Residual neural Network (EAND-ARN) for robust inverse ECG modeling. Our method employs numerical differentiation to compute the spatiotemporal derivative, enabling EP constraints to be applied across a local spatiotemporal region, thereby strengthening the overall EP enforcement. Additionally, we design an adaptive residual network to improve gradient flow, enhancing predictive accuracy and mitigating issues with poor initialization. Experimental results show that EAND-ARN significantly outperforms existing methods in current practice.