Physics-constrained deep active learning for spatiotemporal modeling of cardiac electrodynamics

Abstract

The development of computational modeling and simulation have immensely benefited the study of cardiac disease mechanisms and facilitated the optimal disease diagnosis and treatment design. The dynamic propagation of cardiac electrical signals are often described by electrophysiological models in the form of partial differential equations (PDEs), which are commonly solved by the finite element method (FEM). However, FEM-based simulation only provides the numerical solution of the PDEs and is incapable of incorporating real clinical measurements into the modeling for optimal decision making. Additionally, electrical signals from the heart are commonly collected through cardiac catheterization, which acquires cardiac signals from limited spatial locations. Such sparse sensor measurements significantly challenge traditional machine learning methods for reliable predictive modeling. This paper presents a physics-constrained deep active learning (P-DAL) framework to model spatiotemporal cardiac electrodynamics. Specifically, we adapt the physics-constrained deep learning (P-DL) framework developed in our prior work to integrate the physical laws of the cardiac electrical wave propagation with deep learning for robust predictive modeling of the heart electrical behavior from sparse sensor measurements. Furthermore, we develop a novel active learning strategy to seek the informative spatial locations on the heart surface for data collection to further increase the predictive power of the P-DL method. This active learning criterion combines both the prediction uncertainty of the P-DL and the space-filling design over the heart geometry. We evaluate the performance of the proposed framework to model cardiac electrodynamics in both healthy and diseased heart systems. Numerical results show that the proposed P-DL approach significantly outperforms traditional modeling methods. Specifically, P-DL achieves up to 48.3% and 28.0% reduction in the estimated Relative Error (RE) compared with that from the traditional spatiotemporal Gaussian process (STGP) models in the healthy and diseased systems, respectively. We also demonstrate the efficacy of the proposed active learning procedure by comparing it with traditional learning strategies. Specifically, RE generated from the proposed P-DAL achieves 16.3% and 28.0% (11.1% and 21.2%) reduction compared with RE generated from the P-DL method based on pure space-filling design (i.e., P-DSL) and random data sampling strategy (P-DRL) in the healthy (diseased) heart system, respectively.

Keywords: Active learning; Cardiac electrodynamics; Physics-constrained deep learning; Spatiotemporal Gaussian process.