School of Industrial Engineering and Management, Oklahoma State University, Stillwater, OK, USA, 74078.
School of Industrial Engineering and Management, Oklahoma State University, Stillwater, OK, USA, 74078.
Comput Biol Med. 2022 Jul;146:105586. doi: 10.1016/j.compbiomed.2022.105586. Epub 2022 May 10.
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.
计算建模和模拟的发展极大地促进了心脏疾病机制的研究，并有助于优化疾病诊断和治疗设计。心脏电信号的动态传播通常用偏微分方程（PDE）的形式来描述，这通常是用有限元法（FEM）来解决的。然而，基于 FEM 的模拟只能提供 PDE 的数值解，无法将真实的临床测量纳入建模，以实现最佳决策。此外，心脏的电信号通常通过心导管术采集，这种方法只能从有限的空间位置获取心脏信号。这种稀疏的传感器测量对传统的机器学习方法进行可靠的预测建模提出了重大挑战。本文提出了一种物理约束深度主动学习（P-DAL）框架来对心脏电动力学进行建模。具体来说，我们采用我们之前工作中开发的物理约束深度学习（P-DL）框架，将心脏电传播的物理规律与深度学习相结合，对稀疏传感器测量的心脏电行为进行稳健的预测建模。此外，我们开发了一种新的主动学习策略，在心脏表面寻找信息丰富的空间位置进行数据采集，以进一步提高 P-DL 方法的预测能力。这种主动学习准则结合了 P-DL 的预测不确定性和心脏几何形状上的空间填充设计。我们评估了所提出的框架在健康和患病心脏系统中对心脏电动力学进行建模的性能。数值结果表明，所提出的 P-DL 方法在性能上明显优于传统的建模方法。具体来说，在健康和患病系统中，P-DL 方法的相对误差（RE）估计值分别比传统的时空高斯过程（STGP）模型降低了 48.3%和 28.0%。我们还通过与传统学习策略进行比较，验证了所提出的主动学习过程的有效性。具体来说，与基于纯空间填充设计（即 P-DSL）和随机数据采样策略（P-DRL）的 P-DL 方法生成的 RE 相比，所提出的 P-DAL 生成的 RE 在健康（患病）心脏系统中分别降低了 16.3%和 28.0%（11.1%和 21.2%）。
