Gaussian Process-Based Spatiotemporal Modeling of Electrical Wave Propagation in Human Atrium*

Rhythm regularity of the heart depends on how electrical impulses spread through the cardiac conduction system. Any abnormal activities in the electrical impulses can lead to serious cardiac disorders or sudden death. It is important to understand the electrical activities of the human heart in both healthy and diseased conditions to determine the cause of cardiac disorders and explore the best therapeutic designs. Mathematical models calibrated with clinical and/or in-vitro data are popularly used to study cardiac function and investigate treatment effects. Most of the current human heart models are highly integrated and couple over a hundred equations across different organizational scales of ion channel, cell, and muscle. The model complex poses a significant computational challenge on cardiac simulation. This study developed a metamodel to replace the time-consuming simulation model. Specifically, Gaussian Process (GP) is used to reconstruct the spatiotemporal variations of the cell membrane potential in left atrium. Four different covariance functions were used to infer the potential distributions. The GP model provides an accurate estimation of the spatiotemporal propagation of electrical waves with a small set of data and shows great advantage in computations as compared to traditional models.

心脏的节律规律取决于电脉冲如何在心脏传导系统中传播。电脉冲的任何异常活动都可能导致严重的心脏疾病或猝死。了解健康和患病状态下人类心脏的电活动对于确定心脏疾病的病因以及探索最佳治疗方案非常重要。用临床和/或体外数据校准的数学模型被广泛用于研究心脏功能和探究治疗效果。目前大多数人类心脏模型高度集成，在离子通道、细胞和肌肉的不同组织层面耦合了一百多个方程。这种模型复杂性对心脏模拟提出了重大的计算挑战。本研究开发了一种元模型来替代耗时的模拟模型。具体而言，使用高斯过程（GP）来重建左心房细胞膜电位的时空变化。使用了四种不同的协方差函数来推断电位分布。与传统模型相比，GP模型用少量数据就能对电波的时空传播进行准确估计，并且在计算方面显示出巨大优势。