Collaborative Research: The dual effect of ephaptic coupling on arrhythmogenesis in the heart

心脏是一个肌肉器官，位于循环系统的中心。它执行向全身泵送含氧血液的重要功能。在这个过程之前，心脏细胞之间进行电通信。人们普遍认为隙结耦合是导电的主要机制。然而，最近的实验观察引起了人们对在没有间隙连接的情况下传导能否持续的关注。eppatic偶联（eppatic coupling, EpC）是在相邻细胞间的嵌入盘（intercalated disc， ID）处产生的电场效应，被认为是在间隙连接受损时介导细胞间电通信的另一种方式。然而，证明EpC存在的直接实验证据仍然缺乏。因此，我们试图通过揭示EpC在心脏中的生理作用来间接证明其存在。该合作提案旨在开发第一个多尺度模型，将非均质纳米级ID结构纳入具有多离子多域电扩散的二维离散模型中。该框架无缝连接了不同空间和时间尺度的生物物理反应，有助于了解EpC对心脏心律失常的潜在影响。因此，提出的研究是高度跨学科的，并提供数学建模和心脏电生理之间的桥梁。此外，本研究具有较高的临床意义，为结构异常心脏、心力衰竭、心肌病患者的抗心律失常策略和治疗奠定了坚实的基础。该项目是普渡大学和明尼苏达大学双城分校的合作项目，提供有价值的教育、培训和推广机会。研究生和本科生将通过联合会议在多学科环境中进行合作。该项目将通过将ID的纳米级结构集成到健康的非化学心脏中，开发出首个EpC的多尺度离散模型。特别是，以下新特征将被纳入不同层次的模型：(1)亚细胞水平：使用多室ID开发的均匀和/或异构分布的EpC；(2)细胞水平：多个离子在多个区域之间的电扩散；(3)组织水平：缺血区融入心脏的复杂解剖结构。这个框架是一个普通代数微分方程系统，在不同的空间和时间尺度上具有大量的非线性项。因此，需要一种有效的数值格式来降低组织水平的计算成本。因此，本文旨在开发一种自适应时间步进算法，并设计一种广义最小残差法的预条件，以有效地求解该系统。该模型将评估ID的纳米级结构、EpC的各种分布、离子电扩散和缺血区域的复杂结构对心律失常的发生、终止和动力学的影响。为了验证数值结果并间接证明EpC作为心脏细胞间通信的替代机制的存在，将使用高分辨率光学作图技术进行全心脏动物实验。该奖项反映了美国国家科学基金会的法定使命，并通过使用基金会的知识价值和更广泛的影响审查标准进行评估，被认为值得支持。

The heart is a muscular organ at the center of the circulation system. It carries out the vital function of pumping oxygenated blood around the body. This process is preceded by the electrical communication between cardiac cells. It is widely accepted that gap junctional coupling is the primary mechanism for the electrical conduction. Nevertheless, recent experimental observation raised the concern of whether conduction can be sustained in the absence of gap junctions. Ephpatic coupling (EpC) is an electric field effect developed at the intercalated disc (ID) between adjacent cells, which has been suggested as an alternative way in mediating intercellular electrical communication when gap junctions are impaired. However, the direct experimental evidence demonstrating the existence of EpC is still absent. Therefore, attempts were made to indirectly demonstrate the existence of EpC by revealing its physiological role in the heart. This collaborative proposal aims for developing the very first multiscale model to incorporate the heterogeneous nanoscale ID structure into a two-dimensional discrete model with multidomain electrodiffusion of multiple ions. This framework seamlessly bridges biophysical responses of different space and time scales, which helps understand the potential impact of EpC on arrhythmogenesis in the heart. Therefore, the proposed research is highly inter- disciplinary and provides a bridge between mathematical modeling and cardiac electrophysiology. Moreover, this study is of high clinical significance, which lays a solid ground for developing anti-arrhythmic strategies and therapies for patients with structurally abnormal hearts, heart failure, and cardiomyopathy. The project is a collaboration between Purdue University and the University of Minnesota-Twin Cities and offers valuable educational, training, and outreach opportunities. Graduate and undergraduate students are trained and will collaborate in multidisciplinary environment via joint meetings.This project will develop the very first multiscale discrete model of EpC through integration of the nanoscale structure of ID into the healthy and is- chemic heart. In particular, the following novel features will be incorporated to the model at different levels: (1) subcellular level: homogeneously and/or heterogeneously distributed EpC developed using a multi-compartment ID; (2) cellular level: electrodiffusion of multiple ions between multiple domains; (3) tissue level: complex anatomical structure of ischemic region incorporated in the heart. This framework is a system of ordinary algebraic differential equations with a significantly large number of nonlinear terms at different spatial and time scales. Therefore, an effective numerical scheme is required to reduce the computational cost at the tissue level. This proposal thus aims for developing an adaptive time stepping algorithm and designing a preconditioner for generalized minimal residual method to efficiently solve the system. This model will evaluate the impact of nanoscale structure of ID, various distributions of EpC, ionic electrodiffusion and complex structure of ischemic regions on initiation, termination and dynamics of cardiac arrhythmias. In order to validate the numerical findings and indirectly demonstrate the presence of EpC as an alternative mechanism of cell-to-cell communication in the heart, whole-heart animal experiments using high resolution optical mapping technique will be performed.This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.