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

心脏是位于循环系统中心的肌肉器官。它的重要功能是将含氧血液输送到全身。这个过程之前是心脏细胞之间的电通信。人们普遍认为，间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的关注，是否传导可以持续在没有缝隙连接。Ephthalocyte偶联（EpC）是在相邻细胞之间的闰盘（ID）处产生的电场效应，其已被建议作为当间隙连接受损时介导细胞间电通信的替代方式。然而，直接的实验证据表明EpC的存在仍然是缺乏的。因此，人们试图通过揭示其在心脏中的生理作用来间接证明EpC的存在。这项合作提案的目的是开发第一个多尺度模型，将异质纳米级ID结构纳入一个二维离散模型与多域多离子电扩散。该框架无缝地连接了不同空间和时间尺度的生物物理反应，这有助于了解EpC对心脏心律失常发生的潜在影响。因此，本研究具有高度的跨学科性，为数学建模和心脏电生理学之间的研究提供了一座桥梁.此外，本研究具有很高的临床意义，这为开发抗心律失常策略和治疗结构异常心脏、心力衰竭和心肌病患者奠定了坚实的基础。该项目是普渡大学和明尼苏达大学双城分校之间的合作，提供了宝贵的教育，培训和推广机会。研究生和本科生将通过联席会议在多学科环境中进行培训和合作。该项目将通过将ID的纳米级结构整合到健康和缺血的心脏中来开发EpC的第一个多尺度离散模型。具体而言，以下新特征将在不同水平上并入模型中：（1）亚细胞水平：使用多隔室ID开发的均匀和/或不均匀分布的EpC;（2）细胞水平：多个域之间的多个离子的电扩散;（3）组织水平：并入心脏中的缺血区域的复杂解剖结构。这个框架是一个系统的普通代数微分方程的显着大量的非线性项在不同的空间和时间尺度。因此，需要一个有效的数值方案，以减少在组织水平的计算成本。因此，该建议的目的是开发一个自适应的时间步长算法和设计一个预条件的广义最小残差方法，以有效地解决该系统。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开始、终止和动力学的影响。为了验证数值结果并间接证明EpC作为心脏细胞间通讯的另一种机制的存在，将使用高分辨率光学映射技术进行全心脏动物实验。该奖项反映了NSF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.