Dynamics of Scroll Waves in Excitable Systems with Application to the Heart: The Role of Cardiac Tissue Structure

在工业化国家，室颤是心源性猝死的主要原因，约占死亡人数的十分之一。利用摄动方法和数值模拟，本项目旨在更好地了解室性心律失常的产生和持续的机制。从心动过速到纤颤的转变特征是通过跨膜电位的螺旋波分解成多个螺旋波，最后进入时空无序状态。尽管有这种重要的联系，但有关螺旋波的基本性质的许多问题至今仍未得到解答。虽然到目前为止的大多数分析工作都将心脏视为均匀的、各向同性的可激发介质，但实际上心脏是一个高度复杂的、具有强各向异性和非平凡几何的异质物理系统。另一方面，使用真实的细胞动力学和几何结构对心脏中的电势传播进行数值模拟在计算上仍然具有挑战性，很难验证。该项目的主要目的是区分心脏组织作为传导介质的“被动”属性(由具有旋转各向异性的细胞内域和胞外域组成)在螺旋的启动和破裂中的作用，以及由心肌细胞电生理学确定的其“主动”属性的作用。这项工作将在两个方面进行：(1)扩展现有的关于各向同性可激发介质中涡旋波的摄动分析的工作，以包括旋转各向异性和双峰，这是对心脏组织的主要描述；以及(2)构建和实现用于易于计算的数值研究的最低限度逼真的左心室纤维结构模型。分析和计算相结合的方法使基本了解几何和光纤结构在螺旋波传播和分解中的作用成为可能。这两条探索线的进一步发展有可能解决兴奋-收缩耦合的作用。该项目将为研究生提供一个跨学科研究领域的培训基础，涉及分析技术、先进的数值方法和高性能计算。更好地了解心脏组织的电特性及其在心律失常发展中的作用可能会导致临床治疗和预防程序。从理想和现实的心脏电波传播模型的分析和计算研究中获得的见解，对于从根本上理解心律失常，以及直接接触这一领域的实验工作和临床经验是必不可少的。该项目将开展的工作可以被视为朝着这些目标迈出的一步。这一主题的性质和将使用的研究工具为推广和教育以及向广大公众广泛传播物理和数学科学在生物和生物医学研究中的作用提供了机会。

Ventricular fibrillation is the main cause of sudden cardiac death in industrialized countries, accounting for approximately one in ten deaths. Using perturbation methods and numerical simulation, this project aims to better understand the mechanisms by which ventricular arrhythmias are generated and sustained. The transition from tachycardia to fibrillation has been characterized as proceeding through the breakdown of a spiral wave of transmembrane potential into multiple spirals and finally into a spatiotemporally disorganized state. Despite this important connection, many questions about basic properties of spiral waves are as yet unanswered. While most of the analytical work to date has treated it as a homogeneous, isotropic excitable medium, in fact the heart is a highly complicated, heterogeneous physical system with strong anisotropy and nontrivial geometry. On the other hand, numerical simulations of electric potential propagation in the heart using realistic cellular kinetics and geometries remain computationally challenging and difficult to validate. The main thrust of this project is to distinguish the role in the initiation and breakdown of spirals of the "passive" properties of cardiac tissue as a conducting medium, described as a bidomain (consisting of intra- and extra-cellular domains) with rotating anisotropy, from that of its "active" properties determined by cardiac cell electrophysiology. This work will proceed on two fronts: (1) extension of the existing body of work on perturbation analyses of scroll waves in isotropic excitable media to include the rotating anisotropy and bidomain description of cardiac tissue; and (2) construction and implementation of a minimally realistic fiber architecture model of the left ventricle for computationally tractable numerical studies. The combined analytical and computational approach makes possible a basic understanding of the role of geometry and fiber architecture in spiral wave propagation and breakup. Further development of both lines of inquiry has the potential to address the role of excitation-contraction coupling. The project will provide a training ground for graduate students in an interdisciplinary area of research, involving analytical techniques, advanced numerical methods and high performance computing.A better understanding of electrical properties of cardiac tissue and their role in the development of cardiac arrhythmias could lead to clinical treatments and preventative procedures. Insights from analytical and computational studies of both idealized and realistic models of electrical wave propagation in the heart are essential for understanding cardiac arrhythmias at a fundamental level, and for making direct contact with experimental work and clinical experience in this area. The work that will be undertaken in this project can be viewed as a step toward these goals. The nature of the subject and the research tools that will be used provide opportunities for outreach and education, as well as for the general conveyance of the role of the physical and mathematical sciences in biological and biomedical research to the public at large.