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.
