Cardiovascular diseases are one of the leading causes of death in the world and manifest themselves in several forms, including arrhythmias. These disruptions in the normal rhythm of the heart inhibit the regular transmission of electrical signals that are essential for the heart to contract and pump blood to the rest of the body. During reentrant arrhythmias, spiral or scroll waves of electrical activation are conducted through the cardiac tissue and excite it repeatedly. As these waves propagate through the heart, they can break up in an irregular manner, leading to the onset of fibrillation. There are several mechanisms by which these reentrant waves can destabilize, but they are known mostly from computational studies. Experimentally, it has not been possible so far to distinguish among these mechanisms based on straightforward observations of the heart's voltage during fibrillation. As a preliminary step in this direction, we aim to determine whether quantifying certain observable properties of the system will allow us to identify the mechanism underlying a given fibrillation episode.

Toward this end, we propose a number of metrics that could help us classify mechanisms underlying fibrillation, including chaos in the system as assessed by the largest Lyapunov exponent; the amount of information (mutual information) and dependency (spatial correlation) shared by various spatial points in the domain; and reentrant wave properties like the number of reentries, wave birth and death rates, reentrant wave lifetimes, and spiral wave tip speeds. We implement and apply these metrics to simulated data obtained by numerically solving partial differential equations describing electrical wave propagation in the heart. Specifically, we analyze data achieved through six different mechanisms of reentrant wave breakup: steep APD restitution, discordant alternans, bistability, Doppler effect, supernormal conduction velocity and periodic boundary conditions. Our results suggest that of the various reentrant wave properties, the distribution of the number of reentries over time serves to be the most useful metric by providing a visual representation of how the breakup proceeds with time for each mechanism. When the mutual information and spatial correlation are studied in the context of the distribution of reentries over time, they help us gauge any spatial dependencies that may be present in the system.

To validate our findings, we carried out a blind test to classify breakup mechanisms in four provided data sets with established breakup mechanisms. Our metrics correctly classified the mechanisms for three of these cases, and we are condent that further optimization could improve the reliability of our approach. Our work forms the basis for future studies that apply these and other metrics towards identifying the mechanisms responsible for fibrillation in experimental settings.

Library of Congress Subject Headings

Ventricular fibrillation--Mathematical models; Atrial fibrillation--Mathematical models; Arrythmia--Mathematical models

Publication Date


Document Type


Student Type


Degree Name

Applied and Computational Mathematics (MS)

Department, Program, or Center

School of Mathematical Sciences (COS)


Elizabeth M. Cherry

Advisor/Committee Member

Elizabeth M. Cherry

Advisor/Committee Member

Tamas Wiandt


Physical copy available from RIT's Wallace Library at RC685.V43 R34 2014


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