Sudden cardiac death is the primary cause of mortality in the industrialized world. Ventricular tachycardia and lethal arrhythmias such as ventricular fibrillation are believed to be the result of reentrant electrical activity, i.e., self-sustained electrical activity which continues to re-excite regions of cardiac tissue independently of the natural pacemaker rhythm. The mechanisms behind fibrillation initiation, maintenance, and termination by a defibrillatory shock are largely unknown.
Cardiac fibrillation is characterized by a complex spatial interaction of non-stationary spiral waves; however, the nature of this interaction is an ongoing topic of investigation. The organizing center of reentry is a topological defect called a phase singularity in two dimensions, a filament in three dimensions; an understanding of fibrillation behavior may be obtained by localizing and tracking these defects. Experimentally, the electrodynamic behavior is typically investigated via optical mapping using voltage-sensitive fluorescent dyes.
In this thesis, a technique to detect phase singularities based upon topological charge was applied to nonlinear time-series and phase portrait analysis of optical signals, and later extended to filament detection; this procedure was shown to be both efficient and mathematically robust. An alternate method to reconstruct the phase portrait was also explored and shown to overcome some of the limitations of the time-series method as well as permitting singularity detection closer to initiation than previously allowed. Numerically examining the interaction dynamics of a simple filament configuration paralleling that seen in experimental preparations indicated that a critical bifurcation in filament life-time exists between attractive and repulsive behavior along with annihilation by mutual collision and collapse by shrinkage; which could be represented by a difference of Yukawa potentials by treating the filaments as a pair of point charges. The inclusion of optical depth effects into a numerical model of three-dimensional filament activity was studied, and suggested that these effects have a significant impact on observed epicardial activity. Finally, a three-dimensional geometric reconstruction of an isolated, perfused heart with the fluorescence information as a texture map, previously developed as a proof-of-concept, was shown to be a viable tool for whole-heart singularity visualization.