title: The topology of defibrillation.
abstract: We describe how Art Winfree's ideas about phase singularities can be used to understand the response of cardiac tissue with a random preexisting pattern of reentrant waves (fibrillation) to a large brief current stimulus. This discussion is organized around spatial dimension, beginning with a discussion of reentry on a periodic ring, followed by reentry in a two-dimensional planar domain (spiral waves), and ending with consideration of three-dimensional reentrant patterns (scroll waves). In all cases, we show how reentrant activity is changed by the application of a shock, describing conditions under which defibrillation is successful or not. Using topological arguments we draw the general conclusion that with a generic placement of stimulating electrodes, large-scale virtual electrodes do not give an adequate explanation for the mechanism of defibrillation.
authors.affiliation: Department of Mathematics, University of Utah, 155 South 1400 East, Salt Lake City, UT 84112, USA. keener@math.utah.edu
authors.forename: James P
authors.initials: JP
authors.lastname: Keener
mesh_terms: D004554:Electric Countershock; D004594:Electrophysiology; D006329:Heart Conduction System / Q000502:physiology; D006801:Humans; D008955:Models, Cardiovascular