title: Criterion for stable reentry in a ring of cardiac tissue.
abstract: We model electrical wave propagation in a ring of cardiac tissue using an mth-order difference equation, where m denotes the number of cells in the ring. Under physiologically reasonable assumptions, the difference equation has a unique equilibrium solution. Applying Jury's stability test, we prove a theorem concerning the local asymptotic stability of this equilibrium solution. Our results yield conditions for sustained reentrant tachycardia, a type of cardiac arrhythmia.
authors.affiliation: Department of Mathematics, Virginia Commonwealth University, 1001 West Main Street, Richmond, VA 23284-2014, USA. jwcain@vcu.edu
authors.forename: John W
authors.initials: JW
authors.lastname: Cain
mesh_terms: D000465:Algorithms; D000818:Animals; D004594:Electrophysiology; D006321:Heart / Q000502:physiology* / Q000503:physiopathology; D006329:Heart Conduction System / Q000502:physiology* / Q000503:physiopathology; D006801:Humans; D007700:Kinetics; D008955:Models, Cardiovascular; D013610:Tachycardia / Q000503:physiopathology