Am J Cardiovasc Dis 2013;3(1):1-16

Review Article
Bifurcation theory and cardiac arrhythmias

Hrayr S Karagueuzian, Hayk Stepanyan, William J Mandel

From the Translational Arrhythmia Research Section, UCLA Cardiovascular Research Laboratory and the Division of
Cardiology, Departments of Medicine David Geffen School of Medicine at UCLA, Los Angeles, California

Received November 26, 2012; Accepted January 16, 2013; Epub February 17, 2013; Published February 27, 2013

Abstract: In this paper we review two types of dynamic behaviors defined by the bifurcation theory that are found to be
particularly useful in describing two forms of cardiac electrical instabilities that are of considerable importance in cardiac
arrhythmogenesis. The first is action potential duration (APD) alternans with an underlying dynamics consistent with the
period doubling bifurcation theory. This form of electrical instability could lead to spatially discordant APD alternans leading
to wavebreak and reentrant form of tachyarrhythmias. Factors that modulate the APD alternans are discussed. The second
form of bifurcation of importance to cardiac arrhythmogenesis is the Hopf-homoclinic bifurcation that adequately describes
the dynamics of the onset of early afterdepolarization (EAD)-mediated triggered activity (Hopf) that may cause ventricular
tachycardia and ventricular fibrillation (VT/VF respectively). The self-termination of the triggered activity is compatible with
the homoclinic bifurcation. Ionic and intracellular calcium dynamics underlying these dynamics are discussed using
available experimental and simulation data. The dynamic analysis provides novel insights into the mechanisms of VT/VF, a
major cause of sudden cardiac death in the US. (AJCD1211003).

Keywords: Period-doubling bifurcation, Hopf-homoclinic bifurcation, action potential duration alternans, early
afterdepolarization, triggered activity, spatially-discordant alternans, reentry, ventricular tachycardia, ventricular fibrillation

Address correspondence to: Dr. Hrayr S Karagueuzian, Translational Arrhythmia Research Section, Cardiovascular
Research Laboratory, David Geffen School of Medicine at UCLA, 675 Charles E. Young Dr. South MRL 1630. Mail Code:
176022; Phone: 310-825-9360; Fax: 310-206-5777; E-mail:
AJCD Copyright © 2011-present, All rights reserved. Published by e-Century Publishing Corporation, Madison, WI 53711, USA