Dynamics of an Amplitude Equation for Cardiac Alternans in One Dimension

Shu Dai
MBI - Postdoc, The Ohio State University

(November 12, 2009 10:30 AM - 11:18 AM)

Dynamics of an Amplitude Equation for Cardiac Alternans in One Dimension

Abstract

While alternans in a single cardiac cell appears through a simple period-doubling bifurcation, in extended tissue the exact nature of the bifurcation is unclear. In particular, the phase of alternans can exhibit wave-like spatial dependence, either stationary or travelling, which is known as discordant alternans. We study these phenomena in simple cardiac models through a modulation equation proposed by Echebarria-Karma. We perform a bifurcation analysis for their modulation equation. We also find that for some extreme range of parameters, there are chaotic solutions. Chaotic waves in recent years have been regarded to be closely related to dreadful cardiac arrhythmia. Proceeding work illustrates some chaotic phenomena in two- or three-dimensional space, for instance spiral and scroll waves. We show the existence of chaotic waves in one dimension, which may provide a different mechanism accounting for the instabilities in cardiac dynamics.