ABSTRACT
An interesting property observed in certain biological excitable media, specifically the heart muscles, is the phenomenon of alternans. Alternans is the beat-to-beat variation in the response of the cardiac cells. At the cellular level, this beat-tobeat variation is observed in the duration of the action potential and the peak calcium concentration [Kockska¨mper and Blatter 2002]. The former is referred to as APD alternans, and the latter as transient calcium alternans. This beat-to-beat variation is manifested as a T-wave alternans in ECG [Pastore et al. 1999]. The T-wave in the ECG corresponds to the membrane repolarization at the level of the cell. Even micro-volt level variations in the T-wave amplitude could be related to very large alternations of the cellular repolarizations [Wilson and Rosenbaum 2007]. Detecting T-wave alternans is crucial and has implications for the prediction of the onset of fibrillation [Wilson and Rosenbaum 2007]. More generally as the transmembrane voltage and intracellular calcium concentration are two signals that determine the contraction of cardiac myocytes, any variation in the APD and/or peak calcium concentration can cause serious disruption to the normal rhythm of the heart. In fact it is now recognized that T-wave alternans (and the underlying cellular alternans) are pathological conditions that are closely linked to the onset of ventricular arrhythmias [Euler 1999; Pastore et al. 1999; Rosenbaum et al. 1994; Weiss et al. 2006].
