ABSTRACT
Spatiotemporal dynamics of the patterns that arise in homogeneous excitable media (discussed in Chapter 3) is relatively well understood. However, many examples of excitable media that are seen among living systems are heterogeneous in nature. In order to be able to explain the patterns arising in such systems one must therefore try to understand how such heterogeneities affect and alter the characteristic dynamics of homogeneous excitable systems. A particularly important example of heterogeneous excitable medium is the heart. Reentrant waves in the heart giving rise to abnormally rapid excitation can result from an impulse that rotates around an inexcitable obstacle (“anatomical reentry”) [Abildskov and Lux 1995] or within a region of cardiac tissue that is excitable in its entirety (“functional reentry”) [Davidenko et al. 1995; Rudy 1995]. Such deviations from the normal rhythmic functioning of the heart are not desirable, especially because they can lead to complications that may well be fatal [Cross and Hohenberg 1993; Garfinkel et al. 2000; Gray and Chattipakorn 2005; Gray et al. 1995b; Jalife et al. 1998; Winfree 1998; Witkowski et al. 1998]. Trains of local electrical stimuli are widely used to restore normal wave propagation in the heart during tachycardia. Such “antitachycardia pacing” is not always successful and may inadvertently cause tolerated tachycardias to degenerate to life-threatening spatiotemporally irregular cardiac activity such as ventricular fibrillation [Rosenthal and Josephson 1990]. The underlying mechanisms governing the success or failure of antitachycardia pacing algorithms are not yet clear. Understanding these mechanisms is essential, as a better knowledge of the processes involved in the suppression of ventricular tachycardia (VT) through such pacing might aid in the design of more effective therapies.
