ABSTRACT
In Chapter 5, we considered the effect of a localized heterogeneity, specifically a region or a defect having different conduction properties from that of its surrounding medium, on the dynamics of two-dimensional and three-dimensional spatial patterns of excitation. Another kind of heterogeneity often encountered in naturally occurring excitable systems is the spatial gradient. A gradient typically involves the variation of one or many system properties over some spatial extent. Several types of gradients have been observed in naturally occurring excitable systems. Dynamics of spiral and scroll waves are significantly influenced by these gradients. For example, variation of a system property along the gradient causes a spiral wave to drift. Drift is a kind of non-meandering rotation characterized by a significant linear translation motion. While spiral drift has been observed in several contexts such as, in the presence of an electric field [Krinsky et al. 1996; Steinbock et al. 1992] and high frequency stimulation of the medium [Gottwald et al. 2001b], gradient induced drift is especially relevant in the context of biological excitable media. In a heterogeneous excitable medium like the heart, drift can be a significant component of the spiral wave dynamics, so much so that it is believed to be a possible underlying mechanism for arrhythmias like polymorphic ventricular tachycardia [Garfinkel and Qu 2004; Gray et al. 1995a]. Characterized by an aperiodic electrocardiogram, polymorphic ventricular tachycardia may also be a precursor to fully disordered activity that characterizes potentially fatal ventricular fibrillation [Cobbe and Rankin 2005]. Thus understanding the phenomenon of spiral drift has potential clinical significance [Fenton et al. 2002].
