Small-world networks describe many important practical systems among which neural networks consisting of excitable nodes are the most typical ones. In this paper we study self-sustained oscillations of target waves in excitable small-world networks. A dominant phase-advanced driving (DPAD) method, which is generally applicable for analyzing all oscillatory complex networks consisting of nonoscillatory nodes, is proposed to reveal the self-organized structures supporting this type of oscillations. The DPAD method explicitly explores the oscillation sources and wave propagation paths of the systems, which are otherwise deeply hidden in the complicated patterns of randomly distributed target groups. Based on the understanding of the self-organized structure, the oscillatory patterns can be controlled with an extremely high efficiency.

The occurrence of early afterdepolarizations (EADs) and increased dispersion of repolarization are two known factors for arrhythmogenesis in long QT syndrome. However, increased dispersion of repolarization tends to suppress EADs due to the source-sink effect, and thus how the two competing factors cause initiation of arrhythmias remains incompletely understood. Here we used optical mapping and computer simulation to investigate the mechanisms underlying spontaneous initiation of arrhythmias in type 2 long QT (LQT2) syndrome. In optical mapping experiments of transgenic LQT2 rabbit hearts under isoproterenol, premature ventricular complexes (PVCs) were observed to originate from the steep spatial repolarization gradient (RG) regions and propagated unidirectionally. The same PVC behaviors were demonstrated in computer simulations of tissue models of rabbits. Depending on the heterogeneities, these PVCs could lead to either repetitive focal excitations or reentry without requiring an additional vulnerable substrate. Systematic simulations showed that cellular phase 2 EADs were either suppressed or confined to the long action potential region due to the source-sink effect. Tissue-scale phase 3 EADs and PVCs occurred due to tissue-scale dynamical instabilities caused by RG and enhanced L-type calcium current (I), occurring under both large and small RG. Presence of cellular EADs was not required but potentiated PVCs when RG was small. We also investigated how other factors affect the dynamical instabilities causing PVCs. Our main conclusion is that tissue-scale dynamical instabilities caused by RG and enhanced I give rise to both the trigger and the vulnerable substrate simultaneously for spontaneous initiation of arrhythmias in LQT2 syndrome.

T-wave alternans (TWA) and irregular beat-to-beat T-wave variability or T-wave lability (TWL), the ECG manifestations of action potential duration (APD) alternans and variability, are precursors of ventricular arrhythmias in long QT syndromes. TWA and TWL in patients tend to occur at normal heart rates and are usually potentiated by bradycardia. Whether or how TWA and TWL at normal or slow heart rates are causally linked to arrhythmogenesis remains unknown. In the present study, we used computer simulations and experiments of a transgenic rabbit model of long QT syndrome to investigate the underlying mechanisms. Computer simulations showed that APD prolongation and slowed heart rates caused early afterdepolarization-mediated APD alternans and chaos, manifesting as TWA and TWL, respectively. Regional APD alternans and chaos exacerbated pre-existing APD dispersion and, in addition, APD chaos could also induce APD dispersion de novo via chaos desynchronization. Increased APD dispersion, combined with substantially enhanced I , resulted in a tissue-scale dynamical instability that gave rise to the spontaneous occurrence of unidirectionally propagating premature ventricular complexes (PVCs) originating from the APD gradient region. These PVCs could directly degenerate into re-entrant arrhythmias without the need for an additional tissue substrate or could block the following sinus beat to result in a longer RR interval, which further exacerbated the APD dispersion giving rise to the spontaneous occurrence of ventricular arrhythmias. Slow heart rate-induced PVC alternans was observed in experiments of transgenic LQT2 rabbits under isoproterenol, which was associated with increased APD dispersion and spontaneous occurrence of ventricular arrhythmias, in agreement with the theoretical predictions.