Spiral defect drift in the wave fields of multiple excitation patterns

Rotational synchronization of pinned spiral waves

Coupled rotors can spontaneously synchronize, giving rise to a plethora of intriguing dynamics. We present here a pair of spiral waves as two synchronizing rotors, coupled by diffusion. The spirals are pinned to unexcitable obstacles, which enables us to modify their frequencies and restrain their drift. In experiments with the Belousov-Zhabotinsky reaction, we show that two counterrotating spiral rotors, pinned to circular heterogeneities, can synchronize in frequency and phase. The nature of the phase synchronization varies depending on the difference in their characteristic frequencies. We observe in-phase and out-of-phase synchronization, lag synchronization, and phase resetting across the experiments. The time required for the two spirals to synchronize is found to depend upon the relative size of their pinning obstacles and the distance separating them. This distance can also modify the phase lag of the two rotors upon synchronization. Our experimental observations are reproduced and explained further on the basis of numerical simulations of an excitable reaction-diffusion model.

Interaction of multiple spiral rotors in a reaction-diffusion system

Rotors of reaction and diffusion are phase singularities that give rise to spiral waves of chemical activity, which are very similar to spatiotemporal patterns observed across several excitable media. Here we carry out experiments with the Belousov-Zhabotinsky reaction system and numerical simulations based on a reaction-diffusion model to show the possible interactions of multiple spiral rotors. When the cores of two spirals come very close to each other, they could either repel, attract, or remain stationary, depending on their relative chirality, phase, and distance separating them. Multiple pairs of spiral waves, in proximity to each other, could alter the paths of the individual rotors. A spiral core will be influenced most by the rotor that is closest to it, depending on the nature of the corresponding spiral wave arm. We observed rotors lying within a limiting distance of each other attract and annihilate. Otherwise, they push each other away until they reach a critical distance, beyond which all interactions seem to cease. We have established a relationship of this critical distance to the properties of the spiral wave. We also observed spontaneous symmetry-breaking instability for a system of up to eight rotors. Our experiments with the Belousov-Zhabotinsky reaction have successfully demonstrated the validity of the numerical results. A thorough understanding of the dynamics of several spiral rotors within a small area could help us perceive the nature of such excitation waves in cardiac tissue and cell membranes.

Stable and unstable vortex knots in excitable media

We study the dynamics of knotted vortices in a bulk excitable medium using the FitzHugh-Nagumo model. From a systematic survey of all knots of at most eight crossings we establish that the generic behavior is of unsteady, irregular dynamics, with prolonged periods of expansion of parts of the vortex. The mechanism for the length expansion is a long-range "wave-slapping" interaction, analogous to that responsible for the annihilation of small vortex rings by larger ones. We also show that there are stable vortex geometries for certain knots; in addition to the unknot, trefoil, and figure-eight knots reported previously, we have found stable examples of the Whitehead link and 6_{2} knot. We give a thorough characterization of their geometry and steady-state motion. For the unknot, trefoil, and figure-eight knots we greatly expand previous evidence that FitzHugh-Nagumo dynamics untangles initially complex geometries while preserving topology.

Interaction of scroll waves in an excitable medium: Reconnection and repulsion

Scroll waves of reentrant activity and their interactions pose a serious threat to cardiac health. In experiments with the Belousov-Zhabotinsky reaction we demonstrate the interaction of scroll waves. We show that depending on their mutual orientation, two scroll rings can push each other away and rupture on touching the system boundary, or they can reconnect to form a single, large ring. Reconnection only occurs when the filaments lie within one core length of each other. The reconnected filament has extended lifetimes, which could have serious implications in systems where they occur. The experimental results are explained on the basis of a simple numerical model.

Unpinning of scroll waves under the influence of a thermal gradient

Three-dimensional scroll waves of electrical activity are among the mechanisms believed to be responsible for the rapid, unsynchronized contraction of cardiac ventricles, thereby reducing the heart's ability to pump blood. Scroll waves can attach themselves to unexcitable obstacles, and this sometimes highly elongates their life span. Hence, the unpinning and annihilation of these vortices has attracted much attention in recent decades. In this work, we study the influence of a thermal gradient on scroll waves pinned to inert obstacles, in the Belousov-Zhabotinsky reaction. Under a temperature gradient, scroll rings were seen to unpin from these obstacles, thus strikingly reducing their lifetimes. These results were also reproduced by numerical simulations using the Barkley model.

Interaction of a pair of parallel scroll waves

Interactions of pairs of scroll waves in three-dimensional excitable media were studied experimentally in the Belousov-Zhabotinsky reaction by optical tomography. The behavior of two scroll waves depended on the distance d between their filaments. When the interfilament distance was shorter than the wavelength λ of the scroll waves (but larger than the diameter of the spiral core), the filaments repelled each other. Once d ≈ λ, the two scroll waves synchronized, rotating around their filaments with both a common rotation frequency and a common pitch. The interfilament distance of synchronized scroll waves did not change. When fluctuations broke the symmetry of the rotation periods, the scroll with higher rotation frequency displaced the slower rotating one, until the latter was ousted or even annihilated. These behaviors were independent of the sense of rotation (co- or counter-rotating), the filament dynamics (rigidly rotating or meandering tip motion in two-dimensional media), and the presence or absence of a gradient of excitability parallel to the filaments.

Scroll wave filaments self-wrap around unexcitable heterogeneities

Scroll waves are three-dimensional excitation vortices rotating around one-dimensional phase singularities called filaments. In experiments with a chemical reaction-diffusion system and in numerical simulations, we study the pinning of closed filament loops to inert cylindrical heterogeneities. We show that the filament wraps itself around the heterogeneity and thus avoids contraction and annihilation. This entwining steadily increases the total length of the pinned filament and reshapes the entire rotation backbone of the vortex. Self-pinning is fastest for thin cylinders with radii not much larger than the core of the unpinned rotor. The process ends when the filament is attached to the entire length of the cylinder. The possible importance of self-pinning in cardiac systems is discussed.

Electroelastic unpinning of rotating vortices in biological excitable media

Spiral waves in excitable biological media are associated with pathological situations. In the heart an action potential vortex pinned by an obstacle has to be removed through defibrillation protocols fine-tuned theoretically by using electrophysiological nonlinear mathematical models. Cardiac tissue, however, is an electroelastic medium whose electrical properties are strongly affected by large deformations. In this paper we specifically investigate the electroelastic pinning-unpinning mechanism in order to include cardiac contraction in the preexisting theoretically modeled defibrillation scenarios. Based on a two-dimensional minimal electromechanical model, we show numerically the existence of an unpinning band characterized by the size of the obstacle, the pacing site, and the frequency. Similar numerical simulations, performed in the absence of elastic coupling, show small differences in comparison with the electroelastic studies, suggesting for this specific scenario of pinning-unpinning dynamics a nonprominent role of elasticity.