Drift of sparse and dense spiral waves under joint external forces.

Many methods have been employed to investigate the drift behaviors of spiral waves in an effort to understand and control their dynamics. Drift behaviors of sparse and dense spirals induced by external forces have been investigated, yet they remain incompletely understood. Here we employ joint external forces to study and control the drift dynamics. First, sparse and dense spiral waves are synchronized by the suitable external current. Then, under another weak current or heterogeneity, the synchronized spirals undergo a directional drift, and the dependence of their drift velocity on the strength and frequency of the joint external force is studied.

Resonance of scroll rings with periodic external fields in excitable media.

By direct numerical simulations of a chemical reaction-diffusion system coupled to a periodic external AC electric field with frequency equal to double frequency of the scroll wave rotation, we find that scroll rings resonate with the electric field and exhibit various dynamical behaviors, for example, their reversals, collapses, or growths, depending both on the initial phase of AC electric fields and on the initial phase of scroll rings. A kinematical model characterizing the drift velocity of the scroll rings along their radial directions as well as that of the scroll rings along their symmetry axes is proposed, which can effectively account for the numerical observations and predict the behaviors of the scroll rings. Besides, the existence of the equilibrium state of a scroll ring under the AC electric fields is predicted by the kinematical model and the predictions agree well with the simulations.

A theory for spiral wave drift induced by ac and polarized electric fields in chemical excitable media.

Spiral waves are shown to undergo directional drifts in the presence of ac and polarized electric fields when their frequencies are twice of the spiral frequencies. Here, we propose a quantitative description for the spiral wave drift induced by weak electric fields, and provide the explicit equations for the spiral wave drift speed and direction. Numerical simulations are performed to demonstrate the quantitative agreement with analytical results in both weakly and highly excitable media.

Removal of pinned scroll waves in cardiac tissues by electric fields in a generic model of three-dimensional excitable media.

Spirals or scroll waves pinned to heterogeneities in cardiac tissues may cause lethal arrhythmias. To unpin these life-threatening spiral waves, methods of wave emission from heterogeneities (WEH) induced by low-voltage pulsed DC electric fields (PDCEFs) and circularly polarized electric fields (CPEFs) have been used in two-dimensional (2D) cardiac tissues. Nevertheless, the unpinning of scroll waves in three-dimensional (3D) cardiac systems is much more difficult than that of spiral waves in 2D cardiac systems, and there are few reports on the removal of pinned scroll waves in 3D cardiac tissues by electric fields. In this article, we investigate in detail the removal of pinned scroll waves in a generic model of 3D excitable media using PDCEF, AC electric field (ACEF) and CPEF, respectively. We find that spherical waves can be induced from the heterogeneities by these electric fields in initially quiescent excitable media. However, only CPEF can induce spherical waves with frequencies higher than that of the pinned scroll wave. Such higher-frequency spherical waves induced by CPEF can be used to drive the pinned scroll wave out of the cardiac systems. We hope this remarkable ability of CPEF can provide a better alternative to terminate arrhythmias caused by pinned scroll waves.

Unpinning of rotating spiral waves in cardiac tissues by circularly polarized electric fields.

Spiral waves anchored to obstacles in cardiac tissues may cause lethal arrhythmia. To unpin these anchored spirals, comparing to high-voltage side-effect traditional therapies, wave emission from heterogeneities (WEH) induced by the uniform electric field (UEF) has provided a low-voltage alternative. Here we provide a new approach using WEH induced by the circularly polarized electric field (CPEF), which has higher success rate and larger application scope than UEF, even with a lower voltage. And we also study the distribution of the membrane potential near an obstacle induced by CPEF to analyze its mechanism of unpinning. We hope this promising approach may provide a better alternative to terminate arrhythmia.