Hong Zhang

Turbulence control with local pacing and its implication in cardiac defibrillation.

In this review article, we describe turbulence control in excitable systems by using a local periodic pacing method. The controllability conditions of turbulence suppression and the mechanisms underlying these conditions are analyzed. The local pacing method is applied to control Winfree turbulence (WT) and defect turbulence (DT) induced by spiral-wave breakup. It is shown that WT can always be suppressed by local pacing if the pacing amplitude and frequency are properly chosen. On the other hand, the pacing method can achieve suppression of DT induced by instabilities associated with the motions of spiral tips while failing to suppress DT induced by the instabilities of wave propagation far from tips. In the latter case, an auxiliary method of applying gradient field is suggested to improve the control effects. The implication of this local pacing method to realistic cardiac defibrillation is addressed.

Drift of spiral waves controlled by a polarized electric field

The drift behavior of spiral waves under the influence of a polarized electric field is investigated in the light that both the polarized electric field and the spiral waves possess rotation symmetry. Numerical simulations of a reaction-diffusion model show that the drift velocity of the spiral tip can be controlled by changing the polarization mode of the polarized electric field and some interesting drift phenomena are observed. When the electric field is circularly polarized and its rotation follows that of the spiral, the drift speed of the spiral tip reaches its maximal value. On the contrary, opposite rotation between the spiral and electric field locks the drift of the spiral tip. Analytical results based on the weak deformation approximation are consistent with the numerical results. We hope that our theoretical results will be observed in experiments, such as the Belousov-Zhabotinsky reaction.

Evolution of the Chern-Simons vortices

Based on the gauge potential decomposition theory and the

Drift of rigidly rotating spirals under periodic and noisy illuminations

\ensuremath{\varphi}

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

-mapping theory, the topological inner structure of the Chern-Simons-Higgs (CSH) vortex is discussed in detail. The evolution of CSH vortices is also studied from the topological properties of the Higgs scalar field. The vortices are found generating or annihilating at the limit points and encountering, splitting, or merging at the bifurcation points of the scalar field \ensuremath{\varphi}.

Control of defect-mediated turbulence in the complex Ginzburg–Landau equation via ordered waves

Under the weak deformation approximation, the motion of rigidly rotating spirals induced by periodic and noisy illuminations are investigated analytically. We derive an approximate but explicit formula of the spiral drift velocity directly from the original reaction-diffusion equation. With this formula we are able to explain the main features in the periodic and noisy illuminations induced spiral drift problems. Numerical computations of the Oregonator model are carried out as well, and they agree with the main qualitative conclusions of our analytical results.

Control of spiral breakup by an alternating advective field

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.

Drift velocity of rotating spiral waves in the weak deformation approximation

Here, we study the local control of defect-mediated turbulence or spiral turbulence via ordered waves in the two- (2D) and three-dimensional (3D) complex Ginzburg–Landau equation (CGLE) systems. Depending on the local oscillating frequency resulting from the external periodic injection or the localized inhomogeneity, either spiral waves or target waves could be generated and they may successfully suppress the turbulent waves in the CGLE systems. Theoretical analysis combined with numerical analysis is given to reveal the underlying mechanism.

Chiral selection and frequency response of spiral waves in reaction-diffusion systems under a chiral electric field.

The control of spiral breakup due to Doppler instability is investigated. It is found that applying an alternating advective field with suitable amplitude and period can prevent the breakup of spiral waves. Further numerical simulations show that the growing meandering behavior of a spiral tip caused by decreasing the excitability of the medium can be efficiently suppressed by the alternating advective field, which inhibits the breakup of spiral waves eventually.

Analytical approach to the drift of the tips of spiral waves in the complex Ginzburg-Landau equation

The drift velocities of spiral waves driven by a periodic mechanic deformation or a constant or periodic electric field are obtained under the weak deformation approximation around the spiral wave tip. An approximate formula is derived for these drift velocities and some significant results, such as the drift of spiral waves induced by a mechanical deformation with ω=3ω0, are predicted. Numerical simulations are performed demonstrating qualitative agreement with the analytical results.