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

Theory and experiments of spiral unpinning in the Belousov-Zhabotinsky reaction using a circularly polarized electric field

We present the first experimental study of unpinning an excitation wave using a circularly polarized electric field. The experiments are conducted using the excitable chemical medium, the Belousov-Zhabotinsky (BZ) reaction, which is modeled with the Oregenator model. The excitation wave in the chemical medium is charged so that it can directly interact with the electric field. This is a unique feature of the chemical excitation wave. The mechanism of wave unpinning in the BZ reaction with a circularly polarized electric field is investigated by varying the pacing ratio, the initial phase of the wave, and field strength. The chemical wave in the BZ reaction unpins when the electric force opposite the direction of the spiral is equal to or above a threshold. We developed an analytical relation of the unpinning phase with the initial phase, the pacing ratio, and the field strength. This is then verified in experiments and simulations.

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.

Influence of a circular obstacle on the dynamics of stable spiral waves with straining

The current study envisages to investigate numerically, probably for the first time, the combined effect of a circular obstacle and medium motion on the dynamics of a stable rotating spiral wave. A recently reconstructed spatially fourth and temporally second order accurate, implicit, unconditionally stable high order compact scheme has been employed to carry out simulations of the Oregonator model of excitable media. Apart from studying the effect of the stoichiometric parameter, we provide detailed comparison between the dynamics of spiral waves with and without the circular obstacles in the presence of straining effect. In the process, we also inspect the dynamics of rigidly rotating spiral waves without straining effect in presence of the circular obstacle. The presence of the obstacle was seen to trigger transition to non-periodic motion for a much lower strain rate.

Spiral wave drift under optical feedback in cardiac tissue

Spiral waves occur in various types of excitable media and their dynamics determine the spatial excitation patterns. An important type of spiral wave dynamics is drift, as it can control the position of a spiral wave or eliminate a spiral wave by forcing it to the boundary. In theoretical and experimental studies of the Belousov-Zhabotinsky reaction, it was shown that the most direct way to induce the controlled drift of spiral waves is by application of an external electric field. Mathematically such drift occurs due to the onset of additional gradient terms in the Laplacian operator describing excitable media. However, this approach does not work for cardiac excitable tissue, where an external electric field does not result in gradient terms. In this paper, we propose a method of how to induce a directed linear drift of spiral waves in cardiac tissue, which can be realized as an optical feedback control in tissue where photosensitive ion channels are expressed. We illustrate our method by using the FitzHugh-Nagumo model for cardiac tissue and the generic model of photosensitive ion channels. We show that our method works for continuous and discrete light sources and can effectively move spiral waves in cardiac tissue, or eliminate them by collisions with the boundary or with another spiral wave. We finally implement our method by using a biophysically motivated photosensitive ion channel model included to the Luo-Rudy model for cardiac cells and show that the proposed feedback control also induces directed linear drift of spiral waves in a wide range of light intensities.

Terminating spiral waves with a single designed stimulus: Teleportation as the mechanism for defibrillation

Many chemical and biological systems can sustain complex spiral wave dynamics. In the heart, spiral waves of electrical activity induce deadly arrhythmias and must be eliminated with a large, system-wide perturbation to restore a healthy rhythm. However, the high-energy shocks required for defibrillation therapies are very painful and can even damage heart tissue. In this study, we demonstrate a method for eliminating spiral waves with what should be the minimal possible stimulus required in space for termination. To do this, we show how a localized perturbation can be designed to annihilate simultaneously all spiral waves both free and bound. This identified mechanism is applicable to any excitable system and, for the heart, may lead to more efficient defibrillation strategies.

We identify and demonstrate a universal mechanism for terminating spiral waves in excitable media using an established topological framework. This mechanism dictates whether high- or low-energy defibrillation shocks succeed or fail. Furthermore, this mechanism allows for the design of a single minimal stimulus capable of defibrillating, at any time, turbulent states driven by multiple spiral waves. We demonstrate this method in a variety of computational models of cardiac tissue ranging from simple to detailed human models. The theory described here shows how this mechanism underlies all successful defibrillation and can be used to further develop existing and future low-energy defibrillation strategies.

Control of spiral waves in optogenetically modified cardiac tissue by periodic optical stimulation

Resonant drift of nonlinear spiral waves occurs in various types of excitable media under periodic stimulation. Recently a novel methodology of optogenetics has emerged, which allows to affect excitability of cardiac cells and tissues by optical stimuli. In this paper we study if resonant drift of spiral waves in the heart can be induced by a homogeneous weak periodic optical stimulation of cardiac tissue. We use a two-variable and a detailed model of cardiac tissue and add description of depolarizing and hyperpolarizing optogenetic ionic currents. We show that weak periodic optical stimulation at a frequency equal to the natural rotation frequency of the spiral wave induces resonant drift for both depolarizing and hyperpolarizing optogenetic currents. We quantify these effects and study how the speed of the drift and its direction depend on the initial conditions. We also derive analytical formulas based on the response function theory which correctly predict the drift velocity and its trajectory. We conclude that optogenetic methodology can be used for control of spiral waves in cardiac tissue and discuss its possible applications.

Pulsed low-energy stimulation initiates electric turbulence in cardiac tissue

Interruptions in nonlinear wave propagation, commonly referred to as wave breaks, are typical of many complex excitable systems. In the heart they lead to lethal rhythm disorders, the so-called arrhythmias, which are one of the main causes of sudden death in the industrialized world. Progress in the treatment and therapy of cardiac arrhythmias requires a detailed understanding of the triggers and dynamics of these wave breaks. In particular, two very important questions are: 1) What determines the potential of a wave break to initiate re-entry? and 2) How do these breaks evolve such that the system is able to maintain spatiotemporally chaotic electrical activity? Here we approach these questions numerically using optogenetics in an in silico model of human atrial tissue that has undergone chronic atrial fibrillation (cAF) remodelling. In the lesser studied sub-threshold illumination régime, we discover a new mechanism of wave break initiation in cardiac tissue that occurs for gentle slopes of the restitution characteristics. This mechanism involves the creation of conduction blocks through a combination of wavefront-waveback interaction, reshaping of the wave profile and heterogeneous recovery from the excitation of the spatially extended medium, leading to the creation of re-excitable windows for sustained re-entry. This finding is an important contribution to cardiac arrhythmia research as it identifies scenarios in which low-energy perturbations to cardiac rhythm can be potentially life-threatening.

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.