PHYSICAL REVIEW E 88, 052918 (2013) Electric-field-controlled unpinning of scroll waves Zulma A. Jim´ enez, Zhihui Zhang, and Oliver Steinbock Florida State University, Department of Chemistry and Biochemistry, Tallahassee, Florida 32306-4390, USA (Received 23 August 2013; published 27 November 2013) Three-dimensional excitation vortices exist in systems such as chemical reactions and the human heart. Their one-dimensional rotation backbone can pin to unexcitable heterogeneities, which greatly affect the structure, dynamics, and lifetime of the vortex. In experiments with the Belousov-Zhabotinsky reaction, we demonstrate vortex unpinning from a pair of inert and impermeable spheres using externally applied electric fields. Unpinning occurs abruptly but is preceded by a slow reorientation and deformation of the initially circular vortex loop. Our experimental findings are reproduced by numerical simulations of an excitable reaction-diffusion-advection model. DOI: 10.1103/PhysRevE.88.052918 PACS number(s): 05.45.−a, 82.40.Ck, 82.40.Qt I. INTRODUCTION Living systems utilize excitable and oscillatory dynamics to orchestrate a wealth of functions requiring clock-like behavior, macroscopic patterns, and long-range communi- cation [1]. Important examples include circadian rhythms [2], morphogenesis-controlling concentrations fields [3], neu- ronal communication [4], neural representations [5], and cardiac dynamics [6]. Despite the robustness and versatil- ity of the underlying nonlinear phenomena, they can also become the source of dynamic diseases. Two well-known examples are epileptic seizures [7], in which large numbers of neurons synchronize their activity patterns, and cardiac arrhythmias, such as tachycardia and fibrillation [6,8]. The latter, life-threatening conditions are closely related to reen- trant electrical waves that create rhythmic—or chaotic— dynamics with frequencies much higher than the normal heart beat [8,9]. It has long been recognized that tachycardia and fibrillation are the result of vortex-like activation patterns that in the thick ventricles of the human heart require a three-dimensional description [10–13]. In the realm of nonlinear physics and complexity research, such three-dimensional patterns are known as scroll waves [13–15]. They rotate around one- dimensional phase singularities and, if obtained in the normal direction to these filaments, any two-dimensional cross-section reveals locally rotating spiral waves [16]. In the limit of low curvature and twist, the motion of an unperturbed, free filament depends on its local curvature K and two system parameters, α and β , which themselves depend in a very complicated fashion on the underlying reaction-diffusion equations. The parameter α is known as the filament tension and affects the velocity v N in the normal direction to the filament according to v N =−αK . For α> 0, filament loops shrink, converge to circles, and eventually annihilate [17]; for α< 0, filament loops expand and induce scroll wave turbulence [18]. The parameter β affects the speed v B in the binormal direction according to v B = βK . Both parameters can be readily measured from the dynamics of scroll rings with circular filaments (see, e.g., Ref. [19]). Scroll waves are also found in aggregating slime molds [20] and in the autocatalytic Belousov-Zhabotinsky (BZ) reaction [21]. The latter system continues to serve as a simple experimental model for the study of vortex states in living matter as well as a motivational source for theoretical work on excitable reaction-diffusion systems. Despite the numerous similarities between the BZ reaction and biological systems, there are also important differences; for instance, cardiac tissue is, in contrast to the BZ reaction, anisotropic and spatially heterogeneous. In addition, the heart responds to increased action potentials with muscular contraction and vice versa mechanical perturbations can alter the heart’s electric state [22,23]. The heterogeneous nature of the heart is not limited to presence of cells and subcellular structures but extends, in the form of blood vessels and remodeled myocardium [24], to macroscopic length scales. Remodeled myocardium forms after traumatic events, such as myocardial infarction, and contains large numbers of unexcitable myofibroblasts and reduced concentrations of the gap junction protein Connexin43 [25,26]. This “scar tissue” shows contractile dysfunction and slow conduction due to the resulting changes in intracellular coupling that in a core region could block pulse propagation. Remodeled myocardium also plays an important role in the pathogenesis of ventricular tachycardia after infarction. Recent studies suggest that it increases the inducibility of tachycardia and acts in an arrhythmogenic fashion but decreases the reentrance frequency during the arrhythmia [24–26]. At least the latter observation can be interpreted as the consequence of more expansive vortex rotation around regions of reduced excitability. These poorly understood and complex dependencies prompted us to investigate the interaction of scroll waves and unexcitable heterogeneities in isotropic model systems [27,28]. Recent results revealed a variety of unexpected phenomena, including the self-wrapping of filaments around cylindrical wave obstacles [29] and the creation of stationary gradients in rotation phase (twist) [30]. Furthermore, we showed that the curvature-induced shrinking of filament loops can be stopped by local pinning to two or more inert spheres [31,32]. All of these studies demonstrate that heterogeneities dramatically affect the structure and the lifetime of vortex states. Furthermore, pinning is readily accomplished and robust against a wide variety of changes in the filament shape, the initial condition, and the size and shape of the heterogeneity. Here, we show that—despite this robustness— scroll waves can be unpinned by externally applied fields. 052918-1 1539-3755/2013/88(5)/052918(6) ©2013 American Physical Society