VOLUME 77, NUMBER 15 PHYSICAL REVIEW LETTERS 7OCTOBER 1996 Spiral Wave Formation in Three-Dimensional Excitable Media Takashi Amemiya,* Sándor Kádár, Petteri Kettunen, † and Kenneth Showalter ‡ Department of Chemistry, West Virginia University, Morgantown, West Virginia 26506-6045 (Received 16 July 1996) A mechanism for the generation of spiral waves in three-dimensional excitable media is described. Experiments using the photosensitive Belousov-Zhabotinsky reaction show that circular or spiral waves appear in the wake of a propagating wave following a local perturbation in illumination intensity. The induced waves arise from three-dimensional scroll waves striking the upper boundary of the excitable medium. Spiral waves are formed over a range of illumination intensities and perturbation times which place the induced wave in the vulnerable region of the refractory wave back. [S0031-9007(96)01342-7] PACS numbers: 82.20.Wt, 05.45. + b, 47.54. + r Spiral waves are observed in a wide variety of living and nonliving excitable media, e.g., heart tissue [1], ani- mal retina [2], Xenopus laevis oocytes [3], and oscillatory [4,5] and surface catalyzed [6] chemical reactions. Spiral waves in heart tissue have been studied extensively, since they are thought to be a precursor to life-threatening car- diac arrhythmias [7], and studies of biological and chemi- cal excitable media have led to a detailed understanding of spiral wave dynamics [8,9]. Much less is known about the origin of spiral waves, especially their spontaneous appear- ance, although several mechanisms have been advanced [10 – 12]. In this Letter we describe a novel mechanism for spiral wave formation in three-dimensional excitable me- dia. Studies of the photosensitive Belousov-Zhabotinsky (BZ) reaction [13,14] demonstrate that spiral waves may form in the refractory tail of a wave that is perturbed by local changes in excitability in a process involving the for- mation of three-dimensional scroll waves [15]. It is well known that isotropic perturbations cannot give rise to spiral behavior in isotropic, homogeneous media. Spirals can be generated by nonisotropic perturbations, however, such as in cross field stimulation, where a wave is initiated to propagate into the refractory wake of a sec- ond, orthogonal wave [1,10]. Spirals similarly arise when waves are initiated in the vulnerable region of the re- fractory wave back of another wave [16–18]. Spiral be- havior occurs spontaneously in inhomogeneous excitable media, where nonuniform excitability and refractory prop- erties give rise to initiations of irregular wave segments [11,19,20]. Spirals also arise when high frequency waves impinge on impenetrable obstacles [12,21]. The most common technique for producing spirals in the laboratory (or in computer simulations) is to inhibit activity in a wave by lowering the local excitability (or by mechanically breaking the wave), thereby creating free ends around which spiral waves develop. The mechanism for spiral wave generation presented here involves increasing the local excitability transverse to a propagating wave in a three-dimensional medium. Our experiments utilized a thin layer of silica gel [22] with ruthenium(II)-tris-2,2′-bipyridyl catalyst distributed uniformly throughout [23]. The gel was placed into a petri dish and infused with catalyst-free BZ solution. The medium was then exposed (from below) to a constant flux of spatially homogeneous 350–500 nm light. When illuminated with light of this wavelength, the ruthenium- BZ reaction becomes less excitable because Br 2 , an inhibitor in the reaction, is produced in a photochemical cycle [14,23,24]. Since the light is absorbed as it passes through the medium, the excitability is attenuated in the transverse direction. The system was perturbed by using an opaque mask to block the light, thereby changing the local excitability. The perturbation was applied by placing the mask per- pendicular to the front of a propagating wave [Figs. 1(a) and 1(b)]. After a brief period of time, a secondary wave developed in the wake of the primary wave, evolving into either a circular or spiral wave depending on the length of the perturbation and the level of illumination [Figs. 1(c) and 1(d)]. Multiple wave initiations were exhibited for long perturbation times, typically with two circular waves or a spiral wave within a circular wave [Fig. 1(e)]. In all cases, each secondary wave appeared at nearly the same place the primary wave was at the moment the mask was applied. As described below, the secondary waves arise from perturbation-induced, three-dimensional scroll waves [15]. Numerical simulations provide insights into the un- derlying three-dimensional mechanism of the secondary wave generation. Calculations were carried out using the Tyson-Fife scaling [25] of the Oregonator [26], modified to describe the photosensitive BZ reaction [27]: ≠u ≠t  = 2 u 1 1eqw 2 uw 1 u 2 u 2  , (1) ≠y ≠t  u 2y , (2) ≠w ≠t  = 2 w 1 1e 0 f2 qw 2 uw 1 f y , (3) where u, y, and w are the dimensionless concentrations of HBrO 2 , catalyst, and Br 2 , respectively, = 2  ≠ 2 ≠x 2 1 3244 0031-9007 96 77(15) 3244(4)$10.00 © 1996 The American Physical Society