Fast Selective Elimination of Spiral Waves K. Agladze,* ,² V. Voignier, E. Hamm, F. Plaza, and V. Krinsky Institut Non-Lineaire de Nice, 1361 Route des Lucioles, 06560 Valbonne, France ReceiVed: June 19, 1996; In Final Form: September 18, 1996 X Elimination of spiral waves prevents transition to chaotic state in excitable media of different physicochemical nature. In cardiac muscle, to prevent cardiac death, the spiral waves are usually removed together with all propagating waves by a strong electric shock: 5 kV, 20 A (“defibrillation”). We have found an approach to extinguish spiral waves without destroying normally propagating waves. Chemical excitation waves in a spatial open reactor with the Belousov-Zhabotinsky reaction controlled by light were used as an experimental model. We found three different scenarios, depending on the rate of the light change. (i) When the light intensity was increased immediately, the spiral wave was eliminated. (ii) When it was increased slowly enough, the spiral wave survived, increasing its core and diminishing its rotation rate. (iii) When it was increased gradually, at an intermediate rate, the spiral wave survived, but multiple wave breaks appeared at the periphery. Computer modeling has shown that the results obtained are generic and relevant for excitable media of various nature. Introduction Chemical waves in the Belousov-Zhabotinsky (BZ) reaction are a very convenient model to study propagation of excitation in active media. 1-5 They show either a regular propagation, which can be well controlled by various means, 5-11 or an irregular “chaotic” one, which is very hard to control, resulting in turbulent-like patterns. 1,12-14 The complex patterns usually arise when propagating fronts lose stability and can be eventually broken. The wave breaks give birth to rotating spiral waves, or vortices. 2,15 There are two ways to preserve an excitable medium against chaotic wave propagation: either by avoiding the conditions of wave front instability or eliminating quickly already existing vortices. Only a few mechanisms for the spontaneous wave breaking are known: the local inhomogeneties, 15 particular geometry and boundary conditions of the medium, 13,16 and external extrastimulus. 22 Even fewer choices exist for extin- guishing spiral waves: (1) inducing the spiral wave drift and propelling it slowly out of the medium and (2) suppressing totally at the wave propagation in the system. The drift of the spiral wave, caused by various means (synchronization, 21 periodic modulation of the excitability, 6,9 imposed gradient of the excitability, 11 external electric field 7,8 ), is a very slow process, usually several times less in magnitude than the speed of propagating waves. On the contrary, total suppression can be much faster if the appropriate parameter is chosen, but it destroys all wave propagation, so it is costly for biological systems. 22 In the present work, we have found the possibility of eliminating spiral waves with a fast decrease of the excitability, but without suppression of the wave propagation. We also studied the stability of the wave pattern and its possible transitions to the complex state depending on the rate of transition between the two steady states, both situated far from the boundary of stability. As an experimental model, we used the spatial open reac- tor 17,27 with the light-sensitive BZ reaction. 18,19 The intensity of light illumination was used to control the excitability of the medium. Light is known to inhibit the BZ reaction, 18-20 and the change of light illumination gives us the possibility to control the system with the only delay, defined by chemical kinetics, known to be no more than a few seconds. 20 The possibility of destabilizing the wave pattern with an increase of light intensity was already shown in ref 29. A simple regular wave pattern consisting of a single rotating spiral wave was studied. We found three different scenarios for the development of the wave pattern, depending on the rate of light change. First is “shock” when the transition from one excitable state to another one was made instantaneously (much faster than the rate of spiral wave rotation), the initial spiral wave completely disappeared; the wave pattern was eliminated and, because the system remained excitable, after a short period of time developed anew. Second is “adaptation”: when transition was made very slowly (in the characteristic time scale, about 100 periods of rotations of the spiral wave between initial and final states), the spiral wave survived, reshaping its core and changing its rotation rate; no new wave breaks were observed in the medium. Third is “broken wave-train”: when the transition was made with moderate speed, but not slow enough, multiple wave breaks at the periphery of the spiral wave appeared; the transition induced new turbulent elements in the pattern. This means, for the same amplitude of the excitability change, one has a choice (1) to remove “turbulent” elements of the wave pattern (spiral waves); (2) not to change the wave pattern in general features (all already existing spiral waves survive, no new vortices appeared); or (3) to induce “turbulence” (multiple new spiral waves appear). Experimental Method The spatial open reactor was made as is described in ref 17. The 25 mm diameter, 0.4 mm thick disk of Vycor Corning porous glass was set between two CSTRs with the following chemical composition: tank A, H 2 SO 4 0.3 M, NaBrO 3 0.2 M, NaBr 0.05 M, SDS 0.2 mM, CH 2 (COOH) 2 0.1 M; tank B, H 2 SO 4 0.3 M, NaBrO 3 0.2 M, Ru(bpy) 3 0.2 mM. The residence time was 40 min. The reaction takes place only in the porous glass, where chemicals are mixed by diffusion. Illumination and observation of the wave pattern were made through transparent windows at opposite sides of the reactor. For the ² On leave from ITEB, Russian Academy of Sciences, Pushchino, Russia. X Abstract published in AdVance ACS Abstracts, November 1, 1996. 18764 J. Phys. Chem. 1996, 100, 18764-18769 S0022-3654(96)01826-6 CCC: $12.00 © 1996 American Chemical Society