In a simple two-component model of excitable tissue a spiral wave is found to break up into a large number of small spirals. More specifically, we used a modified FitzHugh-Nagumo model. Spiral breakup is found to occur when the recovery variable diffuses at a high rate. The breakup is caused by lateral instability of the wave front. We analyzed this instability using quasi-one-dimensional computations and found that it could be connected to a negative eikonal-curvature relation for the parameter values at which spiral breakup occurs. [S0031-9007(97)02568-4] PACS numbers: 87.10. + e, 05.45. + b, 82.20.Wt, 82.40.Bj Recent studies have demonstrated that spiral waves in excitable media can be generated by a phenomenon called spiral breakup [1][2][3][4][5][6][7][8]. This phenomenon was discussed recently in connection with the mechanisms of cardiac fibrillation [9,10]; spiral breakup has also been found in experiments with the Belousov-Zhabotinskii (BZ) reaction [11 -15]. The mechanism has been discussed in several papers [5][6][7]. It was found to occur in models that show spatiotemporal instabilities of wave trains in onedimensional (1D) excitable media. The mechanism of this 1D instability is believed to be associated with the restitution properties of excitable tissue [16,17].However, experimental data of Markus and Stavridis suggest another possible cause of spiral breakup [12,13].In their experiments the wave fronts develop a curly shape before they break down into chaos. This curly shape is similar to the shape that is expected to occur when the wave front is laterally unstable [18]. The mechanism of this instability is associated with a negative slope of the so-called eikonal-curvature relationship. In this paper we report on the spiral breakup occurring in a two-component FitzHugh-Nagumo (FHN) model due to lateral instability.The lateral instability of a wave front is related to a change in the slope of the eikonal-curvature relationship. This relationship expresses the normal velocity V of a wave as a function of its curvature k. Convex and concave waves are defined by k . 0 and k , 0, respectively. It is possible to derive the following relationship for waves with a small curvature: V V 0 2 Dk, where V 0 is the velocity of a planar wave, and D a constant usually referred to as the effective diffusion coefficient ͑D eff ͒ [19]. Wave instabilities occur if D eff is negative [18]. Therefore we studied the dependence of the velocity of the front on its curvature in a modified FHN model [6] in which we incorporated diffusion for both the recovery and the activator variable. We computed the value of D eff from this dependency, and by using a genetic algorithm we were able to find parameter settings for which D eff , 0. To determine the eikonal relationship, and to calculate D eff , we used fast quasi-1D computations of the eikonal equation with constant curvature of the wave [19]. In this equation, curvature and direction of motion are predefined. The diffusion term is given by Dwhere k is the curvature and j ...

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