Abstract
We consider waves in two-dimensional excitable media. The correct form of the eikonal equation (i.e. the formula that predicts propagation speed as a function of curvature) is a question that has surfaced and resurfaced during the last twenty years or so. Good answers have become available in limiting cases and under certain approximations, notably weak curvatures, low frequencies, and sharp wave fronts. The solution is important in some cardiac pathologies, as well as in our basic understanding of excitable-medium mathematics. After a brief review of curvature effects, particularly in heart tissue, we demonstrate how to obtain a drastically corrected formula that is free of restrictions on frequency and sharpness. (In the original limiting cases the result is unchanged.) Our derivation uses a finite-renormalization method. We illustrate the formula in the context of cardiac tissue. For the sake of definiteness we work in terms of FitzHugh–Nagumo-like models.
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