Eikonal Relation in Highly Dispersive Excitable Media

In an excitable medium, the propagation speed C of a wave front is affected by its curvaturek. At small curvature and low dispersion, a widely used approximation ({open_quotes}eikonal equation{close_quotes}) is C=c-{alpha}k, where c is the plane-wave speed and {alpha} is the diffusivity of the medium. We demonstrate that dispersion can lead to hitherto unrecognized deviations of over 100{percent} in the curvature term of C. We present new corrected formulas that are simple, analytically derived, and in good agreement with computer simulations. {copyright} {ital 1997} {ital The American Physical Society}