The Weiss-Lapicque and the Lapicque-Blair strength-duration curves revisited

The Weiss-Lapicque and Lapicque-Blair relations connecting the strength of a stimulation pulse and its duration in order to attain a threshold are examined here in the case of the nonlinear FitzHugh-Nagumo (FHN) model system. The relation parameters can easilybederived and explained by analyzing the dynamical behavior at very short and very long pulse durations. This explanation should hold true for most nonlinear biological systems. It is seen that, for the FHN, both relations provide only approximations (albeit good ones) to the actual strength-duration curve.