Propagating activity waves in disinhibited neocortical slices have been used as an experimental model of epileptic seizure propagation. A mathematical model of a one dimensional network of synaptically‐coupled neurons with threshold dependant excitability has been developed to describe these propagating waves. Solutions of the mathematical model provide relationships between the various parameters of the system that can be tested against the experimental model. Specifically, the mathematical solutions suggest the following: at low threshold values the waves travel quickly through the network, at higher threshold values the waves travel slowly, and at very high values waves fail to propagate. Since applied electric fields have been shown to polarize neurons and thereby control threshold, we hypothesized, and subsequently confirmed experimentally, that such electric fields could be used to increase or decrease the speed of propagation and, at high enough values, block seizure propagation. © 2004 American Institute of Physics