Estimation of coupling strength in regenerated lamprey spinal cords based on a stochastic phase model.

We present a simple stochastic model of two coupled phase oscillators and a method of fitting the model to experimental spike-train data or to sequences of burst times. We apply the method to data from lesioned isolated lamprey spinal cords. The remaining tracts at the lesion site are either regenerated medial tracts, regenerated lateral tracts, control medial tracts, or control lateral tracts. We show that regenerated tracts on average provide significantly weaker coupling than control tracts. We compare our model-dependent estimate of coupling strength to a measure of coordination based on the size of deflections in the spike-train cross-correlation histogram (CCH). Using simulated data, we show that our estimates are able to detect changes in coupling strength that do not change the size of deflections in the CCH. Our estimates are also more resistant to changes in the level of dynamic noise and to changes in relative oscillator frequency than is the CCH. In simulations with high levels of dynamic noise and in one experimental preparation, we are able detect significant coupling strength although there are no significant deflections in the CCH.