Comparing Kurtosis Score to Traditional Statistical Metrics for Characterizing the Structure in Neural Ensemble Activity

Abstract

This study investigates the range of behaviors possible in ensembles of spiking neurons and the effect of their connectivity on ensemble dynamics utilizing a novel application of statistical measures and visualization techniques. One thousand spiking neurons were simulated, systematically varying the strength of excitation and inhibition, and the traditional measures of spike distributions – spike count, ISI-CV, and Fano factor – were compared. We also measured the kurtosis of the spike count distributions. Visualizations of these measures across the parameter spaces show a range of dynamic regimes, from simple uncorrelated spike trains (low connectivity) through intermediate levels of structure through to seizure-like activity. Like absolute spike counts, both ISI-CV and Fano factor were maximized for different types of seizure states. By contrast, kurtosis was maximized for intermediate regions, which from inspection of the spike raster plots exhibit nested oscillations and fine temporal dynamics. Brain regions exhibit nested oscillations during tasks that involve active attending, sensory processing and memory retrieval. We therefore propose that kurtosis is a useful addition to the statistical toolbox for identifying interesting structure in neuron ensemble activity.