Measuring burstiness and regularity in oscillatory spike trains.

The ability of neurons to emit different firing patterns such as bursts or oscillations is important for information processing in the brain. In dopaminergic neurons, prominent patterns include repetitive, oscillatory bursts, regular pacemakers, and irregular spike trains with nonstationary properties. In order to describe and measure the variability of these patterns, we describe burstiness and regularity in a single model framework. We present a doubly stochastic spike train model in which a background oscillation with independent and normally distributed intervals gives rise to either single spikes or bursty spike events with Gaussian firing intensities. Five easily interpretable parameters allow a classification into bursty or single spike and irregularly or regularly oscillating firing patterns. This classification is based primarily on features of the autocorrelation histogram which are usually studied qualitatively by visual inspection. The present model provides a quantitative and objective classification scheme and relates these features directly to the underlying processes. In addition, confidence intervals visualize the uncertainty of parameter estimation and classification precision. We apply the model to a data set obtained from single dopaminergic substantia nigra neurons recorded extracellularly in vivo. The model is able to represent a high variety of discharge patterns observed empirically, and the classification agrees closely with visual inspection. In addition, changes in the parameters can be studied quantitatively, including also the properties related to bursting behavior. Thus, the proposed model can be used for the description of neuronal firing patterns and the investigation of their dynamical changes with cellular and experimental conditions.