Detecting rhythmic spiking through the power spectra of point process model residuals

Oscillations in neural activity are often studied in signals that reflect electrical currents aggregated over neuronal populations (e.g., local field potentials). Ideally, we could straightforwardly analyze oscillations in individual neurons’ firing, by estimating the power spectral density (PSD) of spike trains. Unfortunately, spike train spectra exhibit a global distortion generated by the neuronal recovery period (“RP”, the post-spike drop in spike probability, which can extend beyond the refractory period). This distortion can increase the rate of false negatives and false positives from statistical tests for oscillatory effects in the PSD. A common procedure (ISI “shuffling”) can correct for RP distortion by removing the spectral component explained by the inter-spike interval (ISI) distribution. However, this procedure sacrifices any oscillation-related structure in the ISIs – which can be considerable for sparsely spiking units – and power at the corresponding frequencies in the PSD.

Here, we ask whether a new “residuals” method can improve upon the shuffling method’s performance. For this method, we first estimate the RP duration from the ISI distribution. We then fit the spike train with an autoregressive Poisson regression model of equivalent order, and compute the PSD of the residuals. We initially compared the residuals and shuffling methods on a diverse set of simulated spike trains. The residuals method demonstrated increased sensitivity in detecting oscillations, particularly when spiking was sparse. Subsequent evaluations used single-unit data acquired from the internal globus pallidus (GPi) and ventrolateral anterior thalamus (VLa) of a parkinsonian monkey, in which pathological alpha-beta oscillations [8-30 Hz] were anticipated. For both regions, we observed examples of candidate alpha-beta oscillations that the residuals method uniquely detected; such examples were most frequent in the sparsely spiking VLa. Overall, these results suggest previous underestimation of rhythmic activity in sparsely spiking units, and encourage further development of the residuals method.