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

Oscillations figure prominently in models of brain function and dysfunction. It would be informative to analyze oscillations at the level of individual neurons, 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 false negative and false positive rates in statistical tests for oscillatory effects. An existing "shuffling" procedure corrects for RP distortion by removing the spectral component explained by the inter-spike interval (ISI) distribution. However, this procedure sacrifices any oscillation-related information in the ISIs, and power at the corresponding frequencies in the PSD. Here, we ask whether a three-step "residuals" method can improve upon the shuffling method's performance. First, we estimate the RP duration (nr) from the ISI distribution. Second, we fit the spike train with a point process model that predicts spike likelihood based on the time elapsed since the most recent of any spikes falling within the preceding nr milliseconds. Third, we compute the PSD of the model's residuals. We initially compared the residuals and shuffling methods' performance over diverse synthetic spike trains. The residuals method generally yielded the most accurate classification of true- versus false-positive oscillatory power, with this result principally driven by enhanced sensitivity to oscillations in sparse spike trains. Subsequent evaluations used single-unit data 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. Over these units, the residuals method reported the greatest incidence of significant alpha-beta power, with low firing rates predicting residuals-selective oscillation detection. Overall, these results encourage further development of the residuals approach, including expansion to capture additional aperiodic spectral features.