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

Abstract

AbstractOscillations 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 precedingnrmilliseconds. 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.Author SummaryModels of brain function propose that some neurons fire action potentials (“spikes”) rhythmically. That is, the spikes arise from a latent rate function that oscillates at a consistent frequency. We might attempt to detect such oscillations by seeking peaks against a flat baseline in a spike train’s power spectrum. Yet the baseline is not flat: The transient post-spike suppression in spike rate (“recovery period”) introduces a distortion that can both obscure true oscillatory peaks and generate false positives. An established method aims to address the distortion by removing the spectral content that can be recreated with shuffled versions of the spike train. However, this procedure can remove some information about spike rhythmicity, thereby hindering sensitivity to true oscillations. We developed an alternative method that uses regression to remove recovery period effects from the spike train, and computes the spectrum of the residuals. Evaluations on synthetic data demonstrated that this “residuals” method improved upon the established method’s sensitivity to true oscillations. In experimentally-acquired data from a primate model of Parkinson’s Disease, the residuals method also returned increased detections of the expected pathological 8-30 Hz oscillations. These results suggest that the residuals method may support future discoveries of otherwise undetected spike rhythms.