Local shuffling of spike trains boosts the accuracy of spike train spectral analysis

Spectral analysis of neuronal spike trains is an important tool in understanding the characteristics of neuronal activity by providing insights into normal and pathological periodic oscillatory phenomena. However, the refractory period creates high-frequency modulations in spike-train firing rate because any rise in the discharge rate causes a descent in subsequent time bins, leading to multifaceted modifications in the structure of the spectrum. Thus the power spectrum of the spiking activity (autospectrum) displays elevated energy in high frequencies relative to the lower frequencies. The spectral distortion is more dominant in neurons with high firing rates and long refractory periods and can lead to reduced identification of low-frequency oscillations (such as the 5- to 10-Hz burst oscillations typical of Parkinsonian basal ganglia and thalamus). We propose a compensation process that uses shuffling of interspike intervals (ISIs) for reliable identification of oscillations in the entire frequency range. This compensation is further improved by local shuffling, which preserves the slow changes in the discharge rate that may be lost in global shuffling. Cross-spectra of pairs of neurons are similarly distorted regardless of their correlation level. Consequently, identification of low-frequency synchronous oscillations, even for two neurons recorded by a single electrode, is improved by ISI shuffling. The ISI local shuffling is computed with confidence limits that are based on the first-order statistics of the spike trains, thus providing a reliable estimation of auto- and cross-spectra of spike trains and making it an optimal tool for physiological studies of oscillatory neuronal phenomena.