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1 Center for Neural Computation, The Hebrew University, Jerusalem, Israel; Department of Physiology, The Hebrew University, Hadassah Medical School, Jerusalem, Israel
2 Center for Neural Computation, The Hebrew University, Jerusalem, Israel; Department of Statistics, The Hebrew University, Jerusalem, Israel
3 Department of Physiology, The Hebrew University, Hadassah Medical School, Jerusalem, Israel
4 Center for Neural Computation, The Hebrew University, Jerusalem, Israel; Department of Physiology, The Hebrew University, Hadassah Medical School, Jerusalem, Israel; Roland Center for Neurodegenerative Diseases, The Hebrew University, Jerusalem, Israel
5 Gonda Brain Research Center, Bar-Ilan University, Ramat-Gan, Israel
* To whom correspondence should be addressed. E-mail: michriv2{at}alice.nc.huji.ac.il.
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, since 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 (auto-spectrum) 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. This leads to reduced identification of low-frequency oscillations (such as the 5-10Hz burst oscillations typical of Parkinsonian basal ganglia and thalamus). We propose a compensation process that uses shuffling of inter-spike intervals (ISI) 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, the improvement extends to identification of low-frequency synchronous oscillations. Finally, the method can be adjusted to compensate for a distortion observed in two neurons recorded by a single electrode. 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.
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