Statistical analysis of sleep spindle occurrences

Abstract

Spindles - a hallmark of stage II sleep - are a transient oscillatory phenomenon in the EEG believed to reflect thalamocortical activity contributing to unresponsiveness during sleep. Currently spindles are often classified into two classes: fast spindles, with a frequency of around 14 Hz, occurring in the centro-parietal region; and slow spindles, with a frequency of around 12 Hz, prevalent in the frontal region. Here we aim to establish whether the spindle generation process also exhibits spatial heterogeneity. Electroencephalographic recordings from 20 subjects were automatically scanned to detect spindles and the time occurrences of spindles were used for statistical analysis. Gamma distribution parameters were fit to each inter-spindle interval distribution, and a modified Wald-Wolfowitz lag-1 correlation test was applied. Results indicate that not all spindles are generated by the same statistical process, but this dissociation is not spindle-type specific. Although this dissociation is not topographically specific, a single generator for all spindle types appears unlikely.

Figure 1. Example amplitude-frequency scatter plot.

Spindle properties of subject 3: amplitude-frequency plots for four scalp locations ((A) frontal Fpz, (B) frontocentral Fz, (C) central Cz, and (D) parietal Pz; according to the 10–20 electrode placement standard). Upon progressing from channel Fpz to Pz, the mean frequency of the cluster of spindles shifts from approx. 11 to 13 Hz.

Figure 2. Example overview of statistical spindle properties.

Statistical properties of spindles in subject 3: in grey, histograms of inter-spindle intervals for four scalp locations ((A) Fpz, (B) Fz, (C) Cz, and (D) Pz; inter-spindle interval taken as center-to-center separation in time of automatically detected spindles of stage 2 sleep; bin width of histograms: 1s); superimposed in solid lines, gamma distributions fit to the distribution of inter-spindle intervals. In all four locations, the maximum likelihood distribution fit yields a gamma distribution with shape parameter close to one, suggesting a Poisson process.

Figure 3. Example of gamma fitting evaluation.

Quality assessment of gamma distribution fits for subject 3 (the fits from Fig. 2) across locations ((A) Fpz, (B) Fz, (C) Cz, and (D) Pz): Kolmogorov-Smirnov plots for each of the four fits of gamma distribution to the spindle interval distribution; dotted lines represent 95% confidence bounds. In all four panels the KS plots lie entirely within the confidence bounds pointing to statistically acceptable agreement between the model and the data.

Figure 4. Subject with clear topographical separation of spindles.

Amplitude-frequency plot of an example subject from the group that exhibits a clear topographical separation of low and high frequency spindles: in the frontal channel, (A) Fpz, most spindles do not exceed 12 Hz, with nearly no activity over 14 Hz; in the parietal channel, (D) Pz, most spindles fall between 13 and 16 Hz, with only a few appearing below 12 Hz.

Figure 5. Subject with topographically restricted HFS.

Amplitude-frequency plot of an example subject from the group that exhibits topographically restricted high-frequency spindles, and non-restricted low-frequency spindles: in the frontal channel, (A) Fpz, most spindles appear below 13 Hz; in the parietal channel, (D) Pz, spindles both below and above 13 Hz are common.

Figure 6. Subject without a clear topographical distinction of spindles.

Amplitude-frequency plot of an example subject from the group that exhibits no clear topographical trends: the distribution is similar across scalp locations, with a dominance of low-frequency spindles and a very faint presence of high-frequency spindles over all channels.

Figure 7. Fitted shape parameter across locations.

Values of the shape parameter of fitted gamma distribution for each subject; each panel represents a different scalp location ((A) Fpz, (B) Fz, (C) Cz, and (D) Pz); unreliable fits (as assessed by the KS plot) were removed; bars denote 95% confidence bounds of fitted parameter. Shape parameter reflects the statistical nature of the generation process and, as can be seen above, most channels and most subjects exhibit hallmarks of a Poisson random process (shape parameter not different than 1).

Figure 8. Fitted shape parameter across subjects.

Values of the shape parameter of fitted gamma distribution for each of the scalp locations, assembled subject-wise; unreliable fits (as assessed by the KS plot) were removed; bars denote 95% confidence bounds of fitted parameter. There is no consistent effect of location on the shape parameter that would be exhibited across subjects and that would point to two distinct statistical processes governing frontal and parietal spindles.