A set of composite, non-redundant EEG measures of NREM sleep based on the power law scaling of the Fourier spectrum

Abstract

Features of sleep were shown to reflect aging, typical sex differences and cognitive abilities of humans. However, these measures are characterized by redundancy and arbitrariness. Our present approach relies on the assumptions that the spontaneous human brain activity as reflected by the scalp-derived electroencephalogram (EEG) during non-rapid eye movement (NREM) sleep is characterized by arrhythmic, scale-free properties and is based on the power law scaling of the Fourier spectra with the additional consideration of the rhythmic, oscillatory waves at specific frequencies, including sleep spindles. Measures derived are the spectral intercept and slope, as well as the maximal spectral peak amplitude and frequency in the sleep spindle range, effectively reducing 191 spectral measures to 4, which were efficient in characterizing known age-effects, sex-differences and cognitive correlates of sleep EEG. Future clinical and basic studies are supposed to be significantly empowered by the efficient data reduction provided by our approach.

Figure 1

The parametrization of non-rapid eye movement (NREM) sleep electroencephalogram (EEG) spectra. (A) Hypnogram and steps of the spectral EEG analyses as exemplified in a representative record of a young male volunteer. Grey shaded areas represent NREM sleep, which is analysed in the present report. Blue-shaded EEG segments are magnified 4 s long epochs, with 2 s overlap and modified with a Hanning window before power spectral analysis via mixed-radix Fast Fourier Transformation (FFT). (B) Average spectral power (P) is characterized by a frequency (f)-dependent exponential decay (α), as well as by an overall, frequency-independent amplitude multiplier (C) and a peak power multiplier at critical frequencies [P_Peak(f)]. (C) The natural logarithm of spectral power (P) is a linear function of the natural logarithm of frequency (f), characterized by a linear slope α (which is equal with α in panel B) and an intercept (the latter being the natural logarithm of the amplitude multiplier, C in panel B). In addition, this linear function has to be summed with the natural logarithm of the peak power multiplier [P_Peak(f), equal to the same frequency-dependent function in panel B]. Please note that “no peak regions” can be compressed in series of all ones, resulting in reduced number of variables as compared to the bins in the original spectra.

Figure 2

Examples for spectral peaks over the antero-posterior cortical axis in one of the subjects. Upper part: periodograms in the double natural logarithmic plane characterized by a combination of linear trends and spectral peaks. Middle panel: whitened power by subtracting the fitted linears: ln P − (ln C + α ln f); note the uniform baseline power (~ 1) and the spectral peaks. Lower panel: enlarged spectral peaks in the spindle frequency range, characterized by lower frequency maxima in the anterior as compared to the posterior recording locations (see colour-coded arrows); maximal antero-posterior shifts in peak frequency emerged between the frontal and central recording sites, demarcating slow-anterior and fast-posterior sleep spindle-related spectral peaks.

Figure 3

Representative scatterplots of the correlations between age and measures of the NREM sleep EEG spectra at the left prefrontal region (F3). (A) Correlation of age with the spectral exponent (α) indicating the flattening of the spectral slope in the aged subjects. (B) Correlations of age with the whitened maximal spectral peak amplitude in the sleep spindle frequency range (P_Peak(f_maxPeak). Note the decrease in whitened spectral peak amplitude in the aged. (C) Correlation of age with the NREM sleep EEG spectral exponent (α) as categorized by intelligence (HIQ high intelligence quotient, AIQ average intelligence quotient). Note the lack of an IQ effect. (D) Correlation of age with NREM sleep EEG maximal spectral peak frequency (f_maxPeak) in the spindle range. Note the age-dependent decline in frequency. Color codes are consistent with Fig. 1: red—spectral slopes, blue—spectral peaks.

Figure 4

Women vs men differences in measured and parametrized mean NREM sleep EEG spectral power at electrode location C4. The natural logarithm of pectral power was averaged in women and men (continuous lines), as where individual fits (dotted lines) acoording to our current method (see details in section “Methods”). Note the overall amplitude differences (women > men), as well as the higher spectral peak frequencies (f_maxPeak) in women and the lack of differences in spectral peak amplitudes (P_Peak(f_maxPeak)). IQR interquartile range.

Figure 5

Correlations between NREM sleep EEG spindle frequency whitened spectral peak amplitudes and IQ in females and males. (A) Categorized scatterplot representing the correlation between whitened spectral peak amplitude of the NREM sleep EEG spindle frequency range (recording site: F4) and IQ in women and men. (B Pearson r-values were transformed to Z-values and represented on topographical maps. C. Significance probability maps of the correlations presented in B.

Figure 6

Determining the optimal alternative intercept for the NREM sleep EEG spectra. (A) Linear fitted to the double logarithmic plot of an average NREM sleep EEG spectral power (P) derived from right frontopolar location (Fp2) in a young female volunteer. Beside the original, violet-coloured intercept at ln f = 0 (f = 1 Hz), alternative intercepts are depicted at 7.4, 10, 12.2, 13.5, 15 and 20 Hz. (B) Between-subject correlations of the potential intercepts (ln C) with the slopes of the spectra (α) in a location-dependent manner. Note the negative correlations for low and the positive correlation for high frequencies, respectively. Zero-correlations are seen in the middle of the sleep spindle frequency range (at 12.2 and 13.5 Hz), although occipital recording locations are characterized by a slightly different pattern.