A new set of composite, non-redundant electroencephalogram measures of non-rapid eye movement sleep based on the power law scaling of the Fourier spectrum
Authors: Bódizs Róbert , Szalárdy Orsolya , Horváth Csenge , Ujma Péter P. , Gombos Ferenc , Simor Péter , Pótári Adrián , Zeising Marcel , Steiger Axel , Dresler Martin 
Published: April 2020

AbstractA novel method for deriving composite, non-redundant measures of non-rapid eye movement (NREM) sleep electroencephalogram (EEG) is developed on the basis of the power law scaling of the Fourier spectra. Measures derived are the spectral intercept, the slope (spectral exponent), as well as the maximal whitened spectral peak amplitude and frequency in the sleep spindle range. As a proof of concept, we apply these measures on a large sleep EEG dataset (N = 175; 81 females; age range: 17–60 years) with previously demonstrated effects of age, sex and intelligence. As predicted, aging is associated with decreased overall spectral slopes (increased exponents) and whitened spectral peak amplitudes in the spindle frequency range. In addition, age associates with decreased sleep spindle spectral peak frequencies in the frontal region. Women were characterized by higher spectral intercepts and higher spectral peak frequencies in the sleep spindle range. No sex differences in whitened spectral peak amplitudes of the sleep spindle range were found. Intelligence correlated positively with whitened spectral peak amplitudes of the spindle frequency range in women, but not in men. Last, age-related increases in spectral exponents did not differ in subjects with average and high intelligence. Our findings replicate and complete previous reports in the literature, indicating that the number of variables describing NREM sleep EEG can be effectively reduced in order to overcome redundancy and Type I statistical errors in future electrophysiological studies of sleep.Author summaryGiven the tight reciprocal relationship between sleep and wakefulness, the objective description of the complex neural activity patterns characterizing human sleep is of utmost importance in understanding the several facets of brain function, like sex differences, aging and cognitive abilities. Current approaches are either exclusively based on visual impressions expressed in graded levels of sleep depth (W, N1, N2, N3, REM), whereas computerized quantitative methods provide an almost infinite number of potential metrics, suffering from significant redundancy and arbitrariness. Our current approach relies on the assumptions that the spontaneous human brain activity as reflected by the scalp-derived electroencephalogram (EEG) are characterized by coloured noise-like properties. That is, the contribution of different frequencies to the power spectrum of the signal are best described by power law functions with negative exponents. In addition, we assume, that stages N2–N3 are further characterized by additional non-random (non-noise like, sinusoidal) activity patterns, which are emerging at specific frequencies, called sleep spindles (9–18 Hz). By relying on these assumptions we were able to effectively reduce 191 spectral measures to 4: (1) the spectral intercept reflecting the overall amplitude of the signal, (2) the spectral slope reflecting the constant ratio of low over high frequency power, (3) the frequency of the maximal sleep spindle activity and (4) the amplitude of the sleep spindle spectral peak. These 4 measures 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.