Sources of Variation in the Spectral Slope of the Sleep EEG

Spectral slope of the EMG. a, Distributions of EMG 30- to 45-Hz spectral slopes, stratified by state and cohort (for statistical information, see Extended Data Fig. 2-1). b, The mean EMG slopes (identical to those in panel a) plotted differently, to emphasize the age-related flattening (for the slope associations with sex and BMI, see Extended Data Figs. 2-4, 2-5, 2-6). Green, blue, and red indicate wake, NREM, and REM, respectively. Also see Extended Data Figures 2-2, 2-3, 2-7, and 2-8 for correlations between EMG and EEG slopes and EMG-EEG coherence. See Extended Data Figure 2-9 for the illustration of reference choice and ECG artifacts.

Spectral power based on LM referencing, excluding SHHS. a, Plots as for Figure 1b but based on the LM referencing scheme (all state differences, matched pair t test p < 10⁻¹⁵) at C3LM (for C4LM channel, see Extended Data Figs. 3-1, 3-2). b, Pearson correlation coefficients in slope between the three sleep states considered (all p < 10⁻⁵) at C3LM (for C4LM channel, see Extended Data Fig. 3-3). Green, blue, and red indicate wake, NREM, and REM, respectively.

State classification using LDA based on spectral slope or absolute β band power. Three bar plots illustrate mean accuracies across individuals of W versus R, W versus N2, and R versus N2 classification and dots represent individual accuracies (orange, spectral slope as a predictor and purple β power as a predictor; see Extended Data Figure 4-1 with power of other classic frequency bands as a predictor); P-values above the bars indicate whether there was a significant difference between accuracies produced by LDA based on spectral slope versus β power. Dashed gray line illustrated chance level performance. For details, see Materials and Methods.

Means, within-person and between-person variability in state-specific spectral power. All analyses based on the LM-referenced dataset, with the SHHS studies excluded. Within-individual variability was based on the SD of epoch-to-epoch differences, calculated for each individual separately and then averaged over all individuals in each cohort. In contrast, between-individual variability was the SD based on differences between individuals’ mean power, calculated once for each cohort. See Extended Data Figure 5-1 for these data plotted individually for each cohort.

Epoch counts, variability in spectral power (within-individual and between-individual), and correlations between mean slope and within-individual slope SD. All analyses based on the LM referencing; all epoch counts refer to the number of epochs passing the stringent QC procedures. Green, blue, and red indicate wake, NREM, and REM, respectively. For details, see Materials and Methods.

Relationships between spectral slopes and spectral power. Top row shows Pearson correlation coefficients between individuals’ mean spectral power and mean spectral slope, conditional on sleep state and cohort (for coherence, see Extended Data Fig. 7-1). Extended Data Figure 7-2 provides similar information for both central channels and extended frequency range. The lower three rows show mean power stratified by a median split on spectral power: means for the group of individuals with steeper slopes are represented by dashed (vs solid) lines. All analyses were based on the LM-referenced dataset. Green, blue, and red indicate wake, NREM, and REM, respectively.

Model parameters. These cartoons illustrate the parameterizations of the aperiodic component of the power spectrum we considered in the simulations. In each case, the green term indicates the aspect of the model that was varied, and the corresponding plots show the impact of power spectra (in linear-linear and log-log coordinates, left and right figures, respectively). For illustrative purposes only, the five lines (from blue to red) show the expected power spectrum for five different parameter values (e.g., α = 1, 1.5, 2, 2.5, and 3). Power absolute values/units (y-axes) are arbitrary and so not shown: these figures are intended only to show some of the qualitative patterns of differences that can arise because of variation in a given model parameter. The w(f) function was similar to those depicted in Extended Data Figure 8-1b, with a 50% value at 25 Hz in this example (lower row). Beyond these factors, the model also allowed slope and intercept to be correlated and specified a stochastic error term (smoothed with respect to frequency). For details, see the text and Materials and Methods.

Observed data, initial and revised model simulation-based predictions. The left column of plots reproduces the observed results from the CFS cohort, for state-dependent slope-power correlations (top row) and mean power stratified by a median-split on slope (lower three rows). Green, blue, and red indicate wake, NREM, and REM, respectively. Based on N = 5000 simulated spectra, the middle and right columns show the equivalent simulation-based results, from the original model parameterization (“variable slope model”, the middle column), assuming a strict power law model with mean α = 1, 2.5, and 3 for wake, NREM, and REM, respectively (and SDs of 0.5, 0.5, and 0.75, approximately following the observed between-individual estimates from Fig. 6), and a revised model (“variable slope model with alternate centers of rotation and tapering”, the right column), with similar population parameters for slope means and variances but allowing different centers of rotation (f_r = 10, 35, and 45 Hz for wake, NREM, and REM, respectively) and setting w(f) such that variation in α had less influence on the slope at lower frequencies (see Extended Data Fig. 8-1b). Whereas the initial model (simply varying mean spectral slope by state) could not recapitulate the observed results, the revised model could. For further details, see text and Materials and Methods.