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Research ArticleResearch Article: New Research, Cognition and Behavior

Sources of Variation in the Spectral Slope of the Sleep EEG

Nataliia Kozhemiako, Dimitris Mylonas, Jen Q. Pan, Michael J. Prerau, Susan Redline and Shaun M. Purcell
eNeuro 19 September 2022, 9 (5) ENEURO.0094-22.2022; DOI: https://doi.org/10.1523/ENEURO.0094-22.2022
Nataliia Kozhemiako
1Department of Psychiatry, Brigham & Women’s Hospital, Harvard Medical School, Boston, MA 02115
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Dimitris Mylonas
2Department of Psychiatry, Massachusetts General Hospital, Harvard Medical School, Boston, MA 02114
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Jen Q. Pan
3Stanley Center for Psychiatric Research, Broad Institute, Cambridge, MA 02142
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Michael J. Prerau
1Department of Psychiatry, Brigham & Women’s Hospital, Harvard Medical School, Boston, MA 02115
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Susan Redline
4Department of Medicine, Brigham & Women’s Hospital, Harvard Medical School, Boston, MA 02115
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Shaun M. Purcell
1Department of Psychiatry, Brigham & Women’s Hospital, Harvard Medical School, Boston, MA 02115
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Figures

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  • Figure 1.
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    Figure 1.

    Spectral power and slopes based on contra-lateral mastoid referencing. For the channel C4-M1 (linked mastoid referencing, see Extended Data Fig. 1-2; for other channels/reference schemes, see Extended Data Fig. 1-3), (a) mean log power spectra (5–46 Hz) as a function of log frequency by sleep state (wake, NREM, and REM) and cohort with shading illustrating the SDs. Dashed vertical lines at 8 and 13 Hz indicate typical modes of oscillatory activity during wake (α rhythms) and N2 (spindles); dashed lines at 30 and 45 Hz indicate the interval within which the spectral slope was estimated. b, Estimated spectral slopes for the set of independent first-wave individuals (CHAT baseline and nonrandomized samples pooled). Gray lines connect the three values for each individual. Note the different scaling of the y-axis for SHHS1 versus the five other datasets (for details, see Extended Data Fig. 1-1). Green, blue, and red indicate wake, NREM, and REM, respectively. See Table 1 for sample size details.

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    Figure 2.

    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.

  • Figure 3.
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    Figure 3.

    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.

  • Figure 4.
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    Figure 4.

    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.

  • Figure 5.
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    Figure 5.

    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.

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    Figure 6.

    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.

  • Figure 7.
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    Figure 7.

    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.

  • Figure 8.
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    Figure 8.

    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.

  • Figure 9.
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    Figure 9.

    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 (fr = 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.

  • Figure 10.
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    Figure 10.

    Repeated spectral slope assessment in the MrOS cohorts (waves 1 and 2). All analyses were based on the LM-referenced dataset. N = 610 individuals had QC+ recordings for all states in both MrOS1 and MrOS2. Visits were typically approximately five years apart (mean ages of 76.4 and 81.1 for waves 1 and 2, respectively). Green, blue, and red indicate wake, NREM, and REM, respectively. See Extended Data Figures 10-1 and 10-2 for same in CHAT dataset. Age-related effects in a cross-sectional analysis are presented in Extended Data Figure 10-3.

Tables

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    Table 1

    Cohort characteristics

    StudyLabelSample N% femaleMean ageMin. ageMax. ageDOI
    Childhood Adenotonsillectomy
    Trial (baseline)
    CHAT(BL)45352%6.6510doi.org/10.25822/d68d-8g03
    Childhood Adenotonsillectomy
    Trial (nonrandomized)
    CHAT(NR)77953%7.1510doi.org/10.25822/d68d-8g03
    Childhood Adenotonsillectomy
    Trial (follow-up)
    CHAT(FU)40751%7.1510doi.org/10.25822/d68d-8g03
    Cleveland Children’s Sleep and
    Health Study
    CCSHS51550%17.71620doi.org/10.25822/cg2n-4y91
    Cleveland Family StudyCFS73055%41.4789doi.org/10.25822/jmyx-mz90
    Sleep Heart Health Study (wave 1)SHHS1579352%63.13990doi.org/10.25822/ghy8-ks59
    Sleep Heart Health Study (wave 2)SHHS2264754%67.64490doi.org/10.25822/ghy8-ks59
    Osteoporotic Fractures in Men
    Study (wave 1)
    MrOS129070%76.46796doi.org/10.25822/kc27-0425
    Osteoporotic Fractures in Men
    Study (wave 2)
    MrOS210250%81.17397doi.org/10.25822/kc27-0425
    Study of Osteoporotic FracturesSOF453100%82.97595doi.org/10.25822/e1cf-rx65
    • All data are available via the NSRR (http://sleepdata.org). CHAT(FU), SHHS2, and MrOS2 cohorts contained repeated PSGs performed on subsets of CHAT(BL), SHHS1, and MrOS1. For post-QC sample description, see Extended Data Table 1-1.

Extended Data

  • Figures
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  • Extended Data Table 1-1

    Pre-QC and post-QC sample sizes and durations of sleep state by cohort. For each cohort, the average duration of each state, following the initial round of QC (based on removing individuals without sufficient duration (at least 10 minutes) after performing various epoch-level exclusions (QC1), e.g. only retaining epochs flanked by similarly staged epochs, rejecting epochs with annotated arousals or respiratory events, as well as signal outliers, etc. The second round of QC (QC2) excluded individuals based upon statistical properties of the derived metrics (e.g. power, slope). See Methods for details. These procedures were collectively designed to be stringent: that they removed large proportions of some cohorts for the final analysis more reflects the choices of QC rather than inherent issues with the data (i.e. many childhood recordings were removed due to low rates of WASO, as we excluded leading and trailing wake epochs from all recordings, but required all studies to have sufficient duration of wake as well as sleep epochs). No SHHS individuals were retained in the linked mastoid dataset, as it was not possible to re-reference the hardwired contralateral mastoid channels; also see ‘Technical factors in the SHHS datasets’ in Results for other technical issues encountered in the SHHS cohorts. Download Table 1-1, DOC file.

  • Extended Data Figure 1-1

    Spectral slopes in SHHS. a) Histograms of W spectral slopes for C3-M2 and C4-M1, for both wave 1 and 2, which indicate a bimodal distribution for C4-M1 only. b) Mean spectral slopes (separately for C3-M2 and C4-M1 in wave 1 and 2) stratified by the ID of the physical recording device (headbox). The same units and IDs were preserved across waves 1 and 2 (albeit with fewer individuals/devices used, as well as a handful of new devices introduced for wave 2). The devices that were outliers for C4-M1 in wave 2 were also outliers in wave 1. Download Figure 1-1, TIF file.

  • Extended Data Figure 1-2

    EEG spectral slopes (CM-referenced dataset). See legend for Figure 1 for details: similar methods were applied to generate these plots, but here listed for both central channels, and separately for all ten samples. Green, blue and red indicate wake, NREM and REM respectively. Download Figure 1-2, TIF file.

  • Extended Data Figure 1-3

    Mean EEG slopes stratified by state and differences between slopes: CM-referenced dataset. See the Methods for details on the calculation of spectral slopes. Download Figure 1-3, DOC file.

  • Extended Data Figure 2-1

    Mean EMG slopes by state and cohort. See Methods for details on the calculation of EMG spectral slopes. Download Figure 2-1, DOC file.

  • Extended Data Figure 2-2

    Associations between EEG and EMG spectral slopes in the CM-referenced dataset. Standardized regression coefficients and associated p-values from a regression of EEG slope on EMG controlling for age (up to 5th-order polynomials), sex, cohort, race, BMI, AHI and AI. All analyses were performed in the CM-referenced dataset. Download Figure 2-2, DOC file.

  • Extended Data Figure 2-3

    EEG-EMG coherence and EEG spectral slopes. a) For beta and gamma bands, median EEG-EMG coherence stratified by state and cohort. All analyses used CM-referencing. b) Correlations between EEG slope and EEG-EMG coherence, by state and cohort. Particularly during NREM, individuals with higher EEG-EMG crosstalk (i.e. coherence) tended to have steeper slopes. Green, blue and red indicate wake, NREM and REM respectively. Download Figure 2-3, TIF file.

  • Extended Data Figure 2-4

    EEG spectral slope associations with sex and BMI in the CM-referenced dataset. Coefficients and p-values from linear regression models of slope on sex and BMI, additionally controlling for age (and higher-order terms), race and cohort. Also see Figure 2-5. Download Figure 2-4, DOC file.

  • Extended Data Figure 2-5

    Summary of sex && BMI associations with the EEG spectral slope. Results indicate the signed -log10 p-value (as an index of relative effect size) from regressions of slope on sex, BMI and other covariates (see Methods). Only associations with p<0.01 are shown. Green, blue and red indicate wake, NREM and REM respectively. Also see tables Figure 2-4 & Figure 2-6. Download Figure 2-5, TIF file.

  • Extended Data Figure 2-6

    EEG spectral slope associations with sex and BMI in the LM-referenced dataset. Coefficients and p-values from linear regression models of slope on sex and BMI, additionally controlling for age (and higher-order terms), race and cohort. The SHHS was excluded from all LM-reference analyses. Download Figure 2-6, DOC file.

  • Extended Data Figure 2-7

    Coherence between EEG and EMG/ECG in the CFS cohort. Blue/red lines indicate mean coherence for males/females. Note that the use of linked mastoid referencing appeared to reduce EMG/ECG contamination, as indexed by spectral coherence with the EEG. Download Figure 2-7, TIF file.

  • Extended Data Figure 2-8

    Associations between EEG and EMG slopes in the LM-referenced dataset.Correlation coefficients and p-values for associations between EEG and EMG slopes in the LM-referenced dataset. Equivalent results are also reported for the CM-derived EEG slopes (in this same dataset). EEG-EMG correlations are attenuated comparing LM-derived to CM-derived estimates (albeit still significantly larger than zero). Similar results were obtained when controlling for age, sex, cohort and other covariates (see legend for Figure 2-2 for details; note: Figure 2-2 shows standardized regression coefficients from the adjusted model, and so the CM results are not directly comparable to the correlation coefficient presented here). Download Figure 2-8, DOC file.

  • Extended Data Figure 2-9

    Choice of reference and ECG artifacts. The upper plot illustrates 10s of N2 from M1-Fpz, M2-Fpz, M1-M2 (the ‘cross-mastoid’) and (M1+M2)/2 (linked mastoid) for a subject from CFS with extreme cardiac interference in C3-M2. Fpz was the recording reference electrode. Both M1 and M2 time series are severely affected by ECG artifacts. Due to the opposite polarity, however, the linked mastoid (M1+M2)/2 signal almost fully eliminates this issue. The bottom plot shows the C3 channel with different referencing (the recording reference Fpz, M2 and (M1+M2)/2) during the same period. Note how the contralateral mastoid reference introduced cardiac artifacts into the C3 channel; however, if C3 in fact contained strong cardiac artifacts prior re-referencing, using the contralateral mastoid would have helped to cancel it out. The vertical black bar on the left corresponds to 100 uV. Download Figure 2-9, TIF file.

  • Extended Data Figure 3-1

    EEG spectral slope for C4-LM and using IRASA method. a. See legend of Figure 3 for details: this plot provides the same analysis but for C4-LM instead of C3-LM. Green, blue and red indicate wake, NREM and REM respectively. Also see Figure 3-2. b. EEG spectral slope in MrOS cohort for C3 referenced to linked mastoids. From left to right: slopes estimated: between 30 - 45 Hz using original method; between 30 - 45 Hz using IRASA method; between 1 - 30 Hz using IRASA method; between 5 - 30 Hz using IRASA method. Download Figure 3-1, TIF file.

  • Extended Data Figure 3-2

    Mean EEG slopes and state differences in the LM-referenced dataset. Comparable state-specific slope means, and tests of state differences as shown in Figure 1-3 (for the CM-dataset/channels), but here for the LM-derived slopes. Download Figure 3-2, DOC file.

  • Extended Data Figure 3-3

    Cross-state correlations in EEG spectral slopes. All statistics based on the LM-reference datasets (slopes for C3-LM and C4-LM). Correlations stratified by cohort, with outliers (+/- 3 SD units) removed. All correlations are significantly greater than 0 (p < 10-10). Download Figure 3-3, DOC file.

  • Extended Data Figure 4-1

    State classification based on the spectral slope or absolute power across classic frequency bands. Six bar plots on the left illustrate mean accuracies across individuals of W vs R, W vs N2, W vs N3, R vs N2, R vs N3 and N2 vs N3 classification and the error bars represent standard deviation in accuracies across individuals. Dashed grey lines illustrate the performance of spectral slope. The bar plot on the right represents the average goodness of fit (R2) of a linear model based on all stages together for a particular spectral metric ( spectral metric ∼ stage [W, N2, N3, R] + error). Download Figure 4-1, TIF file.

  • Extended Data Figure 5-1

    Spectral power means and variability, by sleep state and cohort. See legend of Figure 5 for details: here, figures are plotted separately by cohort rather than super-imposed (as in Figure 5). Green, blue and red indicate wake, NREM and REM respectively. Download Figure 5-1, TIF file.

  • Extended Data Figure 7-1

    State-specific relationships between inter-hemispheric coherence, power and spectral slope. Analyses based on CFS data only, all analyses based on the LM-referenced dataset. Green, blue and red indicate wake, NREM and REM respectively. Coherence was estimated using magnitude squared coherence, see Methods for details. a. Absolute coherence values were generally high (reflecting the common reference) but for beta and gamma frequencies we observed significantly lower coherence during REM compared to wake, with NREM showing an intermediate pattern. b. Coherence values were not independent of spectral power (here averaged across C3-LM and C4-LM), although we observed qualitatively different relationships between states. NREM exhibited a peak in power/coherence correlation in the sigma range (presumably driven by spindle activity), but also increased coherence/power correlation above 30 Hz. In contrast, during REM sleep there was an inflection point at 30 Hz, after which individual differences in coherence and power decoupled. c reproduces the slope/power correlation for CFS (as shown in Figure 7, but here based on the slope and power averaged over the two central channels). Finally, d shows the correlations between average slope (30-45 Hz) and coherence: as for slope and power, there were qualitatively different patterns between all three states. During REM, individuals with steeper slopes tended to show higher C3-C4 coherence, particularly around 30 Hz. In contrast, during NREM, individuals with steeper slopes tended to show lower coherence at higher (>20 Hz) frequencies, whereas for wake, individuals with steeper slopes tended to show lower coherence at slower (<20 Hz) frequencies. These results - alongside the prior results for the spectral power - underscore the types of qualitative state-dependent differences in measures related to the spectral slope, which appear to extend beyond simply differences in means. Download Figure 7-1, TIF file.

  • Extended Data Figure 7-2

    Correlations between EEG spectral slope and power. All analyses based on the LM-referenced dataset. These Figures provide similar information as Figure 7 (top row) in the main text: here, all non-SHHS cohorts are plotted, results for both LM-referenced central channels are given; also, the x-axis extends < 10 Hz whereas Figure 7 excluded that portion of the power spectrum. Green, blue and red indicate wake, NREM and REM respectively. Download Figure 7-2, TIF file.

  • Extended Data Figure 8-1

    Simulated power spectra with estimated power, spectral slopes, and their correlations. Based on N = 5,000 simulated spectra, derived statistics (columns 2 to 6) for a) the original model parameterization, 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 Figure 6), and b) a revised model, with similar population parameters for slope means and variances but allowing different centers of rotation (fr = 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. Green, blue and red indicate wake, NREM and REM respectively. See Methods for details. Download Figure 8-1, TIF file.

  • Extended Data Figure 10-1

    Test-retest correlations and mean differences in the EEG spectral slope (MrOS and CHAT). Also see Figure 10 (MrOS) and Figure 10-2 (CHAT) for plots of test-retest EEG slope distributions. Download Figure 10-1, DOC file.

  • Extended Data Figure 10-2

    Longitudinal analyses of the CHAT cohort. Based on the LM-referenced dataset, scatter-plots show the EEG spectral slope for baseline and follow-up CHAT (childhood) studies (N = 80 pairs post QC, ∼6 months interval) stratified by sleep state and channel (C3-LM and C4-LM). Green, blue and red indicate wake, NREM and REM respectively. See Figure 10-1 for statistical results. Download Figure 10-2, TIF file.

  • Extended Data Figure 10-3

    Cross-sectional analysis of age-related flattening of the spectral slope. All statistics are based on the LM-reference datasets, using a multiple linear regression model of EEG slope (here average of C3-LM and C4-LM) on age (linear) plus covariates, performed within cohort. CCSHS was excluded as there was effectively no variation in age (most participants were either 17 or 18 years of age). Similar patterns of results were obtained for analyses of each individual LM-referenced channel. Download Figure 10-3, DOC file.

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Sources of Variation in the Spectral Slope of the Sleep EEG
Nataliia Kozhemiako, Dimitris Mylonas, Jen Q. Pan, Michael J. Prerau, Susan Redline, Shaun M. Purcell
eNeuro 19 September 2022, 9 (5) ENEURO.0094-22.2022; DOI: 10.1523/ENEURO.0094-22.2022

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Sources of Variation in the Spectral Slope of the Sleep EEG
Nataliia Kozhemiako, Dimitris Mylonas, Jen Q. Pan, Michael J. Prerau, Susan Redline, Shaun M. Purcell
eNeuro 19 September 2022, 9 (5) ENEURO.0094-22.2022; DOI: 10.1523/ENEURO.0094-22.2022
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