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An electrophysiological marker of arousal level in humans

  1. Janna D Lendner  Is a corresponding author
  2. Randolph F Helfrich
  3. Bryce A Mander
  4. Luis Romundstad
  5. Jack J Lin
  6. Matthew P Walker
  7. Pal G Larsson
  8. Robert T Knight
  1. Helen Wills Neuroscience Institute, University of California, Berkeley, United States
  2. Department of Anesthesiology and Intensive Care Medicine, University Medical Center Tuebingen, Germany
  3. Hertie-Institute for Clinical Brain Research, Germany
  4. Department of Neurology and Epileptology, University Medical Center Tuebingen, Germany
  5. Department of Psychiatry and Human Behavior, University of California, Irvine, United States
  6. Department of Anesthesiology, University of Oslo Medical Center, Norway
  7. Department of Neurology, University of California, Irvine, United States
  8. Department of Psychology, University of California, Berkeley, United States
  9. Department of Neurosurgery, University of Oslo Medical Center, Norway
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Cite this article as: eLife 2020;9:e55092 doi: 10.7554/eLife.55092

Abstract

Deep non-rapid eye movement sleep (NREM) and general anesthesia with propofol are prominent states of reduced arousal linked to the occurrence of synchronized oscillations in the electroencephalogram (EEG). Although rapid eye movement (REM) sleep is also associated with diminished arousal levels, it is characterized by a desynchronized, ‘wake-like’ EEG. This observation implies that reduced arousal states are not necessarily only defined by synchronous oscillatory activity. Using intracranial and surface EEG recordings in four independent data sets, we demonstrate that the 1/f spectral slope of the electrophysiological power spectrum, which reflects the non-oscillatory, scale-free component of neural activity, delineates wakefulness from propofol anesthesia, NREM and REM sleep. Critically, the spectral slope discriminates wakefulness from REM sleep solely based on the neurophysiological brain state. Taken together, our findings describe a common electrophysiological marker that tracks states of reduced arousal, including different sleep stages as well as anesthesia in humans.

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Electroencephalogram (EEG for short) is a widespread technique that helps to monitor the electrical activity of the brain. In particular, it can be used to examine, recognize and compare different states of brain consciousness such as sleep, wakefulness or general anesthesia. Yet, during rapid eye movement sleep (the sleep phase in which dreaming occurs), the electrical activity of the brain is similar to the one recorded during wakefulness, making it difficult to distinguish these states based on EEG alone.

EEG records brain activity in the shape of rhythmic waves whose frequency, shape and amplitude vary depending on the state of consciousness. In the EEG signal from the human brain, the higher frequency waves are weaker than the low-frequency waves: a measure known as spectral slope reflects the degree of this difference in the signal strength. Previous research suggests that spectral slope can be used to distinguish wakefulness from anesthesia and non-REM sleep. Here, Lendner et al. explored whether certain elements of the spectral slope could also discern wakefulness from all states of reduced arousal.

EEG readings were taken from patients and volunteers who were awake, asleep or under anesthesia, using electrodes placed either on the scalp or into the brain. Lendner et al. found that the spectral slope could distinguish wakefulness from anesthesia, deep non-REM and REM sleep. The changes in the spectral slope during sleep could accurately track the degree of arousal with great temporal precision and across a wide range of time scales.

This method means that states of consciousness can be spotted just from a scalp EEG. In the future, this approach could be embedded into the techniques used for monitoring sleep or anesthesia during operations; it could also be harnessed to monitor other low-response states, such as comas.

Introduction

General anesthesia is a reversible, pharmaceutically induced state of unconsciousness, while sleep is internally generated and cycles between rapid (REM) and non-rapid eye movement sleep (NREM; Brown et al., 2010; Franks and Zecharia, 2011). Both sleep stages and anesthesia are characterized by a behaviorally similar state of reduced physical arousal (Brown et al., 2010; Franks and Zecharia, 2011; Murphy et al., 2011). Definitions of arousal vary and include e.g. autonomic, behavioral or mental arousal. For this study, we followed an updated version of the framework by Laureys et al. that defined consciousness on two axes – content (awareness) and level (arousal; Boly et al., 2013; Laureys, 2005). While the conscious content is low in NREM sleep and propofol anesthesia, it is high in wakefulness and dreaming states like REM. The arousal level is low during anesthesia and in all sleep states including REM.

Both NREM sleep stage 3 (also called slow-wave sleep) and general anesthesia with propofol exhibit similar electrophysiological features, such as an increase in low frequency activity and the occurrence of prominent slow oscillations (<1.25 Hz; Brown et al., 2010; Franks and Zecharia, 2011; Murphy et al., 2011; Prerau et al., 2017; Purdon et al., 2013). Moreover, propofol anesthesia has been linked to the emergence of a strong frontal alpha oscillation (8–12 Hz; Purdon et al., 2013) whereas spindles (12–16 Hz) typically appear in NREM sleep stage 2 (Prerau et al., 2017). In contrast, REM sleep is characterized by a desynchronized, active pattern in the electroencephalogram (EEG), which resembles wakefulness (Brown et al., 2010; Prerau et al., 2017). The additional defining features of REM sleep are therefore peripheral markers including muscle atonia as detected by electromyography (EMG) combined with rapid eye movements in the electrooculogram (EOG; Prerau et al., 2017). To date, it has been challenging to differentiate REM sleep from wakefulness in humans solely from the electrophysiological brain state (Pal et al., 2016).

Recently, several lines of inquiry highlighted the importance of non-oscillatory, scale-free neural activity for brain physiology and behavior (Miller et al., 2009a; Gao et al., 2017; Voytek et al., 2015; Voytek and Knight, 2015; Miller et al., 2009b; He et al., 2010). The electrophysiological power spectrum is characterized by a 1/f signal drop-off, i.e. higher frequency activity exhibits reduced power as compared to low frequency activity. This scaling law between power and frequency can be estimated from the exponential decay of the power spectrum (He et al., 2010) and has previously been used to assess a variety of cognitive and EEG phenomena (Colombo et al., 2019; Lina et al., 2019; Miskovic et al., 2019; Pereda et al., 1998; Pritchard, 1992; Shen et al., 2003; Susmáková and Krakovská, 2008). Notably, this decay function mainly captures non-oscillatory brain activity, which is not characterized by a defining temporal scale, such as band-limited oscillations (He et al., 2010). Therefore, analyses of scale-free 1/f dynamics might prove especially helpful when analyzing brain states that are not characterized by prominent oscillations such as REM sleep in humans. We hypothesized that markers of 1/f activity, such as the spectral slope of the power spectrum, may provide an electrophysiological signature that distinguishes ‘paradoxical’ REM sleep (Siegel, 2011) from wakefulness.

Importantly, 1/f dynamics can also be observed in a variety of other signals. For instance, long-range temporal correlations of neuronal oscillations (Linkenkaer-Hansen et al., 2001) or the size and duration of neuronal avalanches (Beggs and Plenz, 2003; Palva et al., 2013) also follow a power law but these scale-free behaviors likely have a different neurophysiological basis than the 1/f drop-off of the power spectrum (He et al., 2010).

Recent findings suggested that 1/f dynamics differentiate wakefulness from general anesthesia (Colombo et al., 2019; Gao, 2016). For instance, using intracranial recordings in macaque monkeys, it had been shown that the spectral slope between 30 and 50 Hz reliably tracked changes in arousal level under propofol anesthesia from induction to emergence (Gao et al., 2017). Moreover, it has been reported that that the spectral slope between 1 and 40 Hz in human scalp EEG recordings discriminated states with conscious content, namely wakefulness and ketamine anesthesia, from states where no conscious report was possible, i.e. Xenon and propofol anesthesia (Colombo et al., 2019). Collectively, these studies implied that propofol anesthesia was accompanied by a steeper decay of the power spectrum (Colombo et al., 2019; Gao et al., 2017).

With regard to sleep physiology, it had been observed that the spectral exponent of human scalp EEG becomes more negative during NREM sleep, when estimated e.g. in the 1 to 5 Hz (Shen et al., 2003), 3 to 30 Hz (Pereda et al., 1998) or 0.5 to 35 Hz frequency range (Miskovic et al., 2019). A similar pattern was observed in intracranial recordings with subdural grid electrodes in humans between 10 and 100 Hz (one subject; Freeman and Zhai, 2009) or 1 and 100 Hz (five subjects; He et al., 2010). Note that the 1/f background activity was estimated from frequency bands that were potentially influenced by simultaneously occurring low frequency oscillation i.e. delta (<4 Hz) or slow waves (<1.25 Hz) that might affect the degree of spectral tilt.

General anesthetics like propofol, etomidate and barbiturates act on GABAergic receptors to enhance inhibition (Brown et al., 2011). Recently, computational simulations indicated that the spectral slope might provide a surrogate marker for the excitation to inhibition (E/I) balance with more negative spectral slopes (esp. in the 30 to 50 Hz range) indexing enhanced inhibition (Gao et al., 2017). This model was validated using intracranial recordings in macaques and rodents: A shift in E/I-balance towards inhibition by administrating propofol resulted in a steeper slope of the power spectrum. Likewise, the spectral slope in the rodent hippocampus varied across the depth of hippocampus, directly reflecting the ratio of excitatory to inhibitory cells in the underlying neuronal population. Moreover, a modulation of spectral slope was also observed as a function of the hippocampal theta cycle, likely reflecting rapid shifts in E/I-balance (Gao et al., 2017).

A recent study that employed two-photon calcium imaging in mice provided additional insight into putative changes in E/I-balance during the sleep cycle. Cortical activity in mice was reduced during NREM sleep compared to wakefulness and, notably, even further reduced during REM sleep (Niethard et al., 2016). Crucially, the authors observed a selective increase in inhibitory interneuron activity (parvalbumin-positive interneurons; Niethard et al., 2016) during REM but not NREM sleep revealing an overall shift towards inhibition during REM sleep.

In the present study, we assessed if 1/f spectral dynamics, in particular in the 30 to 50 Hz range, which is devoid of prominent low-frequency oscillatory activity (Gao et al., 2017), could track arousal states in humans both under anesthesia with propofol and during sleep in intracranial and scalp EEG recordings. Specifically, we hypothesized that the spectral slope should become more negative (i.e. the power spectrum steeper) in sleep and under anesthesia compared to wakefulness. Importantly, we also predicted that the spectral slope could discriminate wakefulness from NREM as well as REM sleep. Based on recent reports linking E/I-balance and electrophysiology (Gao et al., 2017; Niethard et al., 2016), we reasoned that the spectral slope, as a putative marker of E/I-balance, should facilitate the detection of REM sleep directly from the current brain state, without complementary information from additional EMG or EOG recordings. While previous studies that included lower frequency power in their slope estimates, found the slope of REM to be close to wakefulness (He et al., 2010), we specifically investigated if the aperiodic background activity in the 30 to 50 Hz range could reliably discriminate REM sleep from wakefulness and NREM sleep.

Results

We tested if non-oscillatory brain activity as quantified by the spectral slope of the electrophysiological power spectrum could discriminate different states of arousal in four independent studies: We obtained both (1) scalp EEG (n = 9) and (2) intracranial EEG (n = 12) under general anesthesia with propofol. Furthermore, we recorded (3) scalp EEG (n = 20) as well as (4) scalp EEG combined with intracranial EEG (n = 10) during a full night of sleep. We utilized both extra- and intracranial recordings to assess the precise spatial extent of the observed effects. In line with previous reports, the spectral slope was defined by a linear fit to the power spectrum in log-log space between 30 and 45 Hz (Gao et al., 2017). Critically, we carefully validated the chosen parameters in a series of control analyses as indicated below.

1/f spectral dynamics during propofol anesthesia

We first tested if the spectral slope discriminates wakefulness and propofol anesthesia in humans in two experiments. In the first study, we recorded scalp EEG during general anesthesia for orthopedic surgery in otherwise healthy adults (Study 1, n = 9). In the second study, we obtained intracranial EEG in epilepsy patients who were implanted with intracranial electrodes for seizure onset localization while they underwent general anesthesia for electrode explantation (Study 2, n = 12; subdural grid electrodes (electrocorticography; ECoG) and stereotactically placed depth electrodes (SEEG; coverage see Figure 1—figure supplement 1a).

In Study 1 (n = 9), we found that the time-resolved spectral slope closely tracked changes in arousal levels while subjects underwent propofol anesthesia (Figure 1a). Specifically, we observed a significant decrease of the spectral slope from wakefulness (−1.84 ± 0.30; mean ± SEM) to anesthesia (−3.10 ± 0.20) when averaged across all electrodes (Figure 1b; permutation t-test: p<0.0001, obs. t8 = 7.09, dWake-Anesthesia = 1.65).

Figure 1 with 4 supplements see all
The spectral slope tracks changes in arousal level under general anesthesia with propofol.

(a) Time-resolved average of three frontal EEG channels (F3, Fz, F4) during anesthesia. Upper panel: Time-frequency decomposition. Dotted white line: Induction with propofol. Middle: Spectral slope (black; mean ± SEM). Lower panel: Slow frequency (<1.25 Hz; gray) and alpha (8–12 Hz; purple) baseline-corrected power (mean ± SEM). Note, elevated slow frequency activity is already present during wakefulness. While alpha frequency activity is steadily increasing in the first minutes of anesthesia, slow frequency activity exhibits a waxing and waning pattern which may reflect the premedication with a sedative. (b) Anesthesia in scalp EEG (n = 9). Upper panel: Spatial extent of spectral slope difference. Cluster permutation test: *p<0.05. Lower panel: Left - Power spectra (mean ± SEM); Right – Spectral slope. Wakefulness (red), anesthesia (blue) and grand average (black; all mean ± SEM). Permutation t-test: ***p<0.001. (c) Anesthesia in intracranial recordings (n = 12). Upper panel: Left – coronal, right – axial view of intracranial channels that followed (magenta) or did not follow (white) the EEG pattern of a lower slope during anesthesia compared to wakefulness. Lower panel: Left – Power spectra; Right – Spectral slope. Wakefulness (red), anesthesia (blue) and grand average (black; mean ± SEM). Permutation t-test: ***p<0.001.

A cluster-based permutation test assessing the spatial extent of this effect on the scalp level resulted in a single large cluster that spanned all 25 electrodes without a clear peak (p<0.001; Figure 1b). To further examine the spatial distribution of the observed scalp EEG pattern and to assess subcortical contributions, we utilized intracranial recordings in Study 2 (n = 12). Again, we observed that the spectral slope was higher during wakefulness (−2.75 ± 0.15) than during anesthesia (−4.34 ± 0.11) when averaged across all electrodes (Figure 1c; permutation t-test: p<0.0001, obs. t11 = 9.93, dWake-Anesthesia = 3.57). This effect was present at the majority of recording sites (470 of 485 SEEG (96.9%); Figure 1c, Table 1). Notably, recordings from subdural grid electrodes (n = 4) showed the same pattern: The spectral slope decreased from wakefulness to anesthesia in the majority of recording sites (129 of 147 ECoG (87.75%); Figure 1—figure supplement 2a).

Table 1
Anatomical distribution of stereotactically placed intracranial depth electrodes in Study 2 – Intracranial anesthesia (n = 12).
Brain regionTotal number of electrodesElectrodes with state-dependent slope modulation
ALL485470 (96.9 %)
Prefrontal Cortex (PFC)179175 (97.8 %)
 medial Prefrontal Cortex (mPFC)2727 (100 %)
 lateral Prefrontal Cortex (lPFC)147143 (97.3 %)
 Orbito-frontal Cortex (OFC)55 (100 %)
Medial temporal Lobe (MTL)401 (95.0 %)
 Hippocampus2624 (92.3 %)
 Amygdala1313 (100 %)
Cingulate Cortex2222 (100 %)
Insula1313 (100 %)
M1/Premotor4847 (97.9 %)
Lateral Temporal Cortex (LTC)5050 (100 %)
Parietal Cortex8478 (92.9 %)
Visual Cortex4947 (95.9 %)

Taken together, we observed a more negative spectral slope under anesthesia compared to wakefulness in both scalp as well as intracranial EEG (Figure 1b,c). Our results indicate that the spectral slope differentiates between wakefulness and general anesthesia in humans. This effect spanned all scalp and the majority of intracranial electrodes, hence, supporting the notion that propofol anesthesia induces a global, brain-wide state change (Brown et al., 2010).

1/f spectral dynamics discriminate wakefulness, NREM and REM sleep

Having established that the spectral slope differs significantly between wakefulness and propofol anesthesia, we next examined if this state-dependent modulation generalized to other forms of decreased arousal, such as sleep. We specifically sought to determine if the spectral slope could discern wakefulness from different sleep stages. We analyzed two datasets obtained during a full night of sleep. In Study 3, we obtained polysomnography recordings from 20 healthy subjects, which included scalp EEG, as well as electrocardiography (ECG), electromyography (EMG) and electrooculography (EOG). To determine the precise spatial extent and subcortical contributions, we again recorded intracranial EEG in a separate cohort for Study 4 (n = 10; electrode coverage see Figure 1—figure supplement 1b). Critically, we combined intracranial EEG with polysomnography (scalp EEG, ECG, EMG, EOG) to enable comparable sleep staging across both the scalp and intracranial studies.

We observed that the time-resolved spectral slope closely tracked the technician-scored hypnogram (Figure 2a). To quantify this effect, we compared spectral slope estimates across wakefulness, N3 and REM sleep. In Study 3, we obtained a separate baseline eyes-closed recording during rest in 14 out of 20 subjects. In this subset, we observed prominent slope differences between quiescent rest (−1.87 ± 0.18; mean ± SEM), N3 sleep (−3.46 ± 0.16) and REM sleep (−4.73 ± 0.23; Figure 2b). These differences were significant when averaged across all scalp EEG channels (repeated-measures ANOVA permutation test: p<0.0001, obs. F1.94, 25.17 = 56.05, dRest-Sleep = 3.07). Notably, N2 sleep exhibited an average slope of −3.67 ± 0.10 that was also significantly below rest (Figure 2—figure supplement 1a; permutation t-test: pRest-N2 <0.0001; obs. t13 = 7.97; dRest-N2 = 3.31). Permutation t-tests revealed a significant difference between rest and N3 (pRest-N3 <0.0001, obs. t13 = 5.69, dRest-N3 = 2.49), between rest and REM (pRest-REM <0.0001, obs. t13 = 11.67, dRest-REM = 3.71) and between N3 and REM sleep (pN3-REM = 0.0001, obs. t13 = 4.44, dN3-REM = 1.70). Importantly, while some overlap of absolute spectral slope values between rest and sleep existed when comparing across individuals (Figure 2—figure supplement 1a), we observed a consistent individual decrease of – 2.06 ± 0.21 (mean ± SEM) between rest and all sleep stages (Figure 2—figure supplement 1b; Rest-N1 = −1.95 ± 0.26, Rest-N2 = −1.81 ± 0.23, Rest-N3 = −1.59 ± 0.28, Rest-REM = −2.86 ± 0.25).

Figure 2 with 11 supplements see all
The spectral slope tracks changes of arousal level in sleep.

(a) Time-resolved average of three frontal EEG channels (F3, Fz, F4) during a night of sleep. Upper panel: Expert-scored hypnogram (black), wake (pink), REM (light green). Upper middle: Time-frequency decomposition. Lower middle: Spectral slope (black; mean ± SEM). Lower panel: Slow frequency (<1.25 Hz) power (gray; mean ± SEM). (b) Sleep in scalp EEG. Upper panel: Left: Slope difference between sleep and rest (n = 14). Cluster permutation test: *p<0.05. Right: Mutual Information (MI) between the time-resolved slope and hypnogram (n = 20). Cluster permutation test against surrogate distribution created by random block swapping: *p<0.05. Lower panel: Left - Power spectra (n = 14; mean ± SEM); Right – Spectral slope (n = 14). Rest (magenta), NREM stage 3 (blue), REM sleep (green) and grand average (black; mean ± SEM). Repeated measures ANOVA permutation test: ***p<0.001. (c) Sleep in intracranial EEG (n = 10). Upper panel: Left – coronal, right – axial view of intracranial channels that followed (magenta) or did not follow (white) the EEG pattern of a lower slope during sleep (REM/N3). Lower panel: Left – Power spectra (mean ± SEM); Right – Spectral slope of simultaneous EEG recordings (Fz, Cz, C3, C4, Oz). Wakefulness (red), NREM stage 3 (N3; blue), REM sleep (green) and grand average (black; mean ± SEM). Repeated measures ANOVA permutation test: ***p<0.001.

Including all available wake periods (before, during and after the night of sleep in all 20 subjects) increased the variance (Figure 2—figure supplement 1c), which can be explained by the fact that subjects were still drowsy and data during state transitions was included. However, the overall pattern was remarkably similar (Figure 2—figure supplement 1b,d). As this approach increased the available amount of data, we utilized all wake trials (referred to as wake) for subsequent analyses.

Next, we assessed the spatial topography of where the slope tracks the hypnogram. Thus, we calculated the Mutual Information (MI) between the time-resolved spectral slope and the hypnogram. MI is ideal to assess the relationship between a discrete variable (hypnogram) and neurophysiologic data (Quian Quiroga and Panzeri, 2009). In addition, we also repeated all analyses based on linear rank correlations, which yielded comparable results (Figure 2—figure supplement 2a,b).

We observed that the spectral slope closely tracked the hypnogram at all electrodes as indicated by a permutation test (n = 20; average z score = 4.14 ± 0.41 (mean ± SEM); all z > 2.8 correspond to a Bonferroni-corrected p<0.01; Figure 2b). This effect peaked over frontal electrodes F3, Fz and F4 (z = 4.90 ± 0.37; Figure 2b). Since frequencies of cranial muscle activity overlap with the frequency range used for spectral slope estimation, we controlled for possible muscle artifacts by repeating the analysis after local referencing (Laplacian; Fitzgibbon et al., 2013). In addition, we utilized partial correlations that considered the slope of the EMG as a confounding variable. These control analyses indicated that excluding these confounds strengthened the observed relationship between the hypnogram and the spectral slope (Laplacian: pSpearman <0.001, pMI <0.0001; partial correlation: pSpearman <0.001; Figure 2—figure supplement 2).

Spatial characteristics of sleep state-dependent spectral slope modulations

We established that the spectral slope closely tracks the hypnogram. However, we observed pronounced differences between scalp electrodes (Figure 2b), thus, raising the question, which brain regions contribute most to the observed effects at the scalp level. In a source level analysis using an LCMV beamformer, prefrontal areas exhibited the strongest sleepstate-dependent modulation (Figure 2—figure supplement 3). To further investigate the contribution of cortical and subcortical regions, we obtained intracranial EEG recordings (Study 4, n = 10), which were combined with simultaneous scalp EEG recordings.

First, we aimed to replicate the results from Study 3. Again, we found that the slope decreased from wakefulness (−2.99 ± 0.32; mean ± SEM) to N3 sleep (−3.69 ± 0.12) and REM sleep (−4.15 ± 0.29; Figure 2c). These three states were significantly different in a repeated-measures ANOVA permutation test (p=0.0009; obs. F1.97, 17.74 = 10.79, dWake-Sleep = 1.12), thus, directly replicating the pattern as observed in Study 3. Permutation t-tests revealed a significant difference between wakefulness and REM (p=0.0002; obs. t9 = 4.78; d = 1.19) and wakefulness and N3 (p=0.0136; obs. t9 = 2.66; d = 0.92) but only marginally between N3 and REM (p=0.0431; obs. t9 = 1.84; d = 0.64).

Second, we directly tested which intracranial SEEG contacts mirrored the observed scalp EEG pattern. We observed the same pattern - a more negative spectral slope in N3 and REM sleep as compared to wakefulness - in 155 of 352 SEEG (44.03%; chi-squared test against chance-level (33%): X2 = 8.20, p=0.0042; Figure 2c, Figure 2—figure supplement 3). Importantly, this analysis revealed that medial prefrontal cortex (mPFC) and medial temporal lobe structures (MTL; details see Table 2, Figure 2—figure supplement 3) exhibit a significantly larger fraction of electrodes showing sleep state-dependent slope modulation compared to their lateral counterparts (chi-squared tests: mPFC - lateral PFC: p<0.0001, X2 = 33.56, MTL – lateral temporal cortex: p<0.0001, X2 = 33.12), hence, converging on the same brain regions known to be the most relevant for sleep-dependent memory consolidation (Dang-Vu et al., 2008; Helfrich et al., 2018; Mander et al., 2013; Murphy et al., 2009).

Table 2
Anatomical distribution of stereotactically placed intracranial depth electrodes in Study 4 – Intracranial sleep (n = 10).
Brain regionTotal number of electrodesElectrodes with state-dependent slope modulation
ALL352155 (44.0 %)
Prefrontal Cortex (PFC)13249 (37.1 %)
 medial Prefrontal Cortex (mPFC)2824 (85.7 %)
 lateral Prefrontal Cortex (lPFC)7315 (20.6 %)
 Orbito-frontal Cortex (OFC)3010 (33.3 %)
Medial Temporal Lobe (MTL)4833 (68.8 %)
 Hippocampus2719 (70.4 %)
 Amygdala1814 (77.8 %)
Cingulate Cortex4031 (77.5 %)
Insula4121 (51.2 %)
M1/Premotor77 (100 %)
Lateral Temporal Cortex (LTC)7913 (16.5 %)
Parietal Cortex00
Visual Cortex31 (33.3 %)
Other20

Note that we did not specifically target any brain regions and in contrast to previous studies using subdural grid electrodes (Gao et al., 2017; He et al., 2010), the majority of our probes were stereotactically placed depth electrodes (for Wake - N3 and Wake - REM see Figure 2—figure supplement 4; subdural grid electrodes see Figure 1—figure supplement 2b,c). Given the spatial heterogeneity of intracranial responses (Parvizi and Kastner, 2018), there was a remarkable convergence on medial PFC that resembled the pattern observed at source level (Figure 2—figure supplement 3) and the overlying scalp EEG electrode Fz (Figure 2).

The spectral slope discriminates wakefulness from states of reduced arousal

Our findings provide evidence that the spectral slope reliably discriminates wakefulness from sleep. Multiple prior reports indicated that slow waves are a hallmark of decreased arousal states (Brown et al., 2010; Franks and Zecharia, 2011; Murphy et al., 2011). We directly compared how well slow wave activity and spectral slopes estimates differentiate arousal states using both a linear discriminant analysis (LDA) and a multivariate general linear Model (GLM) to discriminate different sleep states based on either the spectral slope or slow wave activity in 18 subjects (two subjects had to be excluded due to insufficient wake trials).

Note that both the LDA classifier and the GLM were trained on the same values that were used in the univariate testing. Both the LDA classifier as well as the GLM output provide a quantitative metric, namely the accuracy of correctly classified trials for LDA and the unique explained variance quantified by eta squared for the GLM enabling a direct comparison between different conditions. The GLM offers the additional advantage of facilitating the assessment of the multivariate interaction of the spectral slope and slow wave power. Data were z-scored before modeling with GLM and LDA outputs were logit-transformed before comparison.

Linear Discriminant Analysis

First, we directly tested if the spectral slope is superior in discriminating REM sleep from wakefulness. We found that classifier performance was enhanced using the spectral slope compared to slow wave power (spectral slope: 76.31 ± 3.61% (mean ± SEM), slow wave power: 61.50 ± 1.93%; permutation t-test: p<0.001, obs. t17 = 3.73, d = 1.25; Figure 3a). This finding indicates that the spectral slope constitutes a marker that successfully discriminates REM sleep from wakefulness solely from the electrophysiological brain state. Note that classification performance is bound by the accuracy of the underlying sleep scoring as a ground truth. Since the inter-rater reliability between sleep scoring experts is typically about 80% (Danker-Hopfe et al., 2009), the classifier accurately predicts the experts' ratings in 80% of the time.

Differentiation of wakefulness from sleep and general anesthesia via Linear Discriminant Analysis (LDA) trained classifier and multivariate general linear modeling (GLM).

All LDA classification performances (panel a – c) were logit-transformed and averaged across channels before comparison. (a) Using the 1/f slope (n = 18; two patients had to be excluded due to insufficient wake trials) resulted in a higher percentage of correct classification of wakefulness and REM compared to slow wave (SO) power (<1.25 Hz; SO: 61.50 ± 1.93% (mean ± SEM), slope: 76.31 ± 3.61%; permutation t-test: p<0.001, observed (obs.) t17 = 3.73, d = 1.25). **p<0.01. Dashed line – chance level at 50% (permutation t-test vs. chance): SO: p<0.001, obs. t17 = 5.51, d = 1.84, slope: p<0.001, obs. t17 = 6.03, d = 2.01). (b) The use of SO power and spectral slope resulted in comparable classification of wakefulness and NREM sleep stage 3 (n = 18; SO: 82.09 ± 2.13%, slope: 73.05 ± 2.97%; permutation t-test: p=0.054, obs. t17 = −1.95, d = −0.72). n.s. – not significant. Dashed line – chance level at 50% (permutation t-tests vs. chance): SO: p<0.001, obs. t17 = 11.23, d = 3.71, slope: p<0.001, obs. t17 = 6.63, d = 2.21). (c) The 1/f slope (n = 9) resulted in a higher classification accuracy of wakefulness and anesthesia with propofol compared to SO power (SO: 52.43 ± 1.04%, slope: 76.56 ± 3.56%; permutation t-test: p<0.001, obs. t8 = 6.10, d = 2.63). ***p<0.001. Dashed line – chance level at 50% (permutation t-test vs. chance): SO: p=0.003, obs. t8 = 2.33, d = 1.10, slope: p<0.001, obs. t8 = 6.15, d = 2.89). All predictors for the multivariate GLM (panel d - f) were z-scored before modeling and calculated on data derived from scalp electrode Fz. (d) Between wakefulness and REM sleep (n = 18; two patients had to be excluded due to insufficient wake trials), the unique explained variance as quantified by eta squared (η2) was significantly different between the 1/f slope, SO power and the interaction between the two (slope: 0.12 ± 0.03, SO: 0.17 ± 0.03, interaction: 0.08 ± 0.02; repeated-measures ANOVA permutation test: p<0.001, F1.16, 19.74 = 19.69). ***p<0.001. (e) Variance between wakefulness and NREM sleep stage 3 (n = 18) was equally well explained by the 1/f slope, SO power and their interaction (slope: 0.12 ± 0.03, SO: 0.17 ± 0.03, interaction: 0.08 ± 0.02; repeated-measures ANOVA permutation test: p=0.081, F1.72, 29.28 = 2.55). n.s. – not significant. f, Out of the total variation between wakefulness and general anesthesia with propofol (n = 9), significantly different proportions could be attributed to the 1/f slope, SO power and their interaction (slope: 0.10 ± 0.03, SO: 0.01 ± 0.003; interaction: 0.002 ± 0.001; repeated-measures ANOVA permutation test: p<0.001, F1.01, 8.09 = 14.61). This effect was mainly driven by the 1/f slope. ***p<0.001.

Second, we repeated this analysis to discriminate wakefulness from N3 sleep. Classification performance using slow wave power or spectral slope did not differ significantly (slow wave power: 82.09 ± 2.13%, spectral slope: 73.05 ± 2.97%; permutation t-test: p=0.054, obs. t17 = −1.95, d = −0.72; Figure 3b). This shows that the spectral slope successfully discriminates wakefulness from N3 sleep despite the fact that the defining criterion of N3 sleep is pronounced slow wave activity. If LDA was used to classify all three states simultaneously (wakefulness, N3, REM; chance level = 33%) then the classifier performance was comparable for the spectral slope and slow wave power (spectral slope: 58.09 ± 2.35%; slow wave power: 63.94 ± 2.04%; permutation t-test: p=0.054, obs. t17 = −1.77, d = −0.62) potentially reflecting the respective advantageous classification of either REM or N3 from wakefulness.

We repeated this analysis to discriminate anesthesia from wakefulness (n = 9). We found that classification based on the spectral slope performed better than the one based on slow wave power (spectral slope: 76.56 ± 3.56%, slow wave power: 52.43 ± 1.04%; permutation t-test: p<0.001, obs. t8 = 6.10, d = 2.63; Figure 3c). Note, that slow wave power was already elevated during wakefulness, which may reflect a premedication with a sedative (see Figure 1a and Materials and Methods).

General Linear Model

When discerning wakefulness from REM sleep, information (as quantified by unique explained variance eta squared) about the underlying arousal state was significantly different between the spectral slope, SO power and their interaction (repeated-measures ANOVA permutation test: p<0.001, F1.16, 19.74 = 19.69). Post hoc t-tests (p-values were Bonferroni-corrected for multiple testing) revealed that this effect was predominantly driven by the spectral slope (slope: 0.29 ± 0.05 (mean ± SEM), SO: 0.05 ± 0.01; interaction: 0.06 ± 0.03; post hoc permutation t-tests (Bonferroni-corrected): Slope-SO: p<0.001, obs. t17 = 4.29, d = 1.50, Slope-Int.: p<0.001, obs. t17 = 4.84, d = 1.62; SO-Int.: p=0.63, obs. t17 = 0.82, d = 0.29).

For NREM stage three sleep and wakefulness, there was no difference in explained variance between factors (slope: 0.12 ± 0.03, SO: 0.17 ± 0.03, interaction: 0.08 ± 0.02; repeated-measures ANOVA permutation test: p=0.081, F1.72, 29.28 = 2.55; post hoc permutation t-tests (Bonferroni-corrected): Slope-SO: p=0.406, obs. t17 = −1.11, d = −0.39; Slope-Int.: p=0.422 obs. t17 = 1.09, d = 0.31; SO-Int.: p=0.032, obs. t17 = 2.44, d = 0.88).

Between anesthesia and wakefulness, information about the state was again significantly different between factors (slope: 0.10 ± 0.03, SO: 0.01 ± 0.003; interaction: 0.002 ± 0.001; repeated-measures ANOVA permutation test: p<0.001, F1.01, 8.09 = 14.61). As in the wake-REM differentiation, this could mainly be attributed to the spectral slope (post hoc permutation t-tests (Bonferroni-corrected): Slope-SO: p<0.001, obs. t8 = 3.70, d = 1.75), Slope-Int.: p<0.001, obs. t8 = 3.95, d = 1.87, SO-Int.: p=0.019, obs. t8 = 2.67, d = 1.07).

Taken together, the results from the GLM mirrored the findings from the LDA approach: The spectral slope enabled an improved classification and contained more unique information about arousal state compared to slow wave power when differentiating wakefulness from both propofol anesthesia and REM sleep and was comparable when discerning wakefulness from N3 sleep.

The relationship of slow waves and the spectral slope

N3 sleep and propofol anesthesia are both characterized by the occurrence of prominent slow oscillations (Murphy et al., 2011). Previous reports indicated that low frequency activity might serve as a marker to disentangle different arousal states (Brown et al., 2010; Franks and Zecharia, 2011; Murphy et al., 2011). Our results confirm and extend this observation. However, while slow wave activity (<1.25 Hz) discriminated wakefulness from N3, it was less robust in separating wakefulness from REM sleep or propofol anesthesia Figure 3). We conducted several control analyses to investigate the relationship of slow wave activity and the spectral slope.

First, we found that the interaction of spectral slope and slow wave activity did not explain more unique variance than the sum of the univariate metrics in a GLM, hence, indicating that the slope and slow wave activity provide complimentary information about arousal states (Figure 3). In addition, if lower frequencies (e.g. 1 to 20 Hz) were utilized for spectral slope estimation, MI between the hypnogram and the time-resolved spectral slope decreased (Figure 2—figure supplement 5d) suggesting that lower frequencies and the 30 to 45 Hz range may index distinct processes.

Second, we analyzed the changes in spectral slope during the time course of a slow wave. At the scalp EEG level, the trough of a slow wave is associated with a cortical ‘down-state’, while the peak reflects an ‘up-state’ (Nir et al., 2011; Valderrama et al., 2012). We found, that the spectral slope mirrored up-/down-states during sleep with more negative slopes observed at slow wave troughs compared to peaks (Figure 4). This effect was most pronounced over frontal channels (cluster-based permutation test: p=0.005, dTrough-Peak = −0.65).

The relationship between spectral slope and slow waves in sleep.

(a) Single subject example: Upper panel: Hypnogram. Wake periods are highlighted in pink, REM periods in light green. Upper middle panel: Multitapered spectrogram of electrode Fz. Lower middle panel: Number of slow wave (SO) events during 30 s segments of sleep in electrode Fz. Note the decreasing number of SO events during the course of the night. Lower panel: Spectral slope of SO events occurring in N3 (blue), wakefulness (red) and REM sleep (green) in electrode Fz. Background: Time-resolved slope of electrode Fz in light gray. (b) Right panel: Average spectral slope changes over the time course of all slow waves in scalp EEG (n = 20) during sleep (blue; mean ± SEM); superimposed in red is the average slow wave of all subjects. Highlighted are the following 0.5 s time windows relative to the slow wave trough: −750 to −250 (center −0.5 s; green), −250 to 250 (center 0 s; pink) and 250 to 750 ms (center 0.5 s; purple). Left panel: Power spectra in log-log space within specified time windows during the slow wave: −750 to −250 (center: −0.5 s; green), −250 to 250 (center: 0 s; pink) and 250 to 750 ms (center: 0.5 s; purple). Note the steep power decrease during the trough of the slow wave (pink). (c) Group level (n = 20) average waveforms in electrode Fz during N3 (blue), REM sleep (green) and wakefulness (red; mean ± SEM). (d) Left: Slow wave events per minute in wakefulness (red), N3 (blue) and REM (green) in scalp EEG channel FZ (n = 20). In black mean ± SEM. Permutation t-tests: ***p<0.001. Right: Slope of slow wave events on the group level (n = 20; averaged across all 19 EEG electrodes) in wakefulness (red), N3 (blue) and REM sleep (green). Mean ± SEM in black. Permutation t-tests: ***p<0.001.

Third, slow wave activity is also present to some degree during REM sleep (Funk et al., 2016) as well as wakefulness (Vyazovskiy et al., 2011). Here, we detected a significantly higher number of slow waves during N3 sleep (SON3 = 28.79 ± 0.79 per minute; mean ± SEM at electrode Fz) as compared to REM sleep (SOREM = 2.16 ± 0.89 per minute; permutation t-test: p<0.0001, obs. t19 = 22.64, d = 7.05) and wakefulness (SOWake = 5.05 ± 0.51 per minute; permutation t-test: p<0.0001, obs. t19 = 25.32, d = 6.92; Figure 4d).

Interestingly, the averaged slope at the trough of the slow waves was significantly different between arousal states: −2.26 ± 0.12 in wakefulness, −3.40 ± 0.09 in N3 sleep and −4.00 ± 0.18 in REM sleep (mean ± SEM), mirroring our observation of the overall slope differences (Figure 4c; permutation t-tests: Wake-N3: p<0.0001, obs. t18 = 7.07, d = 2.38; Wake-REM: p<0.0001, obs. t18 = 9.67, d = 2.55, N3-REM: p=0.007, obs. t19 = 2.73, d = 0.91).

Taken together, our control analyses indicate that slow wave activity and the spectral slope may index two distinct processes.

Control analyses

Evaluation of parameters for 1/f spectral slope estimation

Non-oscillatory background activity decays exponentially following a power law with a 1/f shape: PSD(f)~1/fα. The spectral slope (α) of this decay, sometimes also referred to as spectral exponent (β = - α), can be estimated by a linear regression of the PSD in log-log space (both x- and y-axis are logarithms). In this study, we examined the spectral slope in three distinct states of reduced arousal, namely general anesthesia, NREM three and REM sleep, and in both scalp EEG and intracranial EEG recordings. We estimated the spectral slope from a linear fit to the power spectrum in log-log space from 30 to 45 Hz as suggested previously (Gao et al., 2017). There is no consensus on parameters for spectral slope estimation and a variety of settings have been employed. To address this issue, we systematically evaluated the influence of the following parameters:

  1. Power

    1. Method for power calculationUsing a Multitaper approach (Prerau et al., 2017) for power estimation resulted in a better signal to noise ratio in sleep compared to a single Hanning taper, a periodogram or Welch’s method (no overlap, single taper; Figure 2—figure supplement 6) across all examined frequencies (0.5 to 45 Hz; Fig X, p < 0.001).

    2. Segment lengthA change in segments length from 10 to 30 s under anesthesia or 30 to 10 s in sleep did not change the overall observed pattern of spectral slopes (Figure 1—figure supplement 3b,c; Figure 2—figure supplement 7b,c) and estimates from both segment lengths were strongly correlated (p<0.0001; Figure 1—figure supplement 3d; Figure 2—figure supplement 7d).

    3. Reference schemeBilateral linked mastoids, common average, Laplacian and clinical bipolar reference schemes resulted in comparable spectral slope patterns with more negative slopes for sleep than for rest (Figure 2—figure supplement 8b). Although absolute slopes values varied slightly, they were strongly correlated between montages (p<0.001; Figure 2—figure supplement 8c).

  2. Frequency range

    1. Center frequency for fitWe evaluated the relationship between hypnogram and time-resolved slope as a function of different center frequencies (±10 Hz around center frequency, starting from 20 up to 150 Hz) and found that spectral slope estimates only correlated significantly/had significant Mutual Information (MI) with the hypnogram if center frequencies up to 40 Hz were selected for the fit (Figure 2—figure supplement 5a).

    2. Length of fitWe evaluated the relationship between hypnogram and time-resolved slope as a function of fit lengths (from 30 Hz onwards with a 10 Hz increase of fit length up to 100 Hz). The results showed that spectral slopes estimates could be fitted with variable fit length from 30 Hz onwards and still resulted in a significant correlation/MI with the hypnogram (Figure 2—figure supplement 5b).

    3. Fit to low frequenciesWe explored fits to lower frequencies in both propofol anesthesia and sleep. Under anesthesia, spectral slope estimates from fits to 1 to 40 and 30 to 45 Hz resulted in a similar pattern with more negative slopes during anesthesia compared to wakefulness (Figure 1—figure supplement 4c). Effect sizes between states and goodness of fits were comparable in both frequency ranges (Figure 1—figure supplement 4e) while classification performance between states was better for the lower frequency fit (Figure 1—figure supplement 4f), possibly due to including frequency bands that exhibit strong differences between wakefulness and anesthesia (e.g. delta/alpha oscillation; Purdon et al., 2013).For sleep, we evaluated fits to lower frequencies starting from 1 to 5 Hz with an increasing length of additional 5 Hz per fit after discounting the oscillatory components from the power spectrum by means of irregular resampling (IRASA; Wen and Liu, 2016a, Figure 2—figure supplement 5c). When comparing the MI between the spectral slope fits to a random distribution derived from a block swapping procedure, the 30 to 45 frequency range resulted in significantly higher MI than the fits to lower frequencies (Figure 2—figure supplement 5d).

  3. Fit

    1. Linear regressionWe compared a linear regression with the MATLAB polyfit.m function to the eBOSC algorithm (Caplan et al., 2001; Kosciessa et al., 2020a; Whitten et al., 2011) which employs MATLAB’s robustfit.m function. While both algorithms resulted in slightly different absolute slopes estimates (anesthesia: Figure 1—figure supplement 4a,b; sleep: Figure 2—figure supplement 9a), both estimates revealed the same overall pattern with a more negative slope for sleep compared to rest and anestehsia compared to wakefulness. Moreover, slope estimates derived from both algorithms were strongly correlated (p<0.0001; Figure 1—figure supplement 4d; Figure 2—figure supplement 9c) and did not differ in effect size (Figure 1—figure supplement 4e) or their goodness of fit to the power spectrum (Figure 2—figure supplement 9d).

    2. Model fitWe further compared a linear regression with polyfit (see above) and the model fit of the FOOOF algorithm (Haller et al., 2018). Both algorithms resulted in similar slope estimates (anesthesia: Figure 1—figure supplement 4a,b; sleep: Figure 2—figure supplement 9a) and followed the overall slope pattern with a more negative slope for sleep compared to rest and anesthesia compared to wakefulness. Moreover, slope estimates derived from both algorithms were strongly correlated (p<0.0001; Figure 1—figure supplement 4d, Figure 2—figure supplement 9b) and did not differ in effect size (Figure 1—figure supplement 4e) or their goodness of fit to the power spectrum (Figure 2—figure supplement 9d).

Taken together, the pattern of a more negative slope during sleep and anesthesia compared to wakefulness was robustly observed across a wide spectrum of parameters. A Multitaper approach (Prerau et al., 2017) to calculate the power spectral density was characterized by a higher signal-to-noise ratio in comparison to other methods (Figure 2—figure supplement 6). The choice of segment length depends on the cortical state where quasi-stationarity can be assumed (Figure 1—figure supplement 3, Figure 2—figure supplement 7). Here, we observed slope effects on very different timescales ranging from milliseconds (Figure 4) to full night recordings (Figure 2). The reference scheme did not have a significant effect on the overall observed pattern (Figure 2—figure supplement 8) and can be selected depending on the precise research question: e.g. a bipolar or Laplacian reference might be more suited to examine local phenomena. In sleep, center frequencies from 20 Hz up to 40 Hz (±10 Hz) and fit length of 20 Hz or more (from 30 Hz onwards) exhibited a significant relationship with the hypnogram (Figure 2—figure supplement 5a,b). Spectral slope estimated from fits to lower frequencies e.g. 1 to 20 Hz, on the other hand, had a significantly lower MI with the hypnogram than the 30 to 45 Hz frequency range (Figure 2—figure supplement 5d). Under anesthesia, both fits to 1 to 40 and 30 to 45 Hz led to a comparable slope pattern with more negative slopes under anesthesia compared to wakefulness (Figure 1—figure supplement 4). Thus, while the 30 to 45 Hz frequency range is well suited to differentiate wakefulness from both sleep and anesthesia, other frequency ranges might be advantageous when examining only one state (e.g. lower frequency fits under anesthesia than in sleep). The use of different slope fitting algorithms (polyfit, robustfit (eBOSC), FOOOF) did not impact the overall observed slope pattern in both sleep and under anesthesia and the derived slope values were strongly correlated (Figure 1—figure supplement 4, Figure 2—figure supplement 9). Hence, all three algorithms can be used interchangeably in the examined states and frequency ranges. A model fit via e.g. the FOOOF algorithm (Haller et al., 2018) might be the preferred choice when a bend in the PSD (also called ‘knee’) is observed.

The relationship of connectivity and the spectral slope

Rodent studies suggest that fronto-parietal theta and high-gamma network connectivity correlates with arousal levels in both sleep and general anesthesia (Pal et al., 2018; Pal et al., 2016). We tested this notion and directly compared connectivity estimates to the spectral slope metric: We found that the spectral slope was superior to fronto-parietal theta connectivity in tracking sleep stages and in reliably differentiating REM and N3 sleep (Figure 2—figure supplement 10). Note that our dataset did not have a sufficient number of intracranial electrodes in the parietal lobe to analyze fronto-parietal connectivity since the parietal lobe is an infrequent site for clinical exploration for epilepsy. Hence, we restricted our analyses to theta-band connectivity in scalp EEG. Future studies will be needed to address the relationship of high gamma-band connectivity and the spectral slope.

Discussion

Our results demonstrate that the spectral slope, which reflects one parameter describing the aperiodic component of the electrophysiological power spectrum, facilitates the reliable discrimination of wakefulness from propofol anesthesia, NREM and REM sleep. Here, we present results from four independent studies providing converging evidence that the spectral slope constitutes a marker that tracks arousal levels in humans.

Neurophysiological markers of arousal states

Consciousness is commonly assessed on two axes – content (e.g. the experience) and level (e.g. vigilance; Boly et al., 2013; Laureys, 2005). While conscious content is thought to fluctuate during sleep, mostly in the form of dreams during REM (Siclari et al., 2017), the arousal level is generally reduced as compared to wakefulness. Both components are typically judged by verbal report of the research subject or patient leading to the approximation that content is equivalent to conscious experience as related by the subject whereas the arousal level corresponds to the subject’s ability to respond. Notably, there are some obvious restrictions to these definitions (e.g. the reduced arousal level in REM sleep prevents the subject from relating his experience to the experimenter unless awakened), which make more objective electrophysiological measures desirable.

Several neurophysiological metrics of conscious content such as the Perturbational Complexity Index (PCI; Casali et al., 2013) have been introduced. While PCI is decreased in N3 sleep and GABAergic (e.g. propofol) anesthesia, it resembles wakefulness during REM sleep and ketamine anesthesia, which are both associated with vivid dreams (Casali et al., 2013; Pal et al., 2015; Siclari et al., 2017). A recent EEG study under anesthesia with propofol, xenon and ketamine found that the PCI correlated with the spectral exponent derived from the 1 to 40 Hz frequency range (Colombo et al., 2019). A related study reported that the spectral slope derived from the 0.5 to 35 Hz frequency range became progressively steeper from wakefulness to REM sleep, N2 and N3 sleep (Miskovic et al., 2019). Critically, these metrics did not reliably differentiate arousal levels, i.e. they did not generalize to distinguishing wakefulness from REM sleep.

The overall slowing of EEG activity and the occurrence of oscillations in lower frequency bands has previously been linked to reduced arousal levels (e.g. slow waves and spindles in sleep [Prerau et al., 2017], delta waves and alpha oscillation under propofol anesthesia [Purdon et al., 2013]). REM sleep, also called ‘paradoxical’ sleep (Siegel, 2011), is characterized by a ‘wake-like’ EEG without prominent oscillations in humans. Differentiating between wakefulness and REM solely from the electrophysiological brain state has been challenging and to date still requires simultaneous EMG and EOG recordings to detect muscle atonia and rapid eye movements (Iber et al., 2007).

Here, we demonstrate that the non-oscillatory, aperiodic part of the power spectrum, which is devoid of prominent low-frequency oscillatory components and can be approximated by the 1/f decay of the power spectrum estimated from the 30 to 45 Hz frequency range, reliably differentiates wakefulness from all three states of reduced arousal level, namely REM, N3 sleep and general anesthesia with propofol.

The neurophysiologic basis of 1/f dynamics

1/f dynamics are observed across a variety of tasks (He et al., 2010; Miller et al., 2009a; Miller et al., 2009b; Voytek et al., 2015), change with lifespan (Voytek et al., 2015), and exhibit state-dependent variations during sleep (Freeman and Zhai, 2009; Leemburg et al., 2018; Miskovic et al., 2019; Robinson et al., 2011) and anesthesia (Colombo et al., 2019; Gao et al., 2017). Critically, these dynamics can be observed irrespective of the employed recording modality and species (Colombo et al., 2019; Freeman and Zhai, 2009; Gao et al., 2017; He et al., 2010; Leemburg et al., 2018; Miskovic et al., 2019). However, to date, the underlying neural mechanisms giving rise to the prominent 1/f decay of the electrophysiological power spectrum are not well understood (Buzsáki et al., 2012; He et al., 2010; Miller et al., 2009a; Pesaran et al., 2018).

For instance, it had been observed that broadband activity (~2 to 150 Hz) and high frequency power (>80 Hz) correlate with population neuronal firing rates in macaques and humans (Ray and Maunsell, 2011; Manning et al., 2009) as well as task performance across a range of behavioral experiments (Honey et al., 2012; Miller et al., 2009b; Miller et al., 2014). Furthermore, several lines of research indicate that the spectral slope not only tracks the overall firing rate (Buzsáki et al., 2012; Miller et al., 2009a) but also correlates with a variety of related phenomena, including metrics that can be derived from electrophysiological time-series analysis such as entropy (Miskovic et al., 2019), ensemble synchronization (Shen et al., 2003) or signal complexity (Pereda et al., 1998). Moreover, a link to the local balance between excitation and inhibition (E/I-balance; Gao et al., 2017) as well as dendritic filtering (Buzsáki et al., 2012) has been suggested previously.

Notably, the EEG power spectrum in log-log space does not follow a straight line with a constant spectral exponent, but is characterized by the occurrence of so called ‘knees’ (bends). Different knee frequencies have been reported, such as around 1 ~ 2 Hz (He et al., 2010),~20 Hz (Robinson et al., 2011; Robinson et al., 2001) and ~75 Hz (Miller et al., 2009a). The characteristic form of the power spectrum can be modeled by the multiplication of Lorentzian functions (He, 2014; He et al., 2010; Miller et al., 2009a; Miller et al., 2014) where the knee frequencies are directly related to the time constants of the exponential decay (e.g. 2 ~ 3 ms for the 75 Hz knee and ~100 ms for the 1 ~ 2 Hz knee). Although the origin of these time constants remains unclear, it has been suggested that the 2 ~ 3 ms time constant originates from synaptic currents, while the 100 ms time constant reflects membrane leak (He, 2014; Miller et al., 2009a). Other studies attributed the 20 Hz knee to the low pass filtering properties of dendrites (Robinson et al., 2011; Robinson et al., 2001). Critically, the 1/f dynamics in between those knee frequencies exhibit different spectral exponents: While an exponent of 2–3 is observed for center frequencies (~1 to 80 Hz; Freeman and Zhai, 2009; He et al., 2010; Miller et al., 2009a), higher frequencies (80 to 500 Hz) exhibited an exponent closer to 4 (Miller et al., 2009a), thus, suggesting that the spectral slopes in different frequency ranges might be the consequence of different generative mechanisms.

A recent study proposed that the shape of the power spectrum of human intracranial EEG is the product of local (fast) and distributed (slow) recurrent networks that are balancing excitation and inhibition in such a way that the network is tuned to the edge of dynamic instability, thus, maximizing information processing capacities (Chaudhuri et al., 2018). Further in-silico modeling of E/I-balance suggested that the spectral slope in the 30 to 50 Hz range functions as an index of this balance where an increase in inhibition is accompanied by a decrease of spectral slope (Gao et al., 2017). One testable hypothesis that arises from these observations is that cell-type-specific causal manipulations by e.g. optogenetics through selective targeting of excitatory pyramidal or inhibitory parvalbumin- or somatostatin-positive interneurons should bias the spectral slope in opposite directions.

Future studies involving single neuron recordings and optogenetic manipulation will be needed to unravel the precise relationship between population firing statistics and changes in the spectral slope. Comparative studies in rodents (Gao et al., 2017; Leemburg et al., 2018), non-human primates (Gao et al., 2017) and humans (Colombo et al., 2019; He et al., 2010; Miller et al., 2009a; Miller et al., 2009b; Miskovic et al., 2019) combined with modeling work (Chaudhuri et al., 2018; Robinson et al., 2011; Robinson et al., 2001) has the potential to integrate the divergent findings into a coherent framework, which is critical to further elucidate the neurophysiologic basis of 1/f dynamics and their relationship to arousal levels.

Functional significance of 1/f dynamics in arousal states

Here, we found a decreased 1/f slope in N3 sleep, REM sleep and under general anesthesia compared to wakefulness in four independent studies. If the spectral slope reflects the local E/I-balance (Gao et al., 2017), then our results would indicate that decreased arousal states are characterized by increased inhibition. In support of this consideration, several previous studies reported that propofol anesthesia and N3 sleep are associated with increased inhibition (Brown et al., 2011; Gao et al., 2017; Timofeev et al., 2001) as well as prominent changes in neuronal firing rates (Lewis et al., 2012; Timofeev et al., 2001; Vyazovskiy et al., 2009; Watson et al., 2016). Notably, there is little evidence supporting a similar association for REM sleep. However, a recent two-photon calcium imaging study in rodents reported a reduction of the overall cortical firing rate during slow-wave and even further during REM sleep (Niethard et al., 2016). Critically, this study also demonstrated that reduced firing rates during REM sleep were accompanied by a selective increase of inhibitory parvalbumin interneuron activity, thus, reflecting a relative shift towards inhibition (Niethard et al., 2016). These results parallel the pattern as observed in this present study (Figure 2—figure supplement 11) where the steepest decay of the power spectrum (the most negative PSD slope) occurred during REM sleep.

Jointly, these findings imply that REM sleep could be associated with the highest level of cortical inhibition, thus, resulting in a steeper decay of the power spectrum. This notion of increased inhibition during REM sleep offers a likely mechanistic explanation for certain REM-defining phenomena, such as muscle atonia (Scammell et al., 2017) or the clinical observation that epileptic seizures during the night predominantly occur out of more excitable, highly synchronized NREM sleep and only rarely out of less excitable, desynchronized REM sleep (Ng and Pavlova, 2013).

Practical considerations for analyzing 1/f dynamics

A wide array of settings has been employed to examine 1/f features in electrophysiological recordings. Practical guidelines on how to select parameters for spectral slope estimation remain scare. Here, we explored a range of different settings for a series of parameters to reliably estimate 1/f activity in arousal states.

The estimation of 1/f background activity first requires a spectral decomposition of the underlying time-series. Here, we directly compared several algorithms (multiple slepian tapers, single Hanning window, Periodogram, Welch’s method) and found that the Multitaper approach yielded the highest signal-to-noise ratio (Figure 2—figure supplement 6). Critically, window length and spectral smoothing parameters need to be adjusted to a reasonable time window where stationarity of the time series can be assumed (e.g. 30 s segments for sleep; Figure 2—figure supplement 7). The choice of different reference schemes or slope fitting algorithms, namely a linear regression (see Methods), the eBOSC algorithm (Kosciessa et al., 2020a) as well as the FOOOF algorithm (Haller et al., 2018), resulted in a comparable overall spectral slope pattern with strongly correlated slope estimates (Figure 1—figure supplement 4, Figure 2—figure supplement 9).

Additionally, we also explored a range of different fit frequencies (Figure 1—figure supplement 4, Figure 2—figure supplement 5). Collectively, our results indicate that the spectral slope should be approximated in a frequency range where no pronounced oscillatory activity and no prominent bend (‘knee’) are present. Therefore, the optimal choice of frequency range might differ between arousal states.

In sleep, fitting the power spectrum to frequencies above 30 Hz (and <45 Hz to avoid the European line noise frequency at 50 Hz) shared the highest Mutual Information with the hypnogram (Figure 2—figure supplement 5). An inclusion of lower frequencies (e.g. 10 to 30 Hz or various fits length from 1 Hz onwards (compare Figure 2—figure supplement 5a,d) diminished this relationship, indicating a conflation of background and oscillatory activity. Critically, our results from a general linear model demonstrated that the slope in higher frequencies (above 30 Hz) carried independent information from slow oscillatory activity about the current brain state (Figure 3).

Incorporating frequencies below 20 Hz resulted in a better separation between wakefulness and anesthesia (Figure 1—figure supplement 4), possibly due to the inclusion of the alpha range (~8–10 Hz) where prominent oscillations are observed under propofol anesthesia (Figure 1).

Taken together, a fit to the 30 to 45 frequency range reliably differentiated wakefulness from anesthesia, NREM three and REM sleep.

Conclusions

Collectively, our results from four independent studies provide five main advances: First, the spectral slope tracks changes in arousal levels in both propofol anesthesia and sleep in humans with high temporal precision and is observable on a wide range of timescales from sub-second epochs to full night recordings.

Second, our results provide empirical evidence for the notion that the slope in the range from 30 to 45 Hz correlates well with all stages of arousal. Previous studies analyzing the spectral slope during states of reduced arousal have either employed different frequency ranges (Colombo et al., 2019; Freeman and Zhai, 2009; He et al., 2010; Miskovic et al., 2019) or focused either on anesthesia (Colombo et al., 2019; Gao et al., 2017) or sleep (Miskovic et al., 2019; Pereda et al., 1998; Shen et al., 2003). Here, we demonstrate that this frequency range is well suited to track arousal in both anesthesia and different sleep levels including REM and NREM sleep.

Third, the spectral slope mirrored the rapid changes in excitability observed over the course of a slow wave directly tracking cortical ‘up- ‘and ‘down-states’, hence, providing a mechanistic link between the spectral slope and population synchrony during slow oscillations.

Fourth, our observations support the premise that anesthesia is a brain-wide state (Brown et al., 2010), whereas sleep exhibits network-specific activity patterns. Here, we observed that sleep dependent slope modulations were strongest in the medial temporal lobe and medial PFC, two key regions for sleep-dependent memory consolidation (Diekelmann and Born, 2010; Preston and Eichenbaum, 2013; Stickgold and Walker, 2013).

Fifth, the spectral slope can be reliably estimated from scalp EEG recordings, thus, providing an accessible marker that can easily be incorporated into intraoperative neuromonitoring or automatic sleep stage classification algorithms. In the future, this marker could potentially be utilized to monitor other states of reduced arousal such as epileptic seizures, coma, the vegetative or minimally conscious state.

Materials and methods

Key resources table
Reagent type (species) or resourceDesignationSource or referenceIdentifiersAdditional information
Software, algorithmMATLAB Release 2015a and 2018a; Signal Processing Toolbox, Curve Fitting Toolbox, Statistics and Machine Learning ToolboxThe MathWorks Inc, 2020, Natick, Massachusetts, USAID_source:SCR_001622
Software, algorithmAdobe Illustrator CS6 and CC 2018 Adobe Inc, 2020, Dublin, Republic of IrelandID_source:SCR_010279
Software, algorithmFieldTrip 20170829Oostenveld et al., 2011; Stolk et al., 2018ID_source:SCR_004849http://www.fieldtriptoolbox.org/
Software, algorithmEEGLAB_14_0_0bDelorme and Makeig, 2004ID_source:SCR_007292https://sccn.ucsd.edu/eeglab/index.php
Software, algorithmFreeSurfer 5.3.0Dale et al., 1999; Fischl, 2012ID_source:SCR_001847https://surfer.nmr.mgh.harvard.edu/
Software, algorithmLCMV BeamformerVan Veen et al., 1997
Software, algorithmIRASA (Irregular Resampling Auto-Spectral Analysis)Wen and Liu, 2016b
Software, algorithmMultitaper Spectral AnalysisPrerau et al., 2017
Software, algorithmFOOOF (Fitting Oscillations and One Over F)Haller et al., 2018https://pypi.org/project/fooof/
Software, algorithmeBOSC (extended Better OSCillation detection)Kosciessa et al., 2020bhttps://github.com/jkosciessa/eBOSC
Software, algorithmMutual InformationQuian Quiroga and Panzeri, 2009http://prerau.bwh.harvard.edu/multitaper/
Software, algorithmBioSig Toolbox - Logit transformationSchlogl and Brunner, 2008 ID_source:SCR_008428
Software, algorithmGeneral Linear ModelSiegel et al., 2015 
Software, algorithmSlow wave detectionHelfrich et al., 2018Staresina et al., 2015 
Software, algorithmRandom Block Swapping (statistics)Canolty et al., 2006; Aru et al., 2015
Software, algorithmConnectivityiPLV (imaginary Phase Lock Value) - Nolte et al., 2004; rhoortho (orhtogonalized power correlation) - Hipp et al., 2012
OtherNA

Participants

We collected four independent datasets for this study to assess the neurophysiological basis of states of reduced arousal, namely general anesthesia and sleep. We recorded either non-invasive scalp electroencephalography (EEG) or intracranial EEG (electrocorticography; ECoG) using subdural grid and strip electrodes and stereotactically placed depth electrodes (SEEG; for coverage see Figure 1—figure supplement 1).

Anesthesia

The EEG and intracranial anesthesia studies were conducted at the University Hospital of Oslo. All participants or their parents provided informed written consent according to the local ethics committee guidelines (Regional Committees for Medical and Health Research Ethics in Oslo case number 2012/2015 and extension 2012/2015–8) and the Declaration of Helsinki.

Study 1 - Anesthesia scalp EEG

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Ten patients (two female) undergoing anterior cervical discectomy and fusion participated in Study one and received a total intravenous anesthesia with remifentanil and propofol. They had an American Society of Anesthesia status of I - III, were between 46 and 64 years old (53.3 ± 5.7 years; mean ± SD) and otherwise healthy. Data were recorded from the induction of anesthesia to the recovery from 25 channel EEG according to the 10–20 layout (EEG Amplifier, Pleasanton, California, USA) with an additional row of electrodes (F9, F10, T9, T10, P9, P10) at a digitization rate of 512 Hz, or in the case of one patient at 256 Hz. The electrode for referencing was placed at CP1. Three patients were not recorded for the planned entire time span – one recording was only started after induction, while two were stopped before recovery (Juel et al., 2018).

Study 2 - Anesthesia intracranial EEG

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A total of 12 patients (three female) with intractable epilepsy participated in Study 2. They were between 8 and 52 years old (26.6 ± 13.2 years; mean ± SD). Data were collected during the explantation of the intracranial electrodes from induction of anesthesia up to the point of their removal. All patients received total intravenous anesthesia with propofol and remifentanil at the University Hospital of Oslo. All patients were placed back on their usual antiepileptic medication before the procedure. Data were recorded on a Natus NicoletOne system with a 128-channel capacity and a digitization rate of 1024 Hz for up to 64 or 512 Hz for up to 128 channels.

Anesthetic management

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All patients received a premedication with 3.75 to 7.5 mg midazolam (Dormicum, Basel, Switzerland); the anesthesia scalp EEG group (Study 1) received additional 1 g oral paracetamol (Paracet, Weifa, Oslo, Norway) as well as 10 mg oxycodone sustained release tablet (OxyContin, Dublin, Ireland) for postoperative pain management. Propofol (Propolipid, Fresenius Kabi, Uppsala, Sweden) and remifentanil (Ultiva, GlaxoSmithKline, Parma, Italy) were administered by computer-controlled infusion pumps (B Braun Perfusor Space, Melsungen, Germany) using a target-controlled infusion (TCI) program (Schnider for propofol and Minto for remifentanil) in order to achieve plasma concentrations sufficient for anesthesia and analgesia. Prior to start of anesthesia all patients received an infusion of Ringer’s-Acetate (5 ml /kg) to prevent hypotension during anesthesia induction, as well as 3–5 ml 1% lidocaine intravenously to prevent pain during propofol injection. All patients were pre-oxygenated with 100% oxygen and received the non-depolarizing muscle relaxant cisatracurium for intubation (Nimbex, GlaxoSmithKline, Oslo, Norway). After intubation the inspiratory oxygen fraction was reduced to 40%; nitric oxide was not used.

Sleep

Study 3 - Sleep scalp EEG

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Study three was conducted at the University of California at Berkeley. All participants were informed and provided written consent in accordance with the local ethics committee (Berkeley Committee for Protection of Human Subjects Protocol Number 2010-01-595). We analyzed recordings from 20 young healthy participants (20.4 ± 2.0 years, mean ± SD; 12 females). Polysomnography was recorded during an 8 hour period as well as during 5 min quiescent rest with eyes closed before and after sleep. Data were recorded on a Grass Technologies Comet XL system (Astro-Med, Inc, West Warwick, RI) with a 19-channel EEG using the standard 10–20 setup as well as three electromyography (EMG) and four electro-oculography (EOG) electrodes at the outer canthi. The EEG was referenced to the bilateral linked mastoids and digitized at 400 Hz (0.1 to 100 Hz; Helfrich et al., 2018; Mander et al., 2015; Mander et al., 2014; Mander et al., 2013). Sleep staging was carried out by trained personnel (B.A.M.) and according to recent guidelines (Iber et al., 2007).

Study 4 - Sleep intracranial EEG

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Study four was conducted at the University of California at Irvine, Medical Center. Ten epilepsy patients (six females) undergoing invasive pre-surgical localization of their seizure focus were included in this study. All patients provided informed consent according to the local ethics committees of the University of California at Berkeley and at Irvine (University of California at Berkeley Committee for the Protection of Human Subjects Protocol Number 2010-01-520; University of California at Irvine Institutional Review Board Protocol Number 2014–1522, UCB relies on UCI Reliance Number 1817) and gave their written consent before data collection. They were between 22 and 55 years old (33.1 ± 11.5 years; mean ± SD). Electrode placement was solely dictated by clinical criteria (Ad-Tech, SEEG: 5 mm inter-electrode spacing; Integra, Grids: 1 cm, 5 or 4 mm spacing). Data were recorded with a Nihon Kohden recording system (256 channel amplifier, model JE120A), analogue-filtered above 0.01 Hz and digitally sampled at 5 kHz. To facilitate gold-standard sleep staging, simultaneous EOG, electrocardiography (ECG) from five leads and EEG was recorded by exemplary electrodes of the 10–20 setup depending on the localization of the intracranial electrodes but mostly consisting of Fz, Cz, C3, C4 and Oz. A surrogate EMG signal was derived from the ECG and EEG by high-pass filtering above 40 Hz. Sleep staging was carried out by trained personnel (B.A.M.) according to recent guidelines (Iber et al., 2007).

Data preprocessing

Study 1 - Anesthesia scalp EEG

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Data were imported into FieldTrip (Oostenveld et al., 2011) and epoched in 10 s segments. An Independent Component Analysis (fastica; Hyvärinen, 1999) was used to clean the data from systematic artifacts such as the ECG. Further data cleaning was done manually after inspection by a neurologist (R.T.K.) and an anesthesiologist (J.D.L). On average, the patients had 1183 ± 81.42 ten-second epochs of which 196 ± 103.19 were marked as noisy (15.81 ± 3.15%). No channels were excluded or interpolated. Data were referenced using the common average, demeaned and detrended. Wake periods were defined as time before induction and after anesthesia when the patients responded reliably to verbal commands of the study personnel. Anesthesia periods were defined as time after induction until the termination of propofol application.

Study 2 – Anesthesia intracranial EEG

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Data were recorded with a 512 Hz digitization rate in eight patients. Four additional patients were recorded with a digitization rate of 1024 Hz and these datasets were down-sampled to 512 Hz. Data were then imported to FieldTrip (Oostenveld et al., 2011), epoched into ten-second segments and inspected by a neurologist (R.T.K.) for epileptic activity and then manually cleaned of epileptic and other non-neural artifacts. The awake state was defined as time before start of propofol, anesthesia was defined as time after loss of consciousness (unresponsiveness to verbal commands assessed by study personnel and attending anesthetist). After fusing the pre-implantation T1-weighted MRI and the post-implantation Computer Tomography (CT) scans, electrodes were automatically localized by an openly available brain atlas (Freesurfer; Fischl, 2012) using the FieldTrip toolbox (Stolk et al., 2018) and cross-validated by independent manual inspection by two neurologists (R.T.K.; R.F.H.). Contacts in white matter or lesions were discarded. The remaining signals were then bipolar referenced to their lateral neighbor, demeaned and detrended.

Study 3 - Sleep scalp EEG

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The EEG was referenced to bilateral linked mastoids and data were imported to EEGLAB (Delorme and Makeig, 2004) and epoched into 5 s segments. Epochs that contained artifacts (e.g. eye blinks or movement) were manually inspected and rejected by a trained scorer (B.A.M.). None of the channels were discarded or interpolated. On average, the participants had 5748.9 ± 10.01 of these five second epochs and 946.95 ± 542.68 of them were rejected (16.44 ± 2.98%), comparable to the anesthesia scalp EEG recordings. The data from the healthy sleep participants have been reported before and were cleaned in a comparable approach (Helfrich et al., 2018; Mander et al., 2015; Mander et al., 2014; Mander et al., 2013). For further analysis in MATLAB (MATLAB Release R2018b, The MathWorks, Inc, Natick, Massachusetts, United States), the data were then imported into FieldTrip (Oostenveld et al., 2011).

Study 4 – Sleep intracranial EEG

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Data were imported to FieldTrip (Oostenveld et al., 2011), downsampled to 500 Hz and segmented into 30 s segments for subsequent data analysis. Anatomical localization was carried out by fusing pre-implantation T1-weighted Magnetic Resonance Imaging (MRI) scans with post-implantation MRI and both automatic and manual labeling of the electrode position (Stolk et al., 2018). As above, epileptic, white matter and channels with other artifacts were discarded. The data were bipolar referenced, demeaned and detrended.

Spectral analysis

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(1)To obtain average power spectra, after artifact removal the data were epoched into ten-second segments for anesthesia and 30 s segments for sleep. (2) Time-frequency decomposition was accomplished using a Fast Fourier Transformation (mtmfft, FieldTrip (Oostenveld et al., 2011) from 0.5 Hz to 45 Hz in 0.5 Hz steps. The analysis was limited to 45 Hz due to line noise at 50 Hz in the Oslo recordings and then adopted to all consecutive studies for consistency. To obtain reliable spectral estimates we utilized a Multitaper approach (Prerau et al., 2017) based on discrete prolate slepian sequences (dpss; anesthesia: 9 tapers for 10 s segments, no overlap, frequency smoothing of ± 0.5 Hz; sleep: 29 tapers for 30 s segments, no overlap, frequency smoothing of ± 0.5 Hz). (3) The power spectrum of each state was averaged over all samples of the state (wake and anesthesia or rest, wake, non-rapid eye movement sleep stage 3 (N3) and rapid eye movement sleep (REM)), channels and subjects (Figure 1b,c and Figure 2b,c). For better comparison, we visualized the effect at the scalp level. For Study 2 simultaneous EEG recordings were not available.

For the control analysis of the influence of segment length and number of tapers on the spectral slope estimate, anesthesia EEG recordings were epoched into 30 s segments, while sleep was epoched into 10 s segments. Time frequency decomposition was again done with FieldTrip’s mtmfft with a frequency smoothing of ± 0.5 Hz and dpss tapers resulting in 29 for anesthesia and nine for sleep. Note that the number of tapers is a direct result of the choice of segment length and frequency smoothing (Prerau et al., 2017):

Numberofdpsstapers=(2(Segment length (sec)frequency smoothing (Hz)2))1

Comparison of Multitaper, Single-taper, Periodogram and Welch’s Method

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For the comparison of the signal-to-noise ratios of different power calculations (Figure 2—figure supplement 6), the Multitaper spectral decomposition (Prerau et al., 2017) was calculated as outlined above. For all further computations, sleep data were epoched into 30 s segments.

For the Single-taper analysis, power was calculated using the Fast Fourier Transformation mtmfft of FieldTrip (Oostenveld et al., 2011) with no overlap after applying a Hanning taper. Spectral estimates were obtained between 0.5 and 45 Hz in 0.5 Hz steps.

For the calculation of the Periodogram, we used MATLAB’s periodogram.m function (MATLAB and Signal Processing Toolbox Release R2018b, MathWorks, Inc, USA) and the default rectangular window and number of points as defined by the sampling rate of 400 Hz. To get the same number of observations as in the Multi- and Single-taper approaches, the frequencies closest to the ones chosen in the Multi- and Single-taper approach above (0.5 to 45 Hz in 0.5 Hz steps) were chosen for further analysis.

For the Welch's method, power was calculated with a 30 s window size and no overlap resulting in a single Hamming window employing MATLAB’s pwelch.m function (MATLAB and Signal Processing Toolbox Release R2018b, MathWorks, Inc, USA). The number of points were defined by the sampling rate. Again, the frequencies closest to the Multi-/Single-taper approach were selected for further analysis to enable a direct comparison of signal-to-noise ratios (SNR).

SNR was calculated by dividing the average power of each frequency at every channel by the standard deviation of this frequency and channel.

Spectral slope estimation

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We calculated the spectral slope by fitting a linear regression line to the power spectrum in log-log space between 30 and 45 Hz, since it had been shown previously that this range correlates best with changes in arousal in rodents and monkeys, as well as with different excitation-inhibition ratios in simulations (Gao et al., 2017). In line with previous reports, we excluded the low frequencies that contain strong oscillatory activity, which may distort the linear fit as well as the range over 50 Hz, which is confounded by both line noise (50 Hz in Europe, 60 Hz in the US) as well as broad-band muscle artifacts.

We then adapted this range to the calculation of the slope in the other studies for consistency reasons. To compute a time resolved estimate of the spectral slope, we calculated the best line fit to the 10 (anesthesia) or 30 (sleep) second segments of the Multitapered power spectra (see above) in log-log space using polynomial curve fitting (polyfit.m, MATLAB and Curve Fitting Toolbox Release R2015a, The MathWorks, Inc, Natick, Massachusetts, United States). One subject in Study 3 (sleep EEG) exhibited an excessive noise level during wakefulness; therefore, his data had to be excluded from all slope comparisons to wakefulness.

Control analyses of spectral slope estimation

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For the evaluation of different center frequencies for the linear regression, the spectral slope was estimated from intracranial sleep recordings (Study 4) as a function of different center frequencies (±10 Hz around center frequency starting from 20 up to 150 Hz) and different fit lengths (from 30 Hz onward with a 10 Hz increase of fit length up to 100 Hz) using the same procedure as outlined above (Figure 2—figure supplement 5).

Moreover, the spectral slope was estimated from low frequencies in different recordings: (1) Anesthesia scalp EEG (Study 1) in the 1 to40 Hz range as previously reported (Colombo et al., 2019) and (2) in Sleep scalp EEG (Study 3) from 1 to 5 Hz with an increasing length of additional 5 Hz per fit after discounting the oscillatory components from the power spectrum by means of irregular resampling (IRASA; Wen and Liu, 2016a; Figure 2—figure supplement 5c). The rationale for using this method was to exclude strong low frequency oscillations, such as slow waves, which could possibly distort the slope estimate.

Furthermore, we estimated the spectral slope from the 30 to45 Hz range using two additional algorithms, the FOOOF package (Haller et al., 2018) and the eBOSC algorithm (Kosciessa et al., 2020a) in both anesthesia and sleep scalp EEG (Study 1 and 3). While eBOSC performs a linear regression in log-log space using MATLAB’s robustfit.m, FOOOF estimates both the oscillatory and aperiodical part of the power spectrum with a model fit: First an exponential fit is performed to the power spectrum in semi-log space, then this fit is subtracted from the power spectral density (PSD). The residual signal is treated as a combination of oscillations and noise and is repeatedly fit with multiple Gaussian fits to detect possible oscillatory peaks until the noise floor is reached. The detected peaks are then validated against the mixed oscillatory/noise signal and subtracted from the original PSD. The new residual signal is then fit again for a better estimate of the aperiodic signal. Both, the Multi-Gaussian fits and the improved aperiodic fit are then combined into a model (compare to Figure 3 (Haller et al., 2018). When the PSD does not contain a bend, also called knee, in the aperiodic signal, then the algorithm is equivalent to fitting a line in log-log space (Haller et al., 2018).

Mutual Information

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Mutual Information (MI) is an information theoretical metric, which quantifies the mutual dependence of the two signals, specifically the amount of information gained about one variable when observing the other (Quian Quiroga and Panzeri, 2009). This is particularly useful for non-linear, binned signals. Mutual information between the two signals X and Y was defined as

MIX;Y= x Xy Ypx,y*log2(px,ypx*p(y))

where p(x,y) depicts the joint probability function and p(x) and p(y) indicate the class probabilities. Probabilities were normalized by their sum. For MI analysis (Figure 2b, Figure 2—figure supplements 2, 5, 8 and 10), we epoched the time-resolved slope into 30 s segments (the hypnogram was staged in 30 s epochs) and discretized it into five bins (Wake, REM, N1, N2, N3) using the discretize.m function of MATLAB Signal Processing Toolbox Release R2015a (MathWorks Inc, USA). Mutual Information was calculated using the MutualInformation.m function from MATLAB Central File Exchange (Dwinell, 2010).

Beamformer analysis

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We source-localized the slope difference between wakefulness and sleep in scalp EEG (Study 3, n = 19; one patient had to be excluded due to insufficient wake trials; Figure 2—figure supplement 3). Cortical sources of the sensor-level EEG data were reconstructed by using a LCMV (linearly constraint minimum variance) beamforming approach (Van Veen et al., 1997) to estimate the time series for every voxel on the grid. A standard T1 MRI template and a BEM (boundary element method) headmodel from the FieldTrip toolbox (Oostenveld et al., 2011) were used to construct a 3D template grid at 1 cm spacing in standard MNI space. Electrode location was derived from a standard 10/20 template from the FieldTrip toolbox (Oostenveld et al., 2011). Prior to source projection, sensor level data were common average referenced and epoched into 30 s segments. To minimize computational load, we selected a two second data segment from the center of every epoch to construct the covariance matrix. The LCMV spatial filter was then calculated using the covariance matrix of the sensor-level EEG data with 5% regularization. Spatial filters were constructed for each of the grid positions separately to maximally suppress activity from all other sources. The resulting time courses in source space then underwent spectral analysis using a Fourier transform after applying a Hanning window. The PSD slope of every segment was then estimated using linear regression in the range from 30 to 45 Hz as outlined before. Mean slope values during sleep were subtracted from the mean slope during wakefulness at every voxel in source space and then source-interpolated onto a standard template brain in MNI space.

We employed a regions-of-interest (ROI) based approach focusing on prefrontal cortex (PFC) subregions since a reliable source localization of medial temporal lobe (MTL) activity using 19-channel EEG remains challenging. In line with our results from the intracranial sleep study (Study 4, Figure 2C and Figure 2—figure supplement 4), we defined the mPFC and dorsolateral PFC (dlPFC) as ROI. To identify ROI at source level, we used the Automated Anatomical Labeling (AAL) atlas as implemented in FieldTrip (Oostenveld et al., 2011). The ROI mPFC encompassed the following regions: 23 and 24 – ‘Frontal_Sup_Medial_L and R’, 25 and 26 – ‘Frontal_Med_Orb_L and R’, 27 and 28 – ‘Rectus_L and R’, 31 and 32 – Cingulum_Ant_L and R’. The ROI dlPFC consisted of the following atlas tissue labels: 3 and 4 – ‘Frontal_Sup_L and R’, 7 and 8 – ‘Frontal_Mid_L and R’, 11 and 12 – ‘Frontal_Inf_Oper_L and R’, 13 and 14 – ‘Frontal_Inf_Tri_L and R’ and 15 and 16 ‘Frontal_Inf_Orb_L and R’.

Classification analysis

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We employed a linear discriminant analysis (LDA) to assess if slow wave power or the spectral slope were a better predictor of wakefulness or sleep (Figure 1—figure supplement 4, Figure 3a–c). We utilized a leave-one-exemplar-out cross-validation approach that was repeated 50 times after randomly sampling an equal number of sleep and REM trials to equate the number of samples (classify.m, MATLAB and Statistics and Machine Learning Toolbox Release R2015a, MathWorks Inc, USA). Then every sample of the subsampled distribution was held out of the training dataset once. The LDA classifier was trained on the remaining samples and tested on the held-out test sample. The classifier performance was then assessed as percent correct. Two of the 20 sleep EEG participants had to be excluded due to insufficient number of wake trials. LDA performances were logit-transformed (logit.m from the BioSig toolbox (Schlogl and Brunner, 2008) and averaged across channels prior to statistical comparison.

Multivariate General Linear Model

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In order to model the unique contributions as well as the interaction between slow wave power (<1.25 Hz) and spectral slope in the prediction of arousal states, we first scaled both parameters by means of a z-score and then calculated a general linear model using the MATLAB fitlm.m function (MATLAB and Statistics and Machine Learning Toolbox Release R2018b, MathWorks Inc, USA). This method offered the possibility to model both the main effects as well as the interaction between the two predictors (Figure 3d–f). Critically, we utilized an unbalanced design, which implicitly orthogonalizes the contribution of different factors and hence, distills non-overlapping unique explained variance (Siegel et al., 2015), which was subsequently quantified by means of the effect size (eta squared).

Spectral slope estimation during a slow wave

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Slow wave events (Figure 4, Figure 2—figure supplement 10) were detected for each channel based on established algorithms (Helfrich et al., 2018; Staresina et al., 2015): The raw signal was bandpass-filtered between 0.16 and 1.25 Hz and zero crossings were detected. Events were then selected using a time (0.8 to 2 s duration) and an amplitude criterion (75% percentile). The raw data were then epoched relative to the trough of the slow wave (±2.5 s). Time-frequency decomposition was computed in 500 ms time windows with a 250 ms overlap using FieldTrip (Oostenveld et al., 2011) (mtmfft, frequency smoothing of ±2 Hz and one dpss taper). The spectral slope was calculated by the best line fit in these time windows in log-log space between 30 and45 Hz using polynomial curve fitting (polyfit.m, MATLAB and Curve Fitting Toolbox Release R2015a, MathWorks Inc, USA).

Statistical testing

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The spectral slope of the awake and anesthetized state was compared using Student’s t-test for paired samples (Figure 1b,c). The observed t-values were then compared against a surrogate distribution after re-calculating the test statistic 10,000 times with randomly shuffled labels (called permutation t-test in the manuscript). Post hoc t-tests were Bonferroni-corrected for multiple comparisons.

To compare three states (awake, NREM and REM), we utilized Greenhouse-Geisser corrected 1-way repeated measures analysis of variance (Figure 2b and c; RM-ANOVA). We adopted an approach similar to the permutation t-test, where the original RM-ANOVA output was compared to a shuffled distribution after randomly flipping condition labels 10,000 times (repeated-measures ANOVA permutation test). Effect size was calculated using Cohen’s d.

To assess the spatial extent of the observed effects in EEG, we calculated cluster-based permutation tests to correct for multiple comparisons as implemented in FieldTrip (Oostenveld et al., 2011) (Monte-Carlo method; maxsize criterion; 1000 iterations). A permutation distribution was obtained by randomly shuffling condition labels and then compared to the actual distribution to obtain an estimate of significance. Spatial clusters are formed by thresholding independent t-tests of slope differences between wake and anesthesia (Figure 1b) or wake and sleep (Figure 2b) at a p value < 0.05. All results were Bonferroni-corrected for multiple comparisons. In order to control for EMG as a potential confound in the sleep EEG (Study 3), we utilized a partial correlation (Spearman) that partialled the slope of the EMG out of the correlation before computing the cluster-based permutation test (Figure 2—figure supplement 2b). Correlation coefficients (r-values) were transformed into t-values using the following formula (N = number of subjects):

t=r*sqrt(N-2)sqrt(1-r2)

For statistical assessment of the Mutual Information (MI), we employed surrogate testing (Figure 2b, Figure 2—figure supplement 2a). To obtain a surrogate distribution from the observed data, we utilized a random block swapping procedure (Aru et al., 2015; Canolty et al., 2006). The number of repetitions was equal to the number of available sleep stages. On every iteration, we re-calculated the MI of these block swapped hypnograms with the discretized time-resolved slope to create a surrogate distribution against which we could compare our original observation. To compare the results across subjects, we z-scored the values by subtracting the mean of the surrogate distribution from the observed MI and dividing by the standard deviation of the surrogate distribution. Note that a z = 1.96 reflects an uncorrected two-tailed p-value of 0.05, while a z-score of >2.8 indicates a Bonferroni-corrected significant p-value (p<0.05/19 channels=0.0026). The z-values were transformed into p-values for topographic depiction (Figure 2b; Figure 2—figure supplement 2a) based on a normal cumulative distribution function (two-tailed).

Connectivity

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For the analysis of fronto-parietal connectivity (Figure 2—figure supplement 10), we choose electrode Fz and Pz in our sleep EEG recordings (Study 3; n = 20) to calculate the magnitude squared coherence from frequencies of 0.1 to 64 Hz in 0.1 Hz steps using the mscohere.m function from the MATLAB Signal Processing Toolbox (Release R2015a, MathWorks, Inc, USA) as described previously (Pal et al., 2016; Pal et al., 2015). Note that coherence estimates reflect both power changes as well as changes in phase synchrony. Therefore, we also calculated the Phase-Locking Value (PLV) and amplitude correlations (rho) to disentangle the effects of phase and power, respectively. To discount the effects of volume spread, we calculated the imaginary PLV (Nolte et al., 2004) (iPLV) and orthogonalized power correlations (Hipp et al., 2012) (rhoortho).

We then quantified the Mutual Information (MI; see above) to compare how well the results capture the changes between different sleep stages across the night (Quian Quiroga and Panzeri, 2009). For this analysis we only utilized the slope values of electrode Fz (as we were calculating the other measures in Fz-Pz) and defined theta from 4 to 10 Hz analog to Pal et al., 2016; Pal et al., 2015.

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Decision letter

  1. Saskia Haegens
    Reviewing Editor; Columbia University College of Physicians and Surgeons, United States
  2. Laura L Colgin
    Senior Editor; University of Texas at Austin, United States
  3. Giovanni Piantoni
    Reviewer; Massachusetts General Hospital, United States

In the interests of transparency, eLife publishes the most substantive revision requests and the accompanying author responses.

Acceptance summary:

This study relies on both invasive and non-invasive EEG recordings in humans who were either awake, anesthetized or sleeping, and shows that a particular marker of neural activity – the slope of the EEG power spectrum – can be used to distinguish between different states of arousal. Importantly, this measure can be reliably estimated from scalp EEG recordings, and accurately separates REM sleep from wakefulness, which to date had been challenging using EEG. Furthermore, the authors show that anesthesia reflects a brain-wide state, while sleep patterns are observed in specific networks.

Decision letter after peer review:

Thank you for submitting your article "An Electrophysiological Marker of Arousal Level in Humans" for consideration by eLife. Your article has been reviewed by three peer reviewers, one of whom is a member of our Board of Reviewing Editors, and the evaluation has been overseen by Laura Colgin as the Senior Editor. The following individual involved in review of your submission has agreed to reveal their identity: Giovanni Piantoni (Reviewer #3).

The reviewers have discussed the reviews with one another and the Reviewing Editor has drafted this decision to help you prepare a revised submission. In recognition of the fact that revisions may take longer than the two months we typically allow, until the research enterprise restarts in full, we will give authors as much time as they need to submit revised manuscripts.

Summary:

Lendner and colleagues assess 1/f EEG activity as a proxy of arousal by comparing both invasive and non-invasive recordings of awake, anesthetized and sleeping humans. The authors calculated the slope in the log-log power spectral density during periods of wakefulness, N3 and REM sleep and propofol anesthesia. They consistently found across four studies (both intracranial and scalp EEG) that the slope is shallower for wakefulness as compared to the other states of reduced arousal. A series of control analyses (LDA, changes in center frequency and width of the frequency range, link to slow waves) confirmed the main finding. The findings are exciting and well tested over multiple studies and recording setups. Particularly intriguing is the similarity between propofol and sleep.

Although the study in general represents an important contribution to the field of human electrophysiological research, we are not entirely convinced by the used methods, inferential statistics, and by the way the findings are integrated into the existing literature. The analysis of multiple data sets in order to draw inferences on various levels is compelling and impressive but warrants a more consistent methodological approach and the acknowledgement of earlier findings.

Essential revisions:

1) Overall, the manuscript is lacking connection with existing literature, leading to unwarranted novelty claims and rather unspecific hypotheses. Authors should integrate the existing literature more thoroughly.

This is especially of importance for the Introduction and Discussion sections. For example, the authors cite Colombo et al., 2019, in the Introduction but do not acknowledge that this study performed a comparison of EEG spectral exponents between the awake state and anesthesia under different drugs, including Propofol, and found a steepening of the spectrum under Propofol anesthesia compared to awake rest. Similarly, the authors cite Miskovic et al., 2019 without noting that the cited study compared PSD exponents between different sleep stages and found results comparable to those of the current manuscript.

It is essential to put the results of the current study into context and note that they replicate earlier findings and are not the first of their kind in data from human subjects. The appeal of novelty claims in the Introduction which states that only non-human animal results exist for the central question of the manuscript, should be omitted. Instead, we suggest to formulate more precise hypotheses regarding the direction of effects (steepening vs. flattening of spectra) and to touch upon E/I balance and neurotransmitters already in the Introduction.

2) We had several concerns regarding the inferential statistics used. Permutation-based or non-parametric tests are more appropriate for the majority of performed tests and should be implemented.

More specifically: Inferential statistics should be adapted to meet the distributional properties of the data they are performed on. The comparison of very small samples (e.g. n = 9) using t-tests should be replaced by non-parametric or permutation-based approaches. Similarly, comparing goodness of fit statistics using t-tests should be omitted (subsection “The relationship of slow waves and the spectral slope”) and replaced by proper model comparisons.

Additionally, performance correct percentages of the used LDA should undergo an appropriate transformation before being tested against each other (e.g. logit).

On a more general note, we suggest to replace the LDA approach with a multivariate model predicting arousal states based on the predictors the authors aim to compare. This way their predictive power can be compared directly (if scaled in the same way, e.g. z-scored) and their shared variance in the dependent variable can be accounted for. Furthermore, the discussion of prediction accuracies should include a reference to the "ground truth" that is predicted here, the ratings of a trained specialist which are 80% reliable.

3) One of the major claims of the paper is that the effect of interest is consistent across techniques (EEG, iEEG) and brain states (propofol, sleep). To support this claim, the authors would need to be consistent in their analysis pipelines of the different datasets. More specifically:

– Why were different length segments (and taper numbers) used for sleep vs anesthesia? Would be better for direct comparison to keep these parameters the same.

– The iEEG studies and the scalp EEG studies use a very different reference. Bipolar for iEEG and common average for the scalp EEG studies (the reference is not clearly specified for study 3 though, please clarify). One would expect that the choice of reference would have a large impact on the slope, but this does not seem the case. For example, local dynamics captured by bipolar referencing are in general very different from global effects such as those observed in scalp EEG. In fact, the Laplacian reference does not change the results. Could the authors discuss in more detail the role of referencing in their interpretation of the neurophysiological basis of 1/f dynamics?

4) Furthermore, we had some concerns regarding anatomical claims.

The fact that sleep stage-slope correlation seems to be dominated by medial PFC/temporal sites is interesting, though might be biased by the iEEG montage, as those are also the regions with the most electrodes due to epilepsy monitoring. There should be a statistical analysis that shows that those regions have a significantly higher proportion of "differentiating" electrodes than other brain regions. In addition to a sound statistical analysis, the authors should provide a table with the number of total electrodes and the number of electrodes showing a significant change in slope, per brain region. As it is, it's hard to define the regions of interest based on the brain plots shown.

Additionally, it would have been much more powerful if the anatomical claims could be corroborated by the EEG recordings. Not sure source localization is possible on the EEG data given low electrode numbers, but that would really have strengthened the story. In current form it remains a little unclear what the main sources of all these effects are.

5) The fitting of 1/f spectral exponents should be improved and frequency ranges should be motivated more clearly.

Although it is correct that Gao et al., 2017, used a frequency range of 30-50 Hz for their 1/f PSD fit, this choice was motivated by the linear decrease of power in LFP recordings within that frequency range. However, oscillatory parts of the spectrum, whether of neural or non-neural origin (line noise), can aptly be fitted and excluded from a 1/f fit using the FOOOF package (https://fooof-tools.github.io/fooof/). The use of this or another software package (e.g. BOSC or eBOSC: https://github.com/jkosciessa/eBOSC) would allow the authors to directly asses the change of PSD exponents across different levels of arousal across wider frequency ranges without having to alter time-series first using IRASA. In fact, Colombo and colleagues show a steepening of the PSD between 1 and 40 Hz from awake rest compared to Propofol anesthesia, a result the authors could try to replicate and discuss using the proposed analyses techniques. Furthermore, goodness of fit statistics for the performed linear fits are missing and should be added for any kind of fitting procedure the authors decide to apply.

6) Discussion could be more in depth in terms of:

– connection with existing literature;

– underlying mechanisms/generation of the recorded signals;

– interpretation of the findings and implications for our understanding of sleep vs wake processes;

– actual discussion of practical use, i.e., how reliable is slope as a measure to distinguish these states on the single subject level.

[Editors' note: further revisions were suggested prior to acceptance, as described below.]

Thank you for resubmitting your work entitled "An Electrophysiological Marker of Arousal Level in Humans" for further consideration by eLife. Your revised article has been evaluated by Laura Colgin (Senior Editor) and Saskia Haegens (Reviewing Editor).

The manuscript has been improved but there are some remaining issues that need to be addressed before acceptance, as outlined below:

We appreciate the very thorough revisions, especially methods wise, and believe they have strengthened the paper considerably. After discussion with one of the original reviewers, we have one remaining point we would still like to see clarified, but other than that all our previous concerns have been adequately dealt with.

The issue we are still unclear on pertains to this claim:

"Critically, the accuracy of this classification is comparable to trained personnel, since the inter-rater reliability between sleep state scoring experts is typically about 80%".

However, if the ground truth here consists of the sleep staging done by trained experts, for whom we know the inter-rater reliability is typically about 80%, then a 100% accuracy of the classifier would be a 100% match with these expert raters (i.e., not necessarily a 100% accurate classification of sleep stage). In other words, the performance of the classifier is bound by the accuracy of the ground truth. Since we do not know the "true" sleep stage, we can only conclude that the classifier accurately predicts the experts' ratings 80% of the time here. Please add some language to make this explicit in the discussion of these results.

https://doi.org/10.7554/eLife.55092.sa1

Author response

Essential revisions:

1) Overall, the manuscript is lacking connection with existing literature, leading to unwarranted novelty claims and rather unspecific hypotheses. Authors should integrate the existing literature more thoroughly.

This is especially of importance for the Introduction and Discussion sections. For example, the authors cite Colombo et al., 2019, in the Introduction but do not acknowledge that this study performed a comparison of EEG spectral exponents between the awake state and anesthesia under different drugs, including Propofol, and found a steepening of the spectrum under Propofol anesthesia compared to awake rest. Similarly, the authors cite Miskovic et al., 2019, without noting that the cited study compared PSD exponents between different sleep stages and found results comparable to those of the current manuscript.

It is essential to put the results of the current study into context and note that they replicate earlier findings and are not the first of their kind in data from human subjects. The appeal of novelty claims in the Introduction which states that only non-human animal results exist for the central question of the manuscript, should be omitted. Instead, we suggest to formulate more precise hypotheses regarding the direction of effects (steepening vs. flattening of spectra) and to touch upon E/I balance and neurotransmitters already in the Introduction.

We apologize about the lack of connection to existing literature. We thank the reviewers for their comments and carefully revisited both the Introduction and Discussion. The revised manuscript features a completely rewritten Introduction and Discussion section with a clearer structure. Critically, we now introduce the concept of E/I-balance early in the Introduction and clearly state our predictions with regard to the hypothesized link between E/I-balance and 1/f features.

Introduction:

“General anesthesia is a reversible, pharmaceutically induced state of unconsciousness, while sleep is internally generated and cycles between rapid (REM) and non-rapid eye movement sleep (NREM; (Brown et al., 2010; Franks and Zecharia, 2011a). […]While previous studies that included lower frequency power in their slope estimates, found the slope of REM to be close to wakefulness (He et al., 2010), we specifically investigated if the aperiodic background activity in the 30 – 50 Hz range could reliably discriminate REM sleep from wakefulness and NREM sleep.”

2) We had several concerns regarding the inferential statistics used. Permutation-based or non-parametric tests are more appropriate for the majority of performed tests and should be implemented.

More specifically: Inferential statistics should be adapted to meet the distributional properties of the data they are performed on. The comparison of very small samples (e.g. n = 9) using t-tests should be replaced by non-parametric or permutation-based approaches.

We thank the reviewers for this suggestion and now employ non-parametric permutation statistics throughout the manuscript. In the previous version of the manuscript, we utilized cluster-based permutation tests when assessing the spatial extent of the data (see e.g. Figure 1B, 2B, Figure 2—figure supplement 2).

In the revised manuscript, we replaced t-tests by permutation t-test in which the original observation was compared against a surrogate distribution after re-calculating the test statistic (e.g. T- or F-values) 10,000 times with randomly shuffled condition labels. The empirically observed t-value was then compared relative to the surrogate distribution of permuted t-values (e.g. Figure 1B, C; Figure 3A-C). For the repeated measures ANOVA, we adopted a similar approach where the original RM-ANOVA output was compared to a shuffled distribution after randomly flipping condition labels 10,000 times (e.g. Figure 2B, C; Figure 3D-F). Post-hoc t-tests were Bonferroni corrected for multiple comparisons.

Similarly, comparing goodness of fit statistics using t-tests should be omitted (subsection “The relationship of slow waves and the spectral slope”) and replaced by proper model comparisons.

We agree with the reviewers and removed the goodness of fit statistic comparison using t-test from the manuscript. Instead we now evaluate the shared variance using a multivariate general linear model:

“First, we found that the interaction of spectral slope and slow wave activity did not explain more unique variance than the sum of the univariate metrics in a GLM, hence, indicating that the slope and slow wave activity provide complimentary information about arousal states (Figure 3). In addition, if lower frequencies (e.g. 1 – 20 Hz) were utilized for spectral slope estimation, MI between the hypnogram and the time-resolved spectral slope decreased (Figure 2—figure supplement 5D) suggesting that lower frequencies and the 30 – 45 Hz range may index distinct processes.”

Additionally, performance correct percentages of the used LDA should undergo an appropriate transformation before being tested against each other (e.g. logit).

We thank the reviewers for this suggestion and performed logit-transformation of the LDA correct percentages before comparison. We edited Figure 3 and revised the results in the manuscript accordingly.

Results:

The spectral slope discriminates wakefulness from states of reduced arousal.

Our findings provide evidence that the spectral slope reliably discriminates wakefulness from sleep. Multiple prior reports indicated that slow waves are a hallmark of decreased arousal states (Brown et al., 2010; Franks and Zecharia, 2011a; Murphy et al., 2011). […] Note, that slow wave power was already elevated during wakefulness, which may reflect a premedication with a sedative (see Figure 1A and Materials and methods).”

On a more general note, we suggest to replace the LDA approach with a multivariate model predicting arousal states based on the predictors the authors aim to compare. This way their predictive power can be compared directly (if scaled in the same way, e.g. z-scored) and their shared variance in the dependent variable can be accounted for.

We thank the reviewers for this recommendation. Accordingly, we calculated a multivariate model to predict the arousal states based on the slope and slow oscillation (SO; < 1.25 Hz) power. This approach enabled us to directly compare the unique variance that was explained by either the spectral slope or SO power. Moreover, this method facilitated a direct assessment of the multivariate interaction of both parameters.

In order to model the unique contributions of the parameters as well as their interaction, we first scaled both by means of a z-score and then calculated their main effects as well as their interaction using a multivariate general linear model. Critically, we utilized an unbalanced design, which implicitly orthogonalizes the contribution of different factors and hence, distills non-overlapping unique explained variance, which was subsequently quantified by means of the eta squared metric.

Author response image 1
Uni- and multivariate discrimination of wakefulness and REM sleep using the spectral slope and slow oscillation power.

Single subject example at scalp EEG electrode Fz. a, While both 1/f slope (z-scored; left panel) and slow oscillation power (SO, < 1.25 Hz; z-scored; right panel) are able to differentiate wakefulness (red) from REM sleep (green; black: mean ± SEM) in a univariate comparison, the 1/f slope provides most of the discriminative power in a multivariate space as seen in panel b (SO power vs. 1/f slope; both z-scored). Note that the states (red – wakefulness; green – REM sleep) are clearly discernible based on the first feature plotted on the x-axis (the spectral slope) while taking SO power (on the y-axis) into account, does not contribute independent information.

In order to better illustrate our approach, we added Author response image 1, which depicts the relationship of uni- and multivariate differences between wakefulness and REM sleep in one subject: While both the z-scored spectral slope and the z-scored SO power discriminate wake and REM in a univariate comparison (panel a), the multivariate display of the same data (panel b) does not contribute additional information. Note that the main discriminating factor, which successfully discriminates both conditions, is the spectral slope, as indicated by a clear separation of the two states along the first dimension (on the x-axis).

When discerning wakefulness from REM sleep, information (as quantified by unique explained variance eta squared) about the underlying arousal state was significantly different between spectral slope, SO power and their interaction (Figure 3D). Post hoc permutation t-tests revealed that this effect was mostly driven by the spectral slope (slope: 0.29 ± 0.05 (mean ± SEM), SO: 0.05 ± 0.01; interaction: 0.06 ± 0.03; post-hoc permutation t-tests (Bonferroni corrected): Slope-SO: p < 0.001, obs. t17 = 4.29, d = 1.50, Slope-Int.: p < 0.001, obs. t17 = 4.84, d = 1.62; SO-Int.: p = 0.63, obs. t17 = 0.82, d = 0.29).

For NREM stage 3 sleep and wakefulness, there was no difference in explained variance between factors (Figure 3E; post-hoc permutation t-tests (Bonferroni corrected): Slope-SO: p = 0.406, obs. t17 = -1.11, d = -0.39; Slope-Int.: p = 0.422 obs. t17 = 1.09, d = 0.31; SO-Int.: p = 0.032, obs. t17 = 2.44, d = 0.88).

Between anesthesia and wakefulness, information about the state was again significantly different between factors (Figure 3F). As in the wake-REM differentiation, this could mostly be attributed to the spectral slope (post-hoc permutation t-tests (Bonferroni corrected): Slope-SO: p < 0.001, obs. t8 = 3.70, d = 1.75), Slope-Int.: p < 0.001, obs. t8 = 3.95, d = 1.87, SO-Int.: p = 0.019, obs. t8 = 2.67, d = 1.07).

The results from the GLM mirrored the findings from the LDA approach: When discerning wakefulness from REM sleep and anesthesia, the spectral slope was more informative about the underlying arousal state than SO power or the interaction of both factors. For NREM sleep stage 3, both slope and SO power contained a comparable amount of information. The interaction of both factors did not explain more unique variance than the sum of the univariate metrics, hence, indicating that the slope and SO power provide complimentary information about arousal states.

We carefully considered the reviewers’ proposal to replace the LDA approach but felt that the results as obtained from the LDA offer an additional advantage, namely a very intuitive comparison as quantified as percent correct to interrater reliability in sleep scoring (80.6% for R&K and 82% for AASM; (Danker-Hopfe et al., 2009). Therefore, we elected to present both approaches side-by-side in the revised manuscript:

“General Linear Model: When discerning wakefulness from REM sleep, information (as quantified by unique explained variance eta squared) about the underlying arousal state was significantly different between the spectral slope, SO power and their interaction (repeated-measures ANOVA permutation test: p < 0.001, F1.16, 19.74 = 19.69). […] The spectral slope enabled an improved classification and contained more unique information about arousal state compared to slow wave power when differentiating wakefulness from both propofol anesthesia and REM sleep and was comparable when discerning wakefulness from N3 sleep.”

Furthermore, the discussion of prediction accuracies should include a reference to the "ground truth" that is predicted here, the ratings of a trained specialist which are 80% reliable.

We thank the reviewers for the recommendation. This information can be found in the following paragraph:

This finding indicates that the spectral slope constitutes a marker that successfully discriminates REM sleep from wakefulness solely from the electrophysiological brain state. Critically, the accuracy of this classification is comparable to trained personnel, since the inter-rater reliability between sleep state scoring experts is typically about 80% (Danker-Hopfe et al., 2009).

3) One of the major claims of the paper is that the effect of interest is consistent across techniques (EEG, iEEG) and brain states (propofol, sleep). To support this claim, the authors would need to be consistent in their analysis pipelines of the different datasets.

We appreciate the reviewers’ input and therefore, carefully assessed the influence of different variables on spectral slope estimation. In particular, we identified the following parameters, which were queried:

Power - Method for power calculation:

To evaluate the impact of different spectral decompoisition methods for subsequent spectral slope estimation, we recalculated the power spectra using the original multi-taper approach, a single Hanning taper, a periodogram and Welch’s method (Figure 2—figure supplement 6). We calculated a signal-to-noise ratio (mean divided by standard deviation) and found that the multitaper approach provides significantly cleaner spectral estimates as compared to the other methods in all tested frequency bands (n = 20; cluster permutation test: p < 0.001).

More specifically:

– Why were different length segments (and taper numbers) used for sleep vs anesthesia? Would be better for direct comparison to keep these parameters the same.

We appreciate the opportunity to clarify our motivation and our rationale for the chosen parameters and then present supporting data.

Motivation and rationale

While we agree with the reviewers that the same settings for all recordings would facilitate an easier direct comparison, we want to point out that sleep and anesthesia are different neurophysiological states. While they share some characteristics including a reduced arousal level, they also exhibit different temporal dynamics and spectral features. Specifically, the duration of these states typically differs – while a full night of sleep often lasts for 6 – 10 hours, surgical anesthesia is often only maintained for 1 – 3 hours or less. Here, we find similar recordings lengths of 7.99 ± 0.01 hours (mean ± SEM) for sleep and 3.81 ± 0.22 hours for anesthesia.

a) Segment Length:

Sleep scoring is typically carried out in 30 second segments under the assumption that neuronal activity stays relatively stationary within this time frame (Prerau et al., 2017). We therefore adapted a 30 second segment length for our slope estimation during sleep as the 30 second staging was the only “ground truth” available.

For anesthesia, no such convention exists. While many studies used 1 to 2 second segments (e.g. (Colombo et al., 2019; Gao et al., 2017), we decided to utilize a longer segment length of 10 seconds as this approach offered the opportunity to use a Multitaper approach for power estimation in the examined frequency range. A segment length of 30 seconds, on the other hand, resulted in pronounced temporal smoothing of slope dynamics under anesthesia compared to 10 second segments (Figure 1—figure supplement 3A).

b) Taper Numbers:

The number of the dpss tapers used in the Multitaper method is a direct result of the segment length and our chosen frequency smoothing of 1 Hz (Prerau et al., 2017):

THBP=SL*fR2 The time-half-bandwidth product (THBP) is a result of the segment length (SL) and the frequency resolution (fR). With this parameter we can now calculate the numbers of tapers (NT) used in the estimate:NT=(2*THBP)1 For anesthesia, we chose a segment length of 10 seconds, and a frequency resolution of 1 Hz, resulting in a THBP of 5:10*12=5 This means for a segment length of 10 seconds and a frequency resolution of 1 Hz, we needed 9 dpss tapers for a clean estimate: (2*5)1=9 Supporting data:

To further evaluate the influence of segment length and number of tapers on our findings, we recalculated the spectral slope estimates for both scalp EEG groups: For anesthesia, we repeated the analysis with 30 second segments (Figure 1—figure supplement 3) and for sleep with 10 second segments (Figure 2—figure supplement 7).

Author response table 1
Scalp EEGoriginalnew
Anesthesia (n = 9)10 second segments30 second segments
Wakefulness-1.84 ± 0.30-1.85 ± 0.33
Anesthesia-3.10 ± 0.20-2.94 ± 0.18
Sleep (n = 20)30 second segments10 second segments
Baseline rest-1.87 ± 0.18-1.90± 0.19
NREM 3-3.46 ± 0.16-3.42 ± 0.16
REM-4.73 ± 0.23-4.72 ± 0.22

Spectral slope estimates with original and new settings under anesthesia with propofol and in sleep, both in scalp EEG (Study 1 and 3; mean ± SEM).

Both new analyses resulted in comparable spectral slope patterns (Author response table 1, Figure 1—figure supplement 3, Figure 2—figure supplement 7), where the original and new observations were strongly correlated with r’s of 1 or 0.98, respectively (Pearson: anesthesia orig.-new: r = 1, p < 0.0001, sleep orig.-new: r = 0.98, p < 0.0001). Under anesthesia, however, the 30 second segment resulted in pronounced temporal smoothing of slope dynamics compared to 10 second segments (Figure 1—figure supplement 3a). We therefore kept the original segment lengths in the main manuscript but added our results as supplemental figures to facilitate a direct comparison between segment lengths and number of tapers.

– The iEEG studies and the scalp EEG studies use a very different reference. Bipolar for iEEG and common average for the scalp EEG studies (the reference is not clearly specified for study 3 though, please clarify).

The reviewers are correct in pointing out that we used different reference schemes in our recordings: For the anesthesia EEG (Study 1) as well as the scalp EEG contacts in intracranial sleep (Study 4) we used a common average reference. The sleep scalp EEG study (Study 3) was already recorded with bilateral linked mastoids as reference.

We agree with the reviewers that the reference scheme for Study 3 was not stated clearly enough (it could only be found in the data collection paragraph of Material and Methods). We therefore added a new sentence to the data preprocessing section: Study 3 – Sleep scalp EEG: The EEG was referenced to bilateral linked mastoids (…)

For both the intracranial recordings under anesthesia and in sleep (Study 2 and 4), we chose a bipolar reference scheme as this is a) the reference scheme commonly used in intracranial recordings (Helfrich et al., 2019) and b) the most conservative approach. For scalp EEG, a variety of reference schemes are possible and there is no consensus on which scheme is used best. The motivation for the different reference schemes was the following:

Study 1 – Anesthesia scalp EEG: The recording environment in the operating room during surgical anesthesia will always be suboptimal in terms of environmental noise. To address this, we employed a common average reference to remove common instrument /movement noise and to improve signal quality.

Study 3 – Sleep Scalp EEG: This dataset was recorded in the quiet setup of a sleep laboratory and was already referenced to linked bilateral mastoids (which were not available in other scalp EEG datasets). However, we did repeat the slope estimation using a Laplacian reference. This method strengthened the observed relationship between the hypnogram and the spectral slope (Laplacian: pSpearman < 0.001, pMI < 0.0001; partial correlation: pSpearman < 0.001; Figure 2—figure supplement 2 and Author response image 2).

Author response image 2
The influence of the choice of reference on the relationship of hypnogram and spectral slope.

Original observation with bilateral linked mastoids reference (left panels) versus Laplacian re-reference (right panels) in scalp EEG recordings during sleep (n = 20). Upper row of topoplots: Cluster permutation test of Spearman rank correlation between hypnogram and time-resolved slope: * p < 0.05. Lower rows of topoplot: Mutual Information between time-resolved slope and hypnogram. Statistics with random block swapping: * p < 0.05.

Study 4 – Sleep Intracranial, scalp EEG contacts: Patients with intracranial electrodes received additional scalp EEG contacts (Fz, Cz, C3, C4, Oz) to facilitate gold-standard sleep scoring. As the coverage was too sparse for e.g. a Laplacian reference, we utilized a common average reference.

Our results replicated the findings from the Study 3, revealing that bilateral linked mastoid reference, Laplacian reference and common average reference provide similar spectral slope estimations. This finding implies that our results were robust to changes in reference schemes. To underscore this observation, we repeated out slope estimation under different reference schemes in the following 3.3 response.

One would expect that the choice of reference would have a large impact on the slope, but this does not seem the case. For example, local dynamics captured by bipolar referencing are in general very different from global effects such as those observed in scalp EEG. In fact, the Laplacian reference does not change the results. Could the authors discuss in more detail the role of referencing in their interpretation of the neurophysiological basis of 1/f dynamics?

We thank the reviewers for this comment and appreciate the opportunity to evaluate the influence of a certain reference scheme on the estimation of the spectral slope. We therefore recalculated the spectral slope for the sleep scalp EEG (Study 3) after using different reference schemes:

The original: bilateral linked mastoids reference

Laplacian reference (already in the initial version of the manuscript; LP)

Common average reference (CAR)

Clinical bipolar, also often called “Double Banana” (DB)

We found that while the absolute slopes values vary slightly, the overall slope pattern with more negative values during sleep compared to wakefulness is remarkably similar (Figure 2—figure supplement 8B). The average across states was comparable between original and CAR (n = 14; paired t-tests (uncorrected): Orig.-CAR: p = 0.065, t13 = 2.02, d = 0.36) and original and DB reference (Paired t-tests (uncorrected): Orig.-DB: p = 0.0875, t13 = -1.85, d = -0.32) but different between original and LP reference (Orig.-LP: p = 0.005, t13 = -3.35, d = -0.64). Slope estimation between original and all other reference schemes were strongly correlated (Pearson: Orig. – CAR: r = 0.90, p < 0.001; Orig. – DB: r = 0.77, p < 0.001; Orig. – LP: r = 0.80, p < 0.001).

When calculating the Mutual Information (MI) between the time-resolved slope and the hypnogram at electrode Fz, there was no significant difference between original and CAR (n = 14; Paired t-tests (uncorrected): Orig.-CAR: p = 0.94, t13 = -0.08, d = -0.01) or original and LP reference (p = 0.109, t13 = 1.72, d = 0.33) but a significantly higher MI for original compared to DB reference (Paired t-tests (uncorrected): Orig.-DB: p = 0.007, t13 = 3.23, d = 0.62).

Taken together, the choice of reference did not affect the overall pattern of results: A more negative slope was observed during sleep as compared to wakefulness. Critically, slope values derived from different reference schemes were strongly correlated.

4) Furthermore, we had some concerns regarding anatomical claims.

The fact that sleep stage-slope correlation seems to be dominated by medial PFC/temporal sites is interesting, though might be biased by the iEEG montage, as those are also the regions with the most electrodes due to epilepsy monitoring. There should be a statistical analysis that shows that those regions have a significantly higher proportion of "differentiating" electrodes than other brain regions. In addition to a sound statistical analysis, the authors should provide a table with the number of total electrodes and the number of electrodes showing a significant change in slope, per brain region. As it is, it's hard to define the regions of interest based on the brain plots shown.

We thank the reviewers for their suggestions. We want to point out that we did not select electrodes in regions of interest but used all available electrodes that were non-epileptic and located in gray matter. See Figure 1—figure supplement 1.

155 out of 352 SEEG (44.03 %) followed the observed scalp EEG pattern of a more negative slope in sleep compared to wakefulness (Figure 2C), significantly more than chance (33 % chance level; chi-squared test: Χ2 = 8.20, p = 0.0042).

We agree with the reviewers that there might be a selection bias in anatomical location of contacts in medial temporal lobe (MTL) regions as temporal epilepsy is the most common form of epilepsy. To access MTL regions, electrodes are inserted through lateral temporal cortex (LTC). To access orbitofrontal, cingulate and insular regions, electrodes are inserted through the lateral prefrontal cortex (PFC). Both implantation schemes lead to a paucity of recording sites in parietal and posterior regions. As the implantation of all the electrodes is purely due to clinical consideration, it will remain one limitation of this method.

We carefully revisited the anatomical localization of the depth electrodes and collected the information about subregions and state- dependent slope modulation in a table, as requested by the reviewers (Table 2). In Study 3 – Intracranial sleep, the majority of sEEG electrodes were located in PFC (132/352, 37.5 %), followed by LTC (79/352; 22.4%) and MTL (48/352; 13.6%).

As the visual impression suggested, medial PFC exhibits a significantly higher fraction of electrodes with sleep state- dependent slope modulation than lateral PFC (chi-squared test: Χ2 = 33.56, p < 0.000). The same was true for MTL compared to LTC (Χ2 = 33.12, p < 0.0001). When comparing mPFC and MTL, which both showed high levels of state- dependent slope modulation, or lPFC and LTC, that showed only little modulation, there was no significant regional difference (mPFC – MTL: Χ2 = 1.89, p = 0.169; lPFC – LTC: Χ2 = 0.19, p = 0.659). These comparisons underscore that the differences in chi squared test are not driven by electrode number.

For completeness, we also included a table (Table 1) with the subregions of electrodes in Study 2 – Intracranial anesthesia although almost all electrodes exhibited a state- dependent slope modulation:

We included the tables in the manuscript and edited the following paragraph:

“We observed the same pattern – a more negative spectral slope in N3 and REM sleep as compared to wakefulness – in 155 of 352 SEEG (44.03 %; chi-squared test against chance-level (33%): Χ2 = 8.20, p = 0.0042; Figure 2C, Figure 2—figure supplement 3). Importantly, this analysis revealed that medial prefrontal cortex (mPFC) and medial temporal lobe structures (MTL; details see Table 2, Figure 2—figure supplement 3) exhibit a significantly larger fraction of electrodes showing sleep state- dependent slope modulation compared to their lateral counterparts (chi-squared tests:mPFC – lateral PFC: p < 0.0001, Χ2 = 33.56, MTL – lateral temporal cortex: p < 0.0001, Χ2 = 33.12), hence, converging on the same brain regions known to be the most relevant for sleep-dependent memory consolidation (Dang-Vu et al., 2008; Helfrich et al., 2018; Mander et al., 2013; Murphy et al., 2009).”

Additionally, it would have been much more powerful if the anatomical claims could be corroborated by the EEG recordings. Not sure source localization is possible on the EEG data given low electrode numbers, but that would really have strengthened the story. In current form it remains a little unclear what the main sources of all these effects are.

We thank the reviewers for this suggestion and we source-localized the slope difference between wakefulness and sleep in scalp EEG (Study 3, n = 19; one patient had to be excluded due to insufficient wake trials).

Cortical sources of the sensor-level EEG data were reconstructed by using a LCMV (linearly constraint minimum variance) beamforming approach (Van Veen et al., 1997) to estimate the time series for every voxel on the grid. A standard T1 MRI template and a BEM (boundary element method) headmodel from the FieldTrip toolbox (Oostenveld et al., 2011) were used to construct a 3D template grid at 1cm spacing in standard Montreal Neurological Institute (MNI) space. Electrode location was derived from a standard 10/20 template from the FieldTrip toolbox (Oostenveld et al., 2011). Prior to source projection, sensor level data was common average referenced and epoched into 30 second segments. To minimize computational load, we selected a two second data segment from the center of every epoch to construct the covariance matrix. The LCMV spatial filter was then calculated using the covariance matrix of the sensor-level EEG data with 5% regularization. Spatial filters were constructed for each of the grid positions separately to maximally suppress activity from all other sources. The resulting time courses in source space then underwent spectral analysis using a Fourier transform after applying a Hanning window. The PSD slope of every segment was then estimated using linear regression in the range from 30-45 Hz as outlined before. To obtain a similar contrast to the intracranial analysis depicted in Figure 2C, mean slope values during sleep were subtracted from the mean slope during wakefulness at every voxel in source space and then source-interpolated onto a standard template brain in MNI space (Figure 2—figure supplement 3). Note that δ slope is reported as positive values whereas slope difference is depicted as a negative value. Both intracranial as well as the source-interpolated scalp EEG results revealed a focus in medial prefrontal areas (mPFC, Figure 2C – magenta, 2—figure supplement 3 – yellow).

Since it is challenging to localize sources to the MTL (in particular in the case of a 19 channel EEG), we employed an ROI-based approach focusing on PFC subregions. In line with our results from the intracranial sleep study (Study 4, Figure 2C and Figure 2—figure supplement 3), we defined the mPFC and dorsolateral PFC (dlPFC) as regions-of-interest (ROI; Figure 2—figure supplement 3). To identify ROI at source level, we used the Automated Anatomical Labeling (AAL) atlas as implemented in FieldTrip (Oostenveld et al., 2011). The ROI mPFC contained the following tissue labels: 23 & 24 – ‘Frontal_Sup_Medial_L & R’, 25 & 26 – ‘Frontal_Med_Orb_L & R’, 27 & 28 – ‘Rectus_L & R’, 31 & 32 – Cingulum_Ant_L & R’. The ROI dlPFC consisted of the following atlas tissue labels: 3 & 4 – ‘Frontal_Sup_L & R’, 7 & 8 – ‘Frontal_Mid_L & R’, 11 & 12 – ‘Frontal_Inf_Oper_L & R’, 13 & 14 – ‘Frontal_Inf_Tri_L & R’ and 15 & 16 ‘Frontal_Inf_Orb_L & R’.

In the mPFC ROI the slope decreased from wakefulness to sleep by 0.54 ± 0.23 (mean ± SEM) whereas in dlPFC it decreased by 0.36 ± 0.22. This slope difference between wakefulness and sleep was significantly different from zero for mPFC (paired t-test: p = 0.018) but not for dlPFC (p = 0.074). This difference in slope modulation between mPFC and dlPFC was significant (p = 0.036) in line with our observations in intracranial EEG.

Taken together, the observed anatomical pattern from the beamformer analysis of the sleep scalp EEG fits the previous results from the intracranial sleep study.

However, a beamformer analysis of only 19 channel EEG has only limited explanatory power and should be interpreted cautiously. We therefore refrained from adding the analysis to the main manuscript, especially since the manuscript already features intracranial recordings in humans. However, we introduced a new supplemental figure (Figure 2—figure supplement 3) depicting the results which is referred to in the following sentence of the result section:

“We established that the spectral slope closely tracks the hypnogram. […] Given the spatial heterogeneity of intracranial responses (Parvizi and Kastner, 2018), there was a remarkable convergence on medial PFC that resembled the pattern observed at source level (Figure 2—figure supplement 3) and the overlying scalp EEG electrode Fz (Figure 2).”

5) The fitting of 1/f spectral exponents should be improved and frequency ranges should be motivated more clearly.

Although it is correct that Gao et al., 2017, used a frequency range of 30-50 Hz for their 1/f PSD fit, this choice was motivated by the linear decrease of power in LFP recordings within that frequency range.

We would like to clarify our motivation to choose the 30 – 45 Hz range for spectral slope estimation. Please note that we now also incorporated a detailed empirical validation in the manuscript.

There is a wide variation of slope estimations from different frequency ranges (Colombo et al., 2019; He et al., 2010; K. J. Miller et al., 2009b; Miskovic et al., 2019; Pereda et al., 1998; Shen et al., 2003). Very low frequencies below 1 Hz were out of reach due to limitations with the DC amplifier in our recordings (He et al., 2010). We also excluded frequencies above 45 Hz as we were careful not to include any filtering artifacts from the 50 Hz line noise in the European recordings. We then adapted this setting for all datasets across recording modalities for reasons of consistency.

The choice to calculate the slope estimate with this particular frequency band stemmed from the following considerations:

(Gao et al., 2017) used a 30 – 50 Hz frequency range in their paper with propofol anesthesia in monkeys; it therefore seemed reasonable to expect that this frequency range would also be suitable in human anesthesia data.

Prominent neuronal oscillations mostly occur below 30 Hz and could possibly confound the estimation of the 1/f slope estimate. Especially states like propofol anesthesia and NREM sleep stage 3 are characterized by strong oscillations (e.g. α at 8 – 12 Hz and δ at 1 – 4 Hz under propofol (Purdon et al., 2013) and slow waves (< 1.25 Hz) and spindles at12 – 16 Hz in sleep (Prerau et al., 2017). To circumvent this problem, we a) used a fit above the frequency range where most oscillations occur and b) validated the choice by a removal of the oscillatory component using irregular resampling (IRASA; (Wen and Liu, 2016).

Note the IRASA method is computationally expensive and time consuming. This would prevent any further use of the marker in a clinical on-line setting like monitoring depth of anesthesia. Hence, we decided to use the approach to fit above the oscillatory frequency domain to offer an easy and computationally effective tool that is not confounded by oscillations.

Additional appeal to use the 30-45 Hz frequency range came from the possible mechanistical explanation: (Gao et al., 2017) showed in the modelling part of their paper that the slope in this frequency range tracks changes in the ratio of inhibition to excitation. As both propofol anesthesia and NREM sleep stage 3 are associated with an increase in inhibition (Brown et al., 2011; Niethard et al., 2016), the slope in that range should reliably track changes from wakefulness to these states of reduced arousal.

We then validated the chosen frequency range in both the sleep study with scalp EEG (Study 3) and the sleep study with intracranial recordings (Study 4). While both sleep studies provided us with a hypnogram that could pose as a “ground truth” for the evaluation of different slope fits, the intracranial sleep data had the additional benefit of allowing slope fits above 45 Hz.

Center frequency for fit:

We evaluated the relationship between hypnogram and time-resolved slope as a function of different center frequencies (± 10 Hz around center frequency starting from 20 up to 150 Hz: 10-30 (20), 20-40 (30), 30-50 (40) and so on) and found that spectral slope estimates only correlated significantly/ had a significant Mutual Information (MI) with the hypnogram if center frequencies up to 40 Hz were selected for the fit Figure 2—figure supplement 5A

Length of fit:

We evaluated the relationship between hypnogram and time-resolved slope as a function of fit lengths (from 30 Hz onwards with a 10 Hz increase of fit length up to 100 Hz: 30-40, 30-50, 30-60 and so on). The results showed that spectral slope estimates could be fitted with variable fit length from 30 Hz onwards and still resulted in a significant correlation/ MI with the hypnogram, see Figure 2—figure supplement 5B

Fit to low frequencies:

We evaluated fits to lower frequencies starting from 1 to 5 Hz with an increasing length of additional 5 Hz per fit after discounting the oscillatory components from the power spectrum by means of irregular resampling (IRASA; Figure 2—figure supplement 5c). The rationale for using a method like IRASA before attempting a slope fit was the occurrence of strong low frequency oscillations like slow waves which could possibly distort the slope estimate. When comparing the MI between the spectral slope fits and the hypnogram to the MIs of a surrogate distribution derived from a random block swapping procedure and the hypnogram, the 30 to 45 frequency range resulted in significantly higher MI than the fits to lower frequencies, see Figure 2—figure supplement 5D.

The results of these calculations were part of the original version of the manuscript (old Figure S6; new Figure 2—figure supplement 5). However, we realize that the organization of the subpanels was non-optimal and led to some confusion about the connection between subpanels. We rearranged the results in the new version of the figure and hope that it is now easier to follow.

Taken together, our analyses regarding the frequency range settings for spectral slope estimation suggested that a center frequency up to 40 Hz with at least a 10 Hz range should be used if calculating the spectral slope for sleep EEG for 30 second segments. A spectral slope estimated from the 30-45 Hz range provided the highest MI with the hypnogram indicating that this frequency range is well suited to distinguish wakefulness from N3 and REM sleep.

However, oscillatory parts of the spectrum, whether of neural or non-neural origin (line noise), can aptly be fitted and excluded from a 1/f fit using the FOOOF package (https://fooof-tools.github.io/fooof/). The use of this or another software package (e.g. BOSC or eBOSC: https://github.com/jkosciessa/eBOSC) would allow the authors to directly asses the change of PSD exponents across different levels of arousal across wider frequency ranges without having to alter time-series first using IRASA.

We thank the reviewers for their suggestions. We would like to highlight that the IRASA method (Wen and Liu, 2016) was only used for one part of the analysis (fitting to frequency ranges below 30 Hz, compare 2c – Fit to lower frequencies). Therefore, all the analyses in the manuscript were performed on the recorded time-series data after artifact rejection, demeaning and detrending.

As suggested by the reviewer, we evaluated the influence of different slope fitting algorithms on spectral slope estimation and recalculated the slopes using both the FOOOF (Haller et al., 2018) and the eBOSC algorithm (Caplan et al., 2001; Kosciessa et al., 2020; Whitten et al., 2011) in Study 1 – Anesthesia scalp EEG (Figure 1—figure supplement 4) and Study 3 – Sleep scalp EEG (Figure 2—figure supplement 9) and added goodness of fit statistics.

Linear regression:

Both our approach as well as the eBOSC algorithm (Kosciessa et al., 2020) perform a linear regression on the PSD in log-log space, albeit with using either the polyfit.m function (in our case) or the robustfit.m in the case of eBOSC.

Model fit:

The FOOOF algorithm follows the following steps to estimate the oscillatory and aperiodic signal: First an exponential fit is performed to the power spectrum in semi-log space, then this fit is subtracted from the PSD. The residual signal is treated as a combination of oscillations and noise and is repeatedly fit with multiple gaussian fits to detect putative oscillatory peaks until the noise floor is reached. The detected peaks are then validated against the mixed oscillatory/noise signal and subtracted from the original PSD. The new residual signal is then fit again for a better estimate of the aperiodic signal. Both, the multi Gaussian fits and the improved aperiodic fit are then combined in a model (compare to Figure 3 (Haller et al., 2018)). When the PSD does not contain a bend, also called knee, in the aperiodic signal, then the algorithm is “equivalent to fitting a line in log-log space” (Haller et al., 2018).

Author response image 3
The influence of different fit algorithms on spectral slope estimation in general anesthesia with propofol.

a, 1/f spectral slope in wakefulness (Wake, red) and under anesthesia (Ana, blue) using the original polyfit (Orig., orange), FOOOF (lblue) or eBOSC (purple) algorithm (n = 9, averaged across electrodes). Paired t-tests (uncorrected): Orig.-FOOOF: p = 0.082, t8 = 1.99, d = 0.18; Orig.- eBOSC: p = 0.369, t8 = -0.95, d = -0.03, FOOOF - eBOSC: p = 0.118, t8 = -1.75, d = -0.21. n.s. – not significant. b, At Fz ,1/f slope from original polyfit (Orig., orange) and FOOOF (blue; left panel: r = 0.98, p < 0.001) and original and eBOSC (purple; right panel: r = 1.00, p < 0.001) are strongly correlated.c, Goodness of fit (R2) of the different slope estimates (Orig. - original polyfit (orange); FOOOF (light blue); eBOSC (purple)) to the power spectra in wakefulness and under propofol anesthesia at electrode Fz (n = 9). Permutation t-tests: Orig. - fooof: p = 0.538, Orig. - eBOSC: p = 0.726, fooof - eBOSC: p = 0.690. n.s. – not significant.

Study 1 – Anesthesia scalp EEG:

We evaluated all three slope fitting algorithms – polyfit, FOOOF and eBOSC – in both the 30 – 45 as well as the 1-40 Hz range (compare 2c – Fit to lower frequencies and Figure 1—figure supplement 4). Note that propofol anesthesia is characterized by strong oscillations, mainly in the δ (1-4) and α range (8-12 Hz) which might distort spectral slope estimates (Purdon et al., 2013).

30 – 45 Hz: When fitting the slope to the 30 – 45 Hz range, there was no significant difference between slope estimated derived from the original polyfit and eBOSC, FOOOF and eBOSC (Figure 1—figure supplement 4a/ Author response image 3A). The slope estimates derived from both FOOOF and eBOSC were strongly correlated with slopes values calculated by polyfit (Figure 1—figure supplement 4b/ Author response image 3B). Between fitting algorithms, there was no difference in effect size (Cohen’s d; Figure 1—figure supplement 4e) or goodness of fit to the power spectra (Author response image 3C).

1 – 40 Hz: When the spectral slope was calculated between 1 – 40 Hz, then the different slope fitting algorithms resulted in small but significantly different slope estimates (Figure 1—figure supplement 4D); possibly because some algorithms are more susceptible to oscillatory peaks in low frequency bands than others. Despite this difference, the slope values were still strongly correlated (Figure 1—figure supplement 4D). There was a significantly higher effect size for the Original compared to eBOSC (Orig.1-40-eBOSC1-40: p = 0.004, obs. t8 = 3.42, d = 0.15) but not for the Original versus FOOOF (Orig.1-40-fooof1-40: p = 0.092, obs. t8 = 1.38, d = 0.15) or FOOOF and eBOSC (fooof1-40- eBOSC1-40: p = 0.656, obs. t8 = 0.40, d = 0.04). When calculating the goodness of fit at electrode Fz, there was no difference between algorithms (Orig.1-40-fooof1-40: p = 0.162, Orig.1-40-eBOSC1-40: p = 0.705, fooof1-40- eBOSC1-40: p = 0.651).

Study 3 – Sleep scalp EEG:

When employing all three slope fitting algorithms, namely the polyfit, FOOOF and eBOSC, the resulting slope estimates were remarkanly similar although some small but consistent differences existed (n = 14; mean difference between slopes values: Orig.-FOOOF: 0.043 ± 0.022, Orig.-eBOSC: -0.003 ± 0.001). These differences were not significant between the original polyfit and the FOOOF algorithm but were between the original and eBOSC (Figure 2—figure supplement 9A). Both slopes derived from FOOOF and eBOSC were strongly correlated with slopes calculated by the original polyfit (Figure 2—figure supplement 9B, C). When calculating the goodness of fit to the PSD, there were no significant differences between the original and both FOOOF or eBOSC (Figure 2—figure supplement 9D).

Taken together, in both sleep and anesthesia, the choice of slope fitting algorithm did not change the observed pattern of more negative slop values during reduced arousal states. Although absolute slope values derived from the algorithms did slightly vary, they were strongly correlated with each other and their goodness of fits were comparable. Hence, the choice of slope fitting algorithm did not impact the ability of the spectral slope to differentiate between arousal states in sleep and anesthesia.

We added the following summary paragraph to the control analysis section in the revised manuscript, see subsection Evaluation of parameters for 1/f spectral slope estimation.

Moreover, we added the following paragraph to the discussion: subsection “Practical considerations for analyzing 1/f dynamics”

In fact, Colombo and colleagues show a steepening of the PSD between 1 and 40 Hz from awake rest compared to Propofol anesthesia, a result the authors could try to replicate and discuss using the proposed analyses techniques.

We appreciate the reviewers’ suggestion and recalculated the spectral slopes under propofol anesthesia using a frequency range from 1 – 40 Hz in line with Colombo et al., 2019 in Study 1 – Anesthesia scalp EEG (n = 9). When the slope was fitted to the 1-40 Hz frequency range, the absolute slope values changed slightly but the overall pattern of a more negative slope for anesthesia than for wakefulness persisted (Figure 1—figure supplement 4). To directly compare the fits to the 30-45 and the 1-40 Hz frequency range, we contrasted the effect sizes (Cohen’s d) of the wakefulness-anesthesia comparison of the two fits (Figure 1—figure supplement 4G) and found no significant difference between the two irrespective of fitting algorithm (Permutation t-test: Orig.30-45 – Orig.1-40: p = 0.773, obs. t8 = -0.84, d = -0.37; fooof30-45 – fooof1-40: p = 0.737, obs. t8 = -0.63, d = -0.28; eBOSC30-45 – eBOSC1-40: p = 0.672, obs. t8 = -0.47, d = -0.20).

Moreover, we recalculated how well both slope fits can differentiate between wakefulness and anesthesia with a Linear Discriminant Analysis (LDA). Both 1/f slope fits result in a higher percentage of correct classification compared to SO power (SO: 52.43 ± 1.04 % (mean ± SEM), slope30-45: 76.56 ± 3.56 %, slope1-40: 83.75 ± 2.31 %; permutation t-tests: Slope30-45 – SO: p < 0.001, observed (obs.) t8 = 6.10, d = 2.63; Slope1-40 – SO: p < 0.001, obs. t8 = 9.24, d = 3.88). When directly comparing the slope fits, the fit to 1-40 Hz performed better than the 30-45 Hz (p = 0.023, obs. t8 = 2.49, d = 0.83).

Taken together, while the absolute slope values varied, the overall slope pattern as well as the effect size between wakefulness and anesthesia was comparable between fits. However, the 1-40 Hz fit had a better wake-anesthesia classification performance. This performance difference might be due to an inclusion of both the low frequency (< 4 Hz) and the α frequency (8 – 12 Hz) range into the 1 – 40 Hz fit. Under propofol anesthesia, these frequency ranges are typically characterized by prominent oscillations (Purdon et al., 2013) that might distort spectral slope estimation leading to overlapping information between the two factors. Notably, this finding is contrast to our results in sleep, where an inclusion of low frequencies hampered the MI between the hypnogram (Figure 2 —figure supplement 5D). This implies that optimal fit ranges for spectral slope estimation could differ between arousal states.

In conclusion, both the 30-45 as well as the 1-40 frequency range seem suited to be used for spectral slope estimation under anesthesia in scalp EEG. However, the 30 – 45 Hz range had the highest MI between the hypnogram and the spectral slope in sleep in scalp EEG indicating that this specific range is well suited to be used in both sleep and anesthesia recordings.

Furthermore, goodness of fit statistics for the performed linear fits are missing and should be added for any kind of fitting procedure the authors decide to apply.

6) Discussion could be more in depth in terms of:

– connection with existing literature;

We thank the reviewers for their comments and carefully revisited the manuscript. The discussion now features a clear structure with several new paragraphs that explore the connection to the existing literature, the underlying physiology and the implications for understanding sleep physiology.

“Neurophysiological markers of arousal states:

Consciousness is commonly assessed on two axes – content (e.g. the experience) and level (e.g. vigilance; (Boly et al., 2013; Laureys, 2005). […]Here, we demonstrate that the non-oscillatory, aperiodic part of the power spectrum, which is devoid of prominent low-frequency oscillatory components and can be approximated by the 1/f decay of the power spectrum estimated from the 30 – 45 Hz frequency range, reliably differentiates wakefulness from all three states of reduced arousal level, namely REM, N3 sleep and general anesthesia with propofol.”

– underlying mechanisms/generation of the recorded signals;

“The neurophysiologic basis of 1/f dynamics:

1/f dynamics are observed across a variety of tasks (He et al., 2010; Kai J. Miller et al., 2009; K. J. Miller et al., 2009b; Voytek et al., 2015), change with lifespan (Voytek et al., 2015), and exhibit state-dependent variations during sleep (Freeman and Zhai, 2009; Leemburg et al., 2018; Miskovic et al., 2019; Robinson et al., 2011), and anesthesia (Colombo et al., 2019; Gao et al., 2017). […] Future studies involving single neuron recordings and optogenetic manipulation will be needed to unravel the precise relationship between population firing statistics and changes in the spectral slope. Comparative studies in rodents (Gao et al., 2017; Leemburg et al., 2018), non-human primates (Gao et al., 2017) and humans (Colombo et al., 2019; He et al., 2010; Kai J. Miller et al., 2009; K. J. Miller et al., 2009b; Miskovic et al., 2019) combined with modeling work (Chaudhuri et al., 2018; Robinson et al., 2011, 2001) has the potential to integrate the divergent findings into a coherent framework, which is critical to further elucidate the neurophysiologic basis of 1/f dynamics and their relationship to arousal levels.”

– interpretation of the findings and implications for our understanding of sleep vs wake processes;

“Functional significance of 1/f dynamics in arousal states:

Here, we found a decreased 1/f slope in N3 sleep, REM sleep and under general anesthesia compared to wakefulness in four independent studies. […] This notion of increased inhibition during REM sleep offers a likely mechanistic explanation for certain REM-defining phenomena, such as muscle atonia (Scammell et al., 2017) or the clinical observation that epileptic seizures during the night predominantly occur out of more excitable, highly synchronized NREM sleep and only rarely out of less excitable, desynchronized REM sleep (Ng and Pavlova, 2013).”

– actual discussion of practical use, i.e., how reliable is slope as a measure to distinguish these states on the single subject level.

“Importantly, while some overlap of absolute spectral slope values between rest and sleep existed when comparing across individuals (Figure 2—figure supplement 1A), we observed a consistent individual decrease of – 2.06 ± 0.21 (mean ± SEM) between rest and all sleep stages (Figure 2—figure supplement 1B; Rest-N1 = -1.95 ± 0.26, Rest-N2 = -1.81 ± 0.23, Rest-N3 = -1.59 ± 0.28, Rest-REM = -2.86 ± 0.25).”

[Editors' note: further revisions were suggested prior to acceptance, as described below.]

The issue we are still unclear on pertains to this claim:

"Critically, the accuracy of this classification is comparable to trained personnel, since the inter-rater reliability between sleep state scoring experts is typically about 80%".

However, if the ground truth here consists of the sleep staging done by trained experts, for whom we know the inter-rater reliability is typically about 80%, then a 100% accuracy of the classifier would be a 100% match with these expert raters (i.e., not necessarily a 100% accurate classification of sleep stage). In other words, the performance of the classifier is bound by the accuracy of the ground truth. Since we do not know the "true" sleep stage, we can only conclude that the classifier accurately predicts the experts' ratings 80% of the time here. Please add some language to make this explicit in the discussion of these results.

We agree with the reviewer’s comment and modified the following paragraph in the manuscript to clarify the accuracy of the classification:

“Note that classification performance is bound by the accuracy of the underlying sleep scoring as a ground truth. Since the inter-rater reliability between sleep scoring experts is typically about 80% (Danker-Hopfe et al., 2009), the classifier accurately predicts the experts' ratings in 80% of the time.”

https://doi.org/10.7554/eLife.55092.sa2

Article and author information

Author details

  1. Janna D Lendner

    1. Helen Wills Neuroscience Institute, University of California, Berkeley, Berkeley, United States
    2. Department of Anesthesiology and Intensive Care Medicine, University Medical Center Tuebingen, Tuebingen, Germany
    Contribution
    Conceptualization, Data curation, Software, Formal analysis, Funding acquisition, Validation, Investigation, Visualization, Methodology, Writing - original draft, Project administration, Writing - review and editing
    For correspondence
    janna.lendner@gmail.com
    Competing interests
    No competing interests declared
    ORCID icon "This ORCID iD identifies the author of this article:" 0000-0002-1967-6110
  2. Randolph F Helfrich

    1. Hertie-Institute for Clinical Brain Research, Tuebingen, Germany
    2. Department of Neurology and Epileptology, University Medical Center Tuebingen, Tuebingen, Germany
    Contribution
    Software, Project administration, Writing - review and editing
    Competing interests
    No competing interests declared
    ORCID icon "This ORCID iD identifies the author of this article:" 0000-0001-8045-3111
  3. Bryce A Mander

    Department of Psychiatry and Human Behavior, University of California, Irvine, Irvine, United States
    Contribution
    Resources, Data curation, Methodology
    Competing interests
    No competing interests declared
  4. Luis Romundstad

    Department of Anesthesiology, University of Oslo Medical Center, Oslo, Norway
    Contribution
    Resources, Project administration
    Competing interests
    No competing interests declared
  5. Jack J Lin

    Department of Neurology, University of California, Irvine, Irvine, United States
    Contribution
    Resources, Investigation, Project administration
    Competing interests
    No competing interests declared
  6. Matthew P Walker

    1. Helen Wills Neuroscience Institute, University of California, Berkeley, Berkeley, United States
    2. Department of Psychology, University of California, Berkeley, Berkeley, United States
    Contribution
    Resources, Data curation, Investigation, Project administration, Writing - review and editing
    Competing interests
    No competing interests declared
  7. Pal G Larsson

    Department of Neurosurgery, University of Oslo Medical Center, Oslo, Norway
    Contribution
    Resources, Data curation, Investigation, Project administration
    Competing interests
    No competing interests declared
  8. Robert T Knight

    1. Helen Wills Neuroscience Institute, University of California, Berkeley, Berkeley, United States
    2. Department of Psychology, University of California, Berkeley, Berkeley, United States
    Contribution
    Conceptualization, Resources, Supervision, Funding acquisition, Methodology, Project administration, Writing - review and editing
    Competing interests
    No competing interests declared

Funding

Deutsche Forschungsgemeinschaft (LE 3863/2-1)

  • Janna Desiree Lendner

National Institute of Neurological Disorders and Stroke (R37NS21135)

  • Robert T Knight

Deutsche Forschungsgemeinschaft (HE 8329/2-1)

  • Randolph F Helfrich

National Institute of Mental Health (R01AG03116408)

  • Matthew P Walker

National Institute of Mental Health (RF1AG05401901)

  • Matthew P Walker

National Institute of Mental Health (RF1AG05410601)

  • Matthew P Walker

National Institute of Mental Health (F32-AG039170)

  • Bryce A Mander

The funders had no role in study design, data collection and interpretation, or the decision to submit the work for publication.

Acknowledgements

This work was supported by Grant LE 3863/2-1 (JDL) and HE 8329/2–1 (RFH) of the German Research Foundation (Deutsche Forschungsgemeinschaft), a National Institute of Neurological Disorders and Stroke Grant R37NS21135 (RTK), the Hertie Foundation (Network of Excellence in Clinical Neurosciences; RFH), R01AG03116408 (MPW), RF1AG05401901 (MPW), RF1AG05410601 (MPW) and F32-AG039170 (BAM), all from the National Institute of Health. We thank Jie Zheng, Julia Kam and the EEG technicians at UC Irvine Medical Center for their assistance and all the patients for their participation.

Ethics

Human subjects: We collected four independent datasets for this study to assess the neurophysiological basis of states of reduced arousal, namely sleep and general anesthesia. Study 1 - Anesthesia scalp EEG: All participants were informed and provided written consent in accordance with the local ethics committee (Regional Committees for Medical and Health Research Ethics in Oslo case number 2012/2015 and extension 2012/2015-8). Study 2 - Anesthesia intracranial EEG: All participants were informed and provided written consent in accordance with the local ethics committee (Regional Committees for Medical and Health Research Ethics in Oslo case number 2012/2015 and extension 2012/2015-8). Study 3 - Sleep scalp EEG: All participants were informed and provided written consent in accordance with the local ethics committee (Berkeley Committee for Protection of Human Subjects Protocol Number 2010-01-595). Study 4 - Sleep intracranial EEG: All patients provided informed consent according to the local ethics committees of the University of California at Berkeley and at Irvine (University of California at Berkeley Committee for the Protection of Human Subjects Protocol Number 2010-01-520; University of California at Irvine Institutional Review Board Protocol Number 2014-1522, UCB relies on UCI Reliance Number 1817) and gave their written consent before data collection.

Senior Editor

  1. Laura L Colgin, University of Texas at Austin, United States

Reviewing Editor

  1. Saskia Haegens, Columbia University College of Physicians and Surgeons, United States

Reviewer

  1. Giovanni Piantoni, Massachusetts General Hospital, United States

Publication history

  1. Received: January 12, 2020
  2. Accepted: July 6, 2020
  3. Accepted Manuscript published: July 28, 2020 (version 1)
  4. Version of Record published: July 31, 2020 (version 2)

Copyright

© 2020, Lendner et al.

This article is distributed under the terms of the Creative Commons Attribution License, which permits unrestricted use and redistribution provided that the original author and source are credited.

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