Slow oscillations in human non-rapid eye movement sleep electroencephalogram: effects of increased sleep pressure

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1 J. Sleep Res. () 9, 8 37 Slow oscillations in human EEG doi:./j x Slow oscillations in human non-rapid eye movement sleep electroencephalogram: effects of increased sleep pressure ALESSIA BERSAGLIERE, and PETER ACHERMANN,,3 Institute of Pharmacology and Toxicology, Neuroscience Center Zurich and 3 Zurich Center for Integrative Human Physiology, University of Zurich, Zurich, Switzerland Accepted in revised form April 9; received January 9 SUMMARY Slow oscillations (< Hz) in the non-rapid eye movement (NREM) sleep electroencephalogram (EEG) result from slow membrane potential fluctuations of cortical neurones, alternating between a depolarized up-state and a hyperpolarized down-state. They are thought to underlie the restorative function of sleep. We investigated the behaviour of slow oscillations in humans under increased sleep pressure to assess their contribution to sleep homeostasis. EEG recordings (C3A) of baseline and recovery sleep after sleep deprivation (eight healthy males, mean age 3 years; h of prolonged wakefulness) were analysed. Half-waves were defined as positive or negative deflections between consecutive zero crossings in the.5 Hz range of the band-pass filtered EEG. Increased sleep pressure resulted in a redistribution of half-waves between.5 and Hz: the number of half-waves per minute was reduced below.9 Hz while it was increased above. Hz. EEG power was increased above Hz. The increase in frequency was accompanied by increased slope of the half-waves and decreased number of multi-peak waves. In both baseline and recovery sleep, amplitude and slope were correlated highly over a broad frequency range and positive half-waves were characterized by a lower frequency than the negative ones, pointing to a longer duration of up- than downstates. We hypothesize that the higher frequency of slow oscillatory activity after prolonged wakefulness may relate to faster alternations between up- and down-states at the cellular level under increased sleep pressure. This study does not question slow-wave activity as a marker of sleep homeostasis, as the observed changes occurred within the same frequency range. keywords electroencephalogram, sleep homeostasis, sleep regulation, slow oscillation, slow wave slope INTRODUCTION Slow waves represent the most prominent feature in the electroencephalogram (EEG) during non-rapid eye movement (NREM) sleep and reflect sleep intensity (Blake and Gerard, 937; Kohlschu tter, 86). Slow-wave activity (spectral EEG power in the.75.5 Hz range) is a well-established marker of sleep intensity reflecting homeostatic sleep pressure: it Correspondence: Peter Achermann, Section of Chronobiology and Sleep Research, Institute of Pharmacology and Toxicology, University of Zurich, Winterthurerstrasse 9, 857 Zurich, Switzerland. Tel.: ; fax: ; acherman@pharma.uzh.ch decreases in the course of sleep and increases as a function of the duration of prior wakefulness (Borbély, 98; Borbe ly and Achermann, 5). Slow components in the EEG are thought to underlie the restorative function of sleep. Tononi and Cirelli (3, 6) have proposed that slow oscillations and slow-wave activity are related to synaptic homeostasis. In their model, synaptic strength is high at the beginning of the night, because of plastic processes occurring during waking, and decreases by means of synaptic down-scaling during sleep. This hypothesis is supported by increasing experimental evidence (Huber et al.,, 6; Riedner et al., 7; Vyazovskiy et al., 7, 8). 8 Ó 9 European Sleep Research Society

2 Slow oscillations and increased sleep pressure 9 Slow oscillations (< Hz) consist, at the cellular level, of depolarizing components (up-states) separated by prolonged hyperpolarizations (down-states). They were first described in anaesthetized cats (Steriade et al., 993a,b) and later in humans (Achermann and Borbe ly, 997; Amzica and Steriade, 997; Steriade et al., 993b). Furthermore, slow oscillations are thought to be involved in the temporal organization of other sleep rhythms such as sleep spindles and delta waves (Massimini et al., 7; Mo lle et al., ; Steriade et al., 993a). Delta and slow oscillations may be dissociated. Previous studies have dissociated delta and slow oscillations based on the finding that power in the low delta (below Hz) range exhibits homeostatic behaviour only partially. In these studies, power below Hz did not decline from the first to the second NREM sleep episode (Achermann and Borbe ly, 997; Campbell et al., 6) and was not increased after sleep deprivation (Borbély et al., 98). Conversely, one study found that power in the -Hz band increased monotonically as a function of the duration of prior wakefulness (Campbell et al., 6). The aim of the present study is to provide a systematic and detailed analysis of slow oscillations in normal sleep and under increased sleep pressure in order to assess whether they are regulated homeostatically. To this end, we combined power spectral analysis with period amplitude analysis (Feinberg et al., 987; Geering et al., 993; Ktonas and Gosalia, 98; Massimini et al., ; Mo lle et al., ; Riedner et al., 7). The purpose of spectral analysis is the decomposition of signals such as the EEG into its constituting frequency components. Period amplitude analysis provides complementary information such as incidence and amplitude of waves. MATERIALS AND METHODS Subjects and EEG recordings Electroencephalogram recordings of eight healthy young males (3 ±.6 years; mean ± SEM) during baseline sleep and after h of sustained wakefulness recovery sleep were analysed (within-subject design, data of a previous study; for details see Finelli et al.,, ). The study protocol was approved by the institutional ethical committee and participants gave their written informed consent. Data were recorded by a polygraphic amplifier (EASYS; Neuroscience Technology Research, Prague, Czech Republic) and sampled with 8 Hz [high-pass filter at.6 Hz ( 3 db); anti-aliasing lowpass filter at 3 Hz]. EEG derivation C3A was analysed. Sleep stages were scored visually in -s epochs according to standard criteria (Rechtschaffen and Kales, 968). Signal analysis Waves below Hz are considered commonly as slow oscillations. However, there is a lack of consensus about what constitutes a slow oscillation in the human EEG. In the present study, we therefore investigated the frequency range from.5 to Hz. Period amplitude analysis was applied to identify waves in this frequency range. This analysis requires narrow band-pass filtering to detect waves reliably (Geering et al., 993; Ktonas and Gosalia, 98). Thus, derivation C3A was band-pass filtered (third-order Chebyshev type II high-pass filter; 3 db at. Hz; sixth-order Chebyshev type II low-pass filter, 3 db at.3 Hz). The filters were applied in the forward and reverse directions, in order to achieve zero-phase distortion resulting in doubling of the filter order. The cut-off frequencies were selected to achieve minimal attenuation in the band of interest (.5 Hz) and good attenuation at neighbouring frequencies, i.e. below.5 and above Hz. Half-waves were determined as negative or positive deflections between two consecutive zero crossings in the band-pass filtered signal (Fig. ) for frequencies between.5 and Hz, and two amplitude thresholds of ±5 lv and ±37.5 lv were applied. The first threshold allows the detection of approximately all waves; the second corresponds to the scoring rules of slow waves (75 lv peak-to-peak, 37.5 lv for positive or negative half-waves; Rechtschaffen and Kales, 968). The frequency of the half-waves was calculated as the inverse of the period, i.e. twice the time interval between the two zero crossings characterizing the half-wave. The number of waves per min and their amplitude were calculated in steps of.-hz between.5 and.5 Hz. In the text, we will refer to the centre bin. For example, the.8-hz bin is the bin centred at.8 Hz, and is comprised of frequencies between.75 and.85 Hz. For each half-wave, the maximal slope was defined as the maximum absolute value of the first derivative of the signal. For positive half-waves, the maximal slope was determined in the ascending phase denoted as initial slope and in the descending phase denoted as final slope, whereas for negative half-waves the initial phase was derived from the descending Figure. Exemplary EEG traces (derivation C3A) of baseline sleep (a,c) and recovery sleep after h of sustained wakefulness (b,d). (a,b) Raw signals; (c,d) band-pass filtered signals (.5 Hz). Detected positive (black) and negative (grey) half-waves are shown for the lower detection threshold (5 lv; thick lines). Arrows indicate halfwaves that are not detected with the higher threshold (37.5 lv). (µv) (µv) 6 8 Time (s) (d) 6 8 Time (s) Ó 9 European Sleep Research Society, J. Sleep Res., 9, 8 37

3 3 A. Bersagliere and P. Achermann phase and the final slope from the ascending phase (Riedner et al., 7). The mean slope was determined as the amplitude of the negative (or positive) peak divided by the time from the previous zero crossing (initial mean slope) or the time until the next zero crossing (final mean slope; Riedner et al., 7). The number of peaks per half-wave was defined as the number of times the first derivative of the band-pass filtered signal crosses the zero line from positive to negative (or negative to positive) values. Electroencephalogram power spectra were calculated for consecutive -s epochs (fast-fourier transform routine, Hanning window, averages of two -s epochs; frequency resolution. Hz) and matched with the corresponding sleep stages. As the peak in the low frequency range of the spectrum may be affected by the analogue high-pass filter of the amplifier (.6 Hz), power in each frequency bin was multiplied by the inverse squared of the frequency response of the amplifier (Achermann and Borbe ly, 997) and subsequently high-pass filtered with a cut-off frequency of.53 Hz. This correction resulted in a shift of the cut-off frequency from.6 to.53 Hz. Artefacts were excluded by visual inspection and based semiautomatically on two criteria: (i) whenever power in the.75.5 Hz or 3 Hz band exceeded a threshold based on a moving average determined over 5 -s epochs (Finelli et al., ); and (ii) whenever power in the.3. Hz band in a single -s epoch exceeded 3.5 times the average power in the corresponding NREM sleep episode. Statistical analysis Statistical analysis was performed using sas (version 8, SAS Institute Inc., Cary, NC, USA) and Matlab (version 7.5, The Math Works Inc, Natick, MA, USA). A paired t-test was used to assess statistical significance of condition (baseline, recovery sleep). Mixed-model analyses of variance (anovas) (random intercept, compound symmetry, maximum likelihood estimation) were performed whenever more than one factor had to be tested. Post hoc testing was performed subsequently using a paired t-test for significant main factors or interactions with the main factor. Prior to statistical evaluation, power density values were log-transformed. The Kolmogorov Smirnov test was used to compare the distributions of slopes. The relationship between amplitude and slope of the waves was assessed by PearsonÕs correlation Stages M W R 3 Hypnogram (d) 5 Detected waves (threshold 5 µv) Detected waves (threshold 37.5 µv) Slow wave activity (.7.5 Hz) (µv ) Time (h) Figure. Hypnogram, number of detected waves and slow-wave activity of a single individual during baseline sleep. Hypnogram [M: movement time; W: wake; R: rapid eye movement (REM) sleep; : non-rem sleep Stages ]. Number of half-waves per min (total of positive and negative half-waves) detected with an absolute threshold of 5 lv and 37.5 lv. (d) Slow-wave activity (spectral power in the range of.7.5 Hz). Dashed lines delimit the beginning and end of REM sleep episodes. Ó 9 European Sleep Research Society, J. Sleep Res., 9, 8 37

4 Slow oscillations and increased sleep pressure 3 coefficients. Statistical evaluation was performed on FisherÕs Z-transformed correlation values. RESULTS Data of an exemplary participant during baseline sleep are illustrated in Fig.. Slow-wave activity showed the typical decline in the course of sleep and is modulated by the NREM REM sleep cycle (Fig. a,d). The number of half-waves per min is depicted for two different threshold values (5 and 37.5 lv). The number of waves per min with an absolute amplitude larger than 37.5 lv (Fig. c) resembled closely the profile of slow-wave activity (PearsonÕs correlation coefficient between slow-wave activity and number of waves per min: r =.77), whereas the waves detected with the 5 lv threshold (i.e. corresponding approximately to all waves; Fig. b) were distributed more uniformly throughout the night (r =.7). A similar trend was observed in all participants during baseline and recovery nights. The average correlation between slow-wave activity and number of waves per min for the higher threshold (37.5 lv) was lower in baseline sleep (.75; range.636.8) than in recovery sleep (.85; range.73.87; P <.5; paired t-test). Further analysis was restricted to slow wave sleep (Stages 3 and ) of the first and second NREM sleep episode where sleep pressure was highest in both conditions, and the effect of sleep deprivation had not yet dissipated. The duration of slow wave sleep during the first sleep episode was 33.6 ± 7.5 min (68 ± % of episode) in baseline sleep and 7. ± 5. min (8 ± %) in recovery sleep (P <.5; paired t-test); during the second episode, it was.9 ± 5. 3 min ( ± %) in baseline and.8 ± 7.6 min (6 ± %) in recovery sleep (P <.5). Power spectra and period amplitude analysis In the first NREM sleep episode, sleep deprivation resulted in an increase of spectral power above Hz only (Fig. 3f). The peak in the spectrum was at a higher frequency after sleep Baseline Recovery.6 Baseline Recovery.6 Baseline Recovery (d) (e) (f) 7 Nb of waves (waves min ) 8 6 Amplitude (µv) 6 5 Power density (µv Hz ) Figure 3. Effect of sleep deprivation on the number of half-waves and half-wave amplitude as a function of frequency, and on power density spectra in slow wave sleep of the first non-rapid eye movement (NREM) sleep episode in baseline (black) and recovery sleep (grey) after h of sustained wakefulness. (a c) Position of the peak (frequency) and its change in response to sleep deprivation in half-waves and half-wave amplitude as a function of frequency and power density spectra. Open bars: waves detected with an absolute threshold of 5 lv; grey bars: with a threshold of 37.5 lv; for power density spectra no threshold was applied. (d) Number of half-waves per min (positive and negative deflections) and (e) amplitude of the half-waves as a function of frequency (.-Hz resolution), (f) mean power density spectra. The frequency of the half-waves was derived from their duration. Thick lines: waves detected with an absolute threshold of 5 lv; thin line: with a threshold of 37.5 lv. The power density spectrum reflects the entire signal and thus is not related to any threshold (no thin line). Mean data ± SEM (n = 8) are illustrated; n significant difference between baseline and recovery sleep (n power spectra and thick lines; P <.5; paired t-test; thin lines). Ó 9 European Sleep Research Society, J. Sleep Res., 9, 8 37

5 3 A. Bersagliere and P. Achermann deprivation (Fig. 3c;.9 Hz) compared to baseline (.8 Hz). This shift, however, was not statistically significant. Period amplitude analysis revealed that the number of detected halfwaves per min was reduced after sleep deprivation in the frequency range between.5 and.8 Hz, while it increased above.3 Hz (Fig. 3a,d). This is also evident in filtered raw EEG traces (see Fig. ), where the number of detected halfwaves increased after sleep deprivation. The amplitude of the half-waves was increased over the entire frequency range (.5 Hz, Fig. 3e) and the peak occurred at a slightly higher frequency (Fig. 3b). Thus, the reduced number of waves and the increased amplitude below Hz account for the observation that there was no change in the power spectrum below Hz. On the contrary, both the increased number of waves and their amplitude above Hz resulted in increased spectral power in this frequency range. This was the case whether all half-waves (threshold 5 lv) or only large amplitude halfwaves (37.5 lv) were analysed (Fig. 3d,e). For the higher threshold, however, the number of waves detected was smaller and the amplitude higher compared to the low threshold (Fig. 3d,e; thin lines). Only minor changes were present in slow wave sleep of the second NREM sleep episode. When the analysis was performed for NREM sleep (first h of baseline and of recovery sleep) or restricted to slow wave sleep (first episode), the results were very similar. In the second h, only minor changes remained between baseline and recovery sleep (data not shown). Positive and negative half-waves Positive and negative half-waves reflect different cellular events related to the slow oscillation (see Discussion). In order to investigate whether there was an asymmetry in their response to sleep deprivation, we performed period amplitude analysis separately for positive and negative half-waves (Fig. ). The incidence of positive and negative half-waves differed between.5 and.5 Hz (factor polarity; both thresholds). Positive half-waves predominated in the lower frequency range, with a peak around.8 Hz (Fig. a), while the negative ones had a peak around. Hz. This held true for both detection thresholds (5 lv, Fig. c; 37.5 lv, Fig. d). Sleep deprivation led to faster frequency waves, a decrease in the number of slow frequency half-waves and an increase of halfwaves with faster frequencies (statistically significant difference between conditions in the frequency range.5.7 Hz and..3 Hz for 5 lv; at.6 Hz and above.9 Hz for 37.5 lv). Threshold 5 µv Positive half-waves Threshold 37.5 µv Positive half-waves (g) Threshold 5 µv Positive half-waves (h) Threshold 37.5 µv Positive half-waves 6 6 Negative half-waves (d) Negative half-waves Amplitude (µv) (i) 6 Negative half-waves Amplitude (µv) (j) 6 Negative half-waves Amplitude (µv) Amplitude (µv) (e) 5 (f) (k) (l) 5 5 *polarity *polarity 5 *polarity 5 *polarity Figure. Effect of sleep deprivation on the number of half-waves (a d) and half-wave amplitude (g j) as a function of frequency in slow wave sleep of the first non-rapid eye movement (NREM) sleep episode analysed separately for positive and negative half-waves (black line: baseline, grey line: recovery sleep). (a,c,g,i) The 5 lv threshold, (b,d,h,j) the 37.5 lv threshold. Mean data ± SEM (n = 8) are illustrated. Significant (e,f,k,l) of linear mixed-model analysis of variance with factor condition (recovery versus baseline) and factor polarity (positive versus negative half-wave) and their interaction are depicted. Significant condition effects and condition polarity interactions were evaluated post hoc with paired t-tests; d P <.5. Ó 9 European Sleep Research Society, J. Sleep Res., 9, 8 37

6 Slow oscillations and increased sleep pressure 33 Sleep deprivation resulted in increased amplitudes of positive and negative half-waves over almost the entire frequency range for the low detection threshold (Fig. g,i) and mainly in the..9 Hz range for the high detection threshold (Fig. h,j). Interestingly, negative half-waves displayed higher amplitude than the positive ones between.9 and. Hz (5 lv; factor polarity) and between. and.7 Hz (37.5 lv). Slope of half-waves The initial and final maximal slope (first- and second-segment slope separated by maximum or minimum) was studied for positive and negative half-waves separately. The slope was steeper during recovery sleep for initial and final, and for positive and negative half-waves. Comparing the distributions of the slopes in baseline and recovery sleep in each individual separately revealed significantly steeper slopes in each individual after sleep deprivation (P <.; Kolmogorov Smirnov Initial slope, positive half-waves 5 Slope (µv s ) Final slope, positive half-waves 5 Slope (µv s ) (e).5.5 Slope (µv s ) Slope (µv s ) Initial slope, negative half-waves (d) Final slope, negative half-waves (f).5.5 Figure 5. Effect of sleep deprivation on maximum slope of slow waves (5 lv threshold) in slow wave sleep of the first non-rapid eye movement (NREM) sleep episode of baseline (black) and recovery sleep (grey) after h of sustained wakefulness. The maximum slope was calculated as the maximum value of the signal derivative; initial and final slope refer to the slope calculated in the first or second segment of the half-wave, respectively, which are separated by the maximum absolute value. Mean data ± SEM (n = 8) are illustrated. Significant (e,f) of linear mixed-model analysis of variance with factor condition (recovery versus baseline) are depicted. Factor polarity (positive versus negative half-waves) and interaction were not significant. Significant condition effects were evaluated post hoc with t-tests; d P <.5. test). In order to assess whether this result is specific for waves with a high (>37.5 lv) or low (<37.5 lv) amplitude, we analysed these waves separately. In both cases, slopes in each individual were steeper after sleep deprivation. Moreover, investigating maximal slope as a function of the frequency of the corresponding half-waves revealed an increase after sleep deprivation over almost the entire frequency range analysed (Fig. 5) for both positive and negative half-waves and initial and final slopes. A mixed-model anova with factors condition (recovery, baseline), type (initial, final slope) and polarity (positive, negative half-wave) revealed significant effects of the factors polarity and condition over the entire frequency range (.5 Hz). The interaction effects were not significant. Similar results were obtained with the mean slope (data not shown). Relationship between slope and amplitude of half-waves In general, the slope of half-waves is dependent upon the period (frequency) and amplitude of the wave. For example, the shorter the period (higher frequency) or the higher the amplitude, the steeper the slope and vice versa. Maximal slope is, to some degree, less dependent on the two parameters. Because both amplitude and maximal slope of the half-waves varied in parallel as a function of frequency and increased after sleep deprivation over a broad frequency range (Figs and 5), we investigated the interdependence of the two measures (detection threshold 5 lv; see Methods). Correlations between slope and amplitude were determined in steps of.-hz in the.5 Hz range. The correlations were independent of condition; in other words, they were not altered by sleep deprivation. Thus, data of baseline and recovery sleep were averaged. In general, slope and amplitude were correlated highly (Fig. 6), explaining 9% of the variance for the maximal slope and 95% for the mean slope. A mixedmodel anova with factors type (initial, final slope) and polarity (positive, negative half-wave) was performed for each frequency bin. Negative half-waves displayed higher correlation values than the positive ones over almost the entire frequency range (Fig. 6). Interestingly, the correlations were highest above Hz. Mixed-model anova (factors: polarity and frequency) revealed significant effects of both factors and their interaction. These results highlight that the correlation between slope and amplitude is both frequency- and polarity-dependent. Similar results were obtained with the mean slope (data not shown). Multi-peak waves We determined the number of half-waves with more than one peak (multi-peak waves). Sleep deprivation resulted in a decreased number of multi-peak half-waves (baseline. ± 3.7% versus recovery 9. ±.3%). Again, there was an asymmetry between positive and negative half-waves. Multi-peak waves were more abundant in positive half-waves Ó 9 European Sleep Research Society, J. Sleep Res., 9, 8 37

7 3 A. Bersagliere and P. Achermann Correlation max slope-amplitude Correlation mean slope-amplitude Correlation Initial positive Final positive Initial negative Final negative Correlation (d) Slope type.5.5 Slope type.5.5 Figure 6. Correlations between slopes [ maximal slope; mean slope] and amplitudes in the.5 Hz frequency range (. Hz bins; n = 8). Significant (c,d) of linear mixed-model analysis of variance with factor polarity (positive versus negative half-wave) and factor slope type (initial, final slope) are depicted. Interactions were not significant. (baseline: positive.9 ± 3.5% versus negative 9.8 ±.%; recovery: positive.8 ±.% versus negative 6.7 ± 3.%). A mixed-model anova with factors condition (recovery, baseline) and polarity (positive, negative half-waves) revealed a significant effect of both factors (P <.), but no significant interaction. Influence of filter settings Period amplitude analysis requires narrow band-pass filtering to detect waves reliably. Thus, we band-pass filtered the EEG in the frequency range of interest (..3 Hz; see Methods for details). We performed a sensitivity analysis in order to investigate the effect of different cut-off frequencies of the band-pass filter:.6.3 Hz;.6 5 Hz; and. 5 Hz (similar to Riedner et al., 7). Detailed results are reported in Figs S and S and Table S. The number of half-waves min ) was dependent on the cut-off frequencies used (Fig. S). When the low-frequency cut-off filter was set at.6 compared to.5 Hz, the shift towards higher frequencies after sleep deprivation was still observed for the negative half-waves, but not for the positive ones. With all four filter settings, amplitudes were increased after sleep deprivation. The correlation between slope and amplitude of the halfwaves was also dependent upon the cut-off frequencies (Fig. S). The correlation was affected mainly by the choice of the low-pass filter. The main results, however, were not dependent upon the cut-off frequency settings. DISCUSSION We investigated the effect of sleep deprivation, i.e. increased sleep pressure on slow oscillations in the sleep EEG. Slow oscillations measured at the level of the scalp EEG in humans are thought to reflect the rhythmic alternation of up- and down-states occurring at the cellular level in the neocortex (Mo lle et al., ; Steriade et al., 993a,b). Slow oscillations commonly encompass waves below Hz (Steriade et al., 993a,b). However, there is no physiological evidence to draw a sharp border at. Hz. Thus, up-states last for..8 s and down-states.3.7 s (Amzica and Steriade, 998), resulting in slow oscillations with frequencies in the range of.65.3 Hz. We therefore used the broader range, i.e. below Hz, as slow oscillations, which is in accordance with recent studies (Dang-Vu et al., 8; Massimini et al.,, 7; Mo lle et al., ; Murphy et al., 9; Riedner et al., 7; Vyazovskiy et al., 7). Our analysis revealed a peak in the EEG power density spectrum of slow wave sleep at.8 Hz (Fig. 3f; baseline) and.9 Hz (recovery), indicating that slow oscillations, on an average, have a frequency below Hz. Intracortical recordings performed in humans may help to clarify the frequency of slow oscillations (Csercsa et al., 8). Ó 9 European Sleep Research Society, J. Sleep Res., 9, 8 37

8 Slow oscillations and increased sleep pressure 35 Power spectra and period amplitude analysis Slow-wave activity, a marker of sleep homeostasis, was highly correlated with the number of large amplitude (>37.5 lv) half-waves per min. In accordance with previous studies, we found that low-frequency components were reflected in the power spectrum of slow wave sleep with a mean peak value at.8.9 Hz (Achermann and Borbe ly, 997; Amzica and Steriade, 997; Riedner et al., 7). Electroencephalogram power in the spectrum below Hz of the first NREM sleep episode did not show significant changes after sleep deprivation (i.e. with increased sleep pressure), while a significant increase was observed at frequencies above Hz. Similarly, a decline in power from NREM sleep episodes one to two, i.e. comparing different levels of sleep pressure, was seen only at frequencies higher than Hz (Achermann and Borbély, 997). Campbell et al. (6) hypothesized that slow oscillations do not increase after sleep deprivation because of saturation effects. According to their hypothesis, at the end of a normal day slow oscillations are at a maximal level, and therefore power below Hz cannot increase further with prolonged wakefulness. In contrast to their interpretation, our analysis indicates that slow oscillations are affected by sleep deprivation in a more complex manner. The number of waves per min decreased at low frequencies (< Hz) and increased at higher frequencies, resulting in a higher average frequency of the waves under increased sleep pressure. These findings are consistent with the observed decrease of the average frequency of waves in the.5 3 Hz band in the course of a normal sleep episode (Church et al., 975). In other words, a decline in sleep pressure resulted in waves with a lower frequency. Similarly, in rats, spontaneously occurring high amplitude slow waves appeared at shorter time intervals (i.e. with a higher frequency) under high sleep pressure during early sleep compared to later, lighter sleep (Vyazovskiy et al., 9). We found no difference in spectral power between baseline and recovery sleep at frequencies below Hz. The decrease in the number of slow half-waves below Hz was counterbalanced by the increase in amplitude and resulted in no observable differences. We hypothesize that the higher frequency of oscillatory activity observed at the level of the EEG reflects a faster alternation between up- and down-states at the cellular level under increased sleep pressure. Taking into account the limitation of comparing different species, our observations fit with data in intracellular recordings of anaesthetized cats, where tonic stimulation of a slow-oscillating cell, to some degree mimicking sleep deprivation, caused a fastening of the sequence of up- and down-states after ending the stimulation (Ôrebound periodõ; F. Amzica, personal communication). Positive and negative half-waves In previous studies, the analysis was restricted to the negative half-waves (Riedner et al., 7) or to a specific morphology of the waves (Massimini et al., ). The positive and negative deflections of low-frequency oscillations in the EEG, however, seem to reflect distinct patterns of the underling neuronal activity. Combined analysis of surface EEG and intracellular recordings in animals has shown a distinct association between the EEG and the hyperpolarizing and depolarizing phases of the slow oscillation at the cellular level (Ji and Wilson, 7; Mukovski et al., 7; Steriade et al., 993b; Vyazovskiy et al., 7). Although such association has not yet been verified in humans, some evidence exists establishing a relationship between what is recorded at the level of the scalp and at the cellular level. For example, Mo lle et al. () demonstrated in humans that spindle activity (8 5 Hz) and beta fluctuations (5 5 Hz) appeared in the EEG at a specific phase relation with the low-frequency EEG oscillations; in particular, the peak of negative half-waves was more likely to be the event triggering spindle activity, which appeared approximately ms later, during the subsequent up-state. A similar relationship was established recently between parahippocampal ripples and the phase of neocortical slow oscillations in intracranial recordings of humans (Clemens et al., 7). Thus, one might consider negative slow deflections to be related to down-states and positive slow deflections to up-states. Therefore, we analysed positive and negative half-waves separately in order to assess potential asymmetries. Positive and negative half-waves showed a different distribution in their incidence in the frequency range of.5 Hz. Negative halfwaves predominated at higher frequencies, whereas the positive ones had a peak at lower frequencies (Fig. 5). Moreover, increased sleep pressure resulted in a shift towards higher frequencies and increased amplitude for both types of half-waves. If we accept that positive and negative half-waves recorded in the scalp EEG correspond to up- and down-states at the cellular level, respectively, the fact that both positive and negative half-waves were characterized by higher frequency after sleep deprivation provides further support for our hypothesis of a faster alternation between up- and downstates under increased sleep pressure. This hypothesis is consistent with gradual shortening of the up-state of the slow oscillation and the related acceleration of the rhythm observed with deepening of sleep, as discussed in Amzica and Steriade (). The contribution of K-complexes is an important issue to be considered. They represent a salient feature of Stage sleep, but are difficult to distinguish from the slow waves occurring during slow wave sleep. They may be generated by similar physiological mechanisms (Amzica and Steriade, 997) and could be ÔforerunnersÕ of slow waves (De Gennaro et al., ). Slope of half-waves It was proposed recently that the slope of the slow oscillations could be a reliable marker of synaptic strength and sleep homeostasis, similar to the slope of evoked potentials, used traditionally in electrophysiological studies of long-term Ó 9 European Sleep Research Society, J. Sleep Res., 9, 8 37

9 36 A. Bersagliere and P. Achermann potentiation and depression (Esser et al., 7; Riedner et al., 7; Vyazovskiy et al., 7, 8). The slope of oscillations in the.5 Hz range increased under higher sleep pressure in all individuals, which is in accordance with recent reports (Esser et al., 7; Riedner et al., 7; Vyazovskiy et al., 7). In addition, we investigated the slope as a function of frequency, as it is related to the period of half-waves. Our analysis revealed steeper slopes after sleep deprivation in the entire frequency range between.5 and Hz. Riedner et al. (7) claimed that maximal slope is independent of the amplitude and frequency of the half-waves. Our analysis, however, revealed a high correlation between the two measures (Fig. 6). Surprisingly, at frequencies below Hz the correlation was lower, pointing to a weaker interdependence of amplitude and slope of slow oscillations below Hz. Furthermore, the difference between positive and negative half-waves was also unexpected. Vyazovskiy et al. (7) showed by means of computer simulation that the lowfrequency peak in the power spectrum can be shifted by varying the slope of the waves. Although our analysis revealed a frequency redistribution of the half-waves, the two results are complementary. Multi-peak waves Increased sleep pressure led to a decreased number of multipeak waves similar to Riedner et al. (7), who compared the first and second part of a baseline sleep episode. We propose that increased sleep pressure may result in higher synchronization of cortical regions leading to a reduction in multi-peak waves. This hypothesis is supported by a large-scale computer model simulation of the thalamocortical system of cats (Esser et al., 7). Interestingly, positive half-waves showed a higher number of multi-peak waves than the negative ones, a further asymmetry of low-frequency oscillations in the human sleep EEG. This may be a further indication that positive half-waves reflect upstates of cortical neurones, the active phase, with neuronal activity that might be reflected in the EEG as oscillations superimposed on positive half-waves resulting in multi-peak waves. Effect of filter settings We performed a sensitivity analysis aimed to investigate the effect of filter settings on the results of period amplitude analysis (see Supporting Information). The band-pass filters applied in different studies varied considerably:.6.7 Hz (Mo lle et al., ),. Hz (Massimini et al., ),.5. Hz (Murphy et al., 9; Riedner et al., 7) and..3 Hz (present study). Our sensitivity analysis revealed that the main results are not dependent upon the cut-off frequencies. However, because filter settings have an impact on absolute values, comparing absolute values across studies should be avoided. CONCLUSIONS Slow oscillations were affected by sleep deprivation. By combining spectral and period amplitude analysis, we were able to achieve a detailed understanding of the impact of sleep deprivation on slow oscillations. Our data revealed a strong asymmetry between positive and negative half-waves of slow oscillations. We found differences in the distribution of the incidence of half-waves, more multipeak waves for positive half-waves and lower correlations between amplitude and slopes of positive half-waves. This indicates that positive and negative half-waves of the sleep EEG reflect distinct patterns at the neuronal level of the cortex. Despite the fact that power below Hz did not increase after sleep deprivation, slow oscillations showed an increase in frequency and amplitude. Therefore, it can be concluded that they are regulated homeostatically. Furthermore, the validity of the slow-wave activity (.75.5 Hz) as a marker of sleep homeostasis is not questioned by our results because the observed changes of slow oscillations in response to sleep deprivation occurred within this frequency range. Our finding of an increased frequency of slow oscillations after sleep deprivation supports the idea that the alternation between up- and down-states occurs faster under higher sleep pressure, resulting in higher frequencies of the detected events. However, further studies at the cellular level or in intracranial recordings are needed to elucidate this issue. DISCLOSURE The authors declare no conflict of interest. ACKNOWLEDGEMENTS We thank F. Amzica, A. Borbe ly, A. Jeroncic and R. Du rr for stimulating discussions and A. Borbe ly, L. Tarokh and I. Tobler for comments on the manuscript. The study was supported by SNSF grant 3-67 and EU LSHM- CT REFERENCES Achermann, P. and Borbély, A. A. 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Please note: Wiley Blackwell Publishing are not responsible for the content or functionality of any supporting material supplied by the authors. Any queries (other than missing material) should be directed to the corresponding author for the article. Ó 9 European Sleep Research Society, J. Sleep Res., 9, 8 37