Sleep Homeostasis and Cortical Synchronization: III. A High-Density EEG Study of Sleep Slow Waves in Humans

Abstract

Study Objectives:

The mechanisms responsible for the homeostatic decrease of slow-wave activity (SWA, defined in this study as electroencephalogram [EEG] power between 0.5 and 4.0 Hz) during sleep are unknown. In agreement with a recent hypothesis, in the first of 3 companion papers, large-scale computer simulations of the sleeping thalamocortical system showed that a decrease in cortical synaptic strength is sufficient to account for the decline in SWA. In the model, the reduction in SWA was accompanied by decreased incidence of high-amplitude slow waves, decreased wave slopes, and increased number of waves with multiple peaks. In a second companion paper in the rat, local field potential recordings during early and late sleep confirmed the predictions of the model.⁴ Here, we investigated the model's predictions in humans by using all-night high-density (hd)-EEG recordings to explore slow-wave parameters over the entire cortical mantle.

Design:

256-channel EEG recordings in humans over the course of an entire night's sleep.

Setting:

Sound-attenuated sleep research room

Patients or Participants:

Seven healthy male subjects

Interventions:

N/A.

Measurements and Results:

During late sleep (non-rapid eye movement [NREM] episodes 3 and 4, toward morning), when compared with early sleep (NREM sleep episodes 1 and 2, at the beginning of the night), the analysis revealed (1) reduced SWA, (2) fewer large-amplitude slow waves, (3) decreased wave slopes, (4) more frequent multipeak waves. The decrease in slope between early and late sleep was present even when waves were directly matched by wave amplitude and slow-wave power in the background EEG. Finally, hd-EEG showed that multipeak waves have multiple cortical origins.

Conclusions:

In the human EEG, the decline of SWA during sleep is accompanied by changes in slow-wave parameters that were predicted by a computer model simulating a homeostatic reduction of cortical synaptic strength.

Citation:

Riedner BA; Vyazovskiy VV; Huber R; Massimini M; Esser S; Murphy M; Tononi G. Sleep homeostasis and cortical synchronization: III. A high-density EEG study of sleep slow waves in humans. SLEEP 2007;30(12):1643-1657.

SLOW WAVES ARE THE MOST OBVIOUS AND RECOGNIZABLE FEATURE OF THE HUMAN SLEEP EEG. IN ADDITION TO BEING INDICATIVE OF SLEEP DEPTH,⁵ SLOW waves are intimately related to sleep regulation: it is well known that SWA (EEG power between 0.5 and 4.0 Hz), which reflects the abundance of low-frequency waves in the EEG, increases as a function of prior waking and declines throughout the course of sleep.^6–8 Although the regulation of SWA is suggestive of a restorative function of sleep, the mechanisms responsible for SWA homeostasis remain unclear.

It was recently suggested that the level of SWA during sleep may be a function of the strength of cortical synapses due to the influence of synaptic efficacy on network synchronization.^{1, 2} According to the hypothesis, at the beginning of sleep, synaptic strength would be high due to learning processes occurring during wakefulness, whereas, by the end of sleep, synaptic strength would have decreased through a sleep-dependent process of synaptic downscaling. The hypothesized relationship between synaptic strength and the level of SWA was investigated in a companion paper using a large-scale model of sleep in the thalamocortical system.³ The simulation showed that decreasing synaptic strength among cortical neurons led to a decrease in sleep SWA.³ Intriguingly, synaptic strength reduction also resulted in characteristic changes to several slow-wave parameters, including a decrease in the number of high-amplitude slow waves, a decrease in the slope of slow waves, and more frequent waves with multiple peaks.

In a second companion paper, we tested the model's predictions by employing local field potential (LFP) recordings in the rat to compare periods of early and late sleep.⁴ We found that the decline in SWA in the LFP was associated with the changes in slow-wave parameters predicted by the model. Furthermore, recovery after sleep deprivation resulted in an increased number of high-amplitude slow waves, steeper slopes, and fewer multipeak waves, suggesting that these observed changes in slow-wave parameters are a result of homeostatic sleep regulation and not circadian time.

In the present paper, we tested the model's predictions in humans. We used all-night high-density EEG (hd-EEG) recordings to compare non-rapid eye movement (NREM) sleep slow waves at the beginning of the night, when the pressure to sleep is highest, to NREM sleep slow waves toward morning, when sleep pressure has largely dissipated. We found that, as predicted by computer simulations, and in line with rat LFP recordings, the homeostatic decline of SWA during sleep is coupled with a decreased incidence of high-amplitude slow waves, a decreased slope of slow waves, and an increased number of multipeak waves. Moreover, we found that individual peaks of the multipeak waves characteristic of late sleep have distinct cortical origins.

METHODS

Subjects and Recordings

Hd-EEG (Geodesic, 256 electrodes) was recorded across an entire night of sleep in 7 healthy male subjects (mean age 28.3 ± 1.5 years, range 24–35). Written informed consent was obtained from each subject following a screening for medical and psychiatric illness. EEG recordings were sampled at 500 Hz. Of the channels overlaying the scalp, noisy ones were rejected based on visual inspection (leaving on average 180 channels per subject). The EEG was visually scored for sleep stages (20-second epochs) based on standard criteria.⁹ SWA was computed based on the fast Fourier transform (Hanning window, averages of five 4-second epochs) of the 0.5- to 40-Hz filtered signal downsampled to 128 Hz and average referenced. Artifacts were rejected on a 4-second basis after visual inspection and if the power exceeded a threshold based on a mean power value in the 0.75- to 4.5-Hz and 20- to 40-Hz bands.¹⁰ NREM sleep episodes were defined according to the modified criteria¹¹ of Feinberg and Floyd.¹²

EEG Wave Detection and Analysis

Wave Detection

After low-pass filtering at 30 Hz, the signal for each channel was rereferenced to the average of the 2 earlobes and band-pass filtered (0.5–4.0 Hz, stopband 0.1 and 10 Hz) using a Chebyshev Type II filter (MATLAB, The Math Works Inc, Natick, MA). The filter parameters were optimized visually on the EEG signal to achieve minimal wave shape and amplitude distortion while allowing the least high-frequency contamination. For each channel, individual half-waves were detected on a 100-Hz signal that had been decimated using the MATLAB function decimate, which uses an eighth-order low-pass Chebyshev Type I filter in the forward and reverse direction to smooth the signal before resampling. Half-waves were defined as negative deflections between 2 zero crossings.¹³ The zero crossing detection was chosen for the analysis due to the high degree of variability in the positive signal deflections compared to the stability of the negative deflections. However, similar results were obtained using peak-to-peak measures. Only waves whose consecutive zero crossings were separated by 0.25 to 1.0 seconds (within an artifact-free NREM epoch) were considered slow waves. The 0.25-second lower limit was selected based on (1) the Rechtschaffen and Kales⁹ criterion for slow waves (2 Hz) and (2) previous work demonstrating that measures of wave incidence and power spectral analysis closely match only for this lower SWA band.^14,15 Negative and positive peaks were determined based on the zero crossings of the signal derivative after applying a 50-millisecond moving average filter. The detection procedures described above are similar in most respects to those employed in previous work on period-amplitude analysis.^14–16

Analysis of Wave Parameters

Negative peak amplitude, average and maximal slopes, and the number of negative peaks between zero crossings were determined for each wave segment. Average slope was defined as the amplitude of the most negative peak divided by the time from the previous zero crossing (first-segment average slope) or the time until the next zero crossing (second-segment average slope). Maximal slopes were defined as the maximum of the signal derivative (after applying a 50-millisecond moving average) following the negative zero crossing (first-segment slope) but before the most negative peak, or subsequent to the most negative peak (second-segment slope) but prior to the positive-going zero crossing. Multipeak waves were defined as waves with more than 1 negative peak between zero crossings. When the number of peaks in multipeak waves was normalized to the corresponding wave duration, there were, on average, 5.14 ± 0.06 peaks per 1 second, indicating that the peaks were unlikely to have resulted from spindles. Multipeak waves were included in all analyses.

Wave Origin and Propagation

To investigate how slow waves travel, we determined, for each channel in which the slow wave was detected, the negative peaks that occurred within ± 200 milliseconds of the peaks in an arbitrarily chosen reference channel (Fp1). The detection window was determined based on earlier results in which the maximum lag between negative peaks was 360 milliseconds.¹⁷ The timing of peaks for each channel involved in an individual wave was used to create a delay map relative to the first peak interpolated on a low-resolution (100×100) grid. To determine the origin and propagation of the waves, component streamlines tangential to the instantaneous velocity direction in the 2-dimensional vector field of delays were determined for each involved electrode. The streamlines for an individual electrode progress in both directions along the vector field (up and down the gradient) until the gradient of delays is broken (i.e., reverses polarity or no longer exists). The beginning of the longest streamline was considered the origin of the wave if it occurred within 20 milliseconds of the earliest peak, and tracing this main streamline gives an indication of the wave propagation. For multipeak waves, the streamline analysis was computed independently for each peak in the reference channel, and it was confirmed that the lag detections did not overlap.

Source Localization

Source localization was performed on individual slow waves using a realistic head model derived from each subject's magnetic resonance image. Electrode positions were digitized and coregistered to the individual's scan by means of an infrared positioning system (Nexstim Ltd., Helsinki, Finland). Current density was then estimated on the cortical surface using the minimum norm least squares (L2) method.^18,19 Modified scripts from the free release Statistical Parametric Mapping Toolbox for MATLAB (version 5) was used for all source analysis.

Statistics

Effects of sleep on SWA and slow-wave parameters were assessed using statistical nonparametric permutation testing (SnPM). These tests have weak distributional assumptions and therefore are particularly appropriate for a small sample size where the normality of the data is difficult to assess.²⁰ Furthermore, such tests can be easily modified to account for multiple comparisons when appropriate.²¹ Briefly, the comparison effect (e.g., frequency bin, percentiles, or electrode) for each subject are randomly shuffled between conditions (e.g., early and late sleep). An effect t-value is computed for each possible permutation, and the maximal t-value for all permutations is used to create a t-value threshold (single threshold corrected). T-values were computed using 2-tailed paired t-tests, and the threshold value was taken as the 95^th percentile. No statistical correction was applied after the procedures equating waves by amplitude and power (Figure 4) because the a priori hypotheses were concerned with the presence of each difference and not with the relationship of individual parameters to each other. Linear regression analysis was used to examine the relationship between SWA (average for the first 4 NREM episodes) and several slow-wave parameters. MATLAB was used for all statistical analysis.

Figure 4.

Fp1 waves between early and late sleep were equated based on the best match of the corresponding 4-s epoch 0.5- to 2.0-Hz electroencephalogram (EEG) power and wave amplitude. A: Representative 4-s epochs with the direct wave comparison between early and late sleep highlighted on the band-pass filtered signal. B-E: Boxplot data for each parameter show average differences from the mean between early and late sleep expressed as a percentage ([late-early]*200/[late+early]) for each subject (n = 7; see text). Average slope measurements are in white, maximum slope measurements are in black. Note that both EEG power and amplitude are equated for all comparisons except in E, where EEG power was not equated. Triangles indicate significance (P < 0.05) and the direction of change based on individual nonparametric permutation tests for each parameter (uncorrected). NREM refers to non-rapid eye movement; SWS, slow-wave sleep.

RESULTS

In order to examine the effect of sleep pressure on slow-wave parameters, we compared NREM sleep at the beginning of the night (early sleep, NREM episodes 1 and 2) to sleep toward the morning (late sleep, NREM episodes 3 and 4). Subjects wore an hd-EEG net with 256 electrodes for the entire duration of the night without reporting complaints about sleep quality or comfort. Indeed, the percentage of time spent in each sleep stage was typical of normal human sleep (Table 1), and all subjects had at least 4 sleep cycles. Table 2 shows the breakdown of several sleep measures by NREM episode. There were no significant difference between the percentage of waking epochs occurring during the first 2 NREM episodes compared with the last 2 episodes (6.1% ± 2.6% and 7.0% ± 1.9%, respectively, P = 0.77 nonparametric permutation test).

Table 1.

Sleep Measures for Entire Night

Total time in bed, min	434.52 ± 16.4
Total sleep time, min	381.38 ± 17.0
Sleep efficiency, %	87.74 ± 2.1
Sleep latency, min	7.33 ± 1.6
WASO, %	9.24 ± 2.3
Stage 1, %	8.11 ± 1.3
Stage 2, %	52.35 ± 2.9
SWS, %	16.69 ± 2.7
NREM, %	69.03 ± 2.2
REM, %	22.86 ± 2.6
Movement time, %	2.53 ± 0.3

Data are expressed as mean ± SEM (n=7). Percentage values are expressed per total sleep time. Sleep efficiency corresponds to total sleep time per time in bed. Sleep latency is to Stage 2. WASO refers to waking after sleep onset; SWS, slow-wave sleep; NREM, non-rapid eye movement; REM, rapid eye movement.

Table 2.

Sleep Measures by NREM Episode

NREM episode	1	2	3	4
Duration, min	71.62 ± 6.7	77.24 ± 3.4	69.92 ± 5.5	56.29 ± 4.8
Sleep efficiency, %	88.81 ± 3.8	91.51 ± 1.5	88.40 ± 2.6	91.74 ± 2.9
Wake, %	7.90 ± 4.1	3.55 ± 1.3	8.82 ± 2.2	4.86 ± 2.7
Stage, 2 %	47.66 ± 3.7	55.98 ± 6.2	73.08 ± 3.0	73.90 ± 6.7
SWS, %	35.65 ± 6.2	30.33 ± 6.0	7.73 ± 2.1	11.38 ± 7.1

Data are expressed as mean ± SEM (n=7). Percentage values are expressed per length of non-rapid eye movement (NREM) episode. Sleep efficiency corresponds to total sleep time per episode duration. SWS refers to slow-wave sleep.

As expected, spectral power analysis of the EEG signal in NREM sleep revealed the well-known homeostatic decline of SWA from early (NREM episodes 1 and 2) to late (NREM episodes 3 and 4) sleep, as well as a decline in adjacent bins up to 8 Hz (Figure 1 A,B). The average SWA (n = 7) mainly declined from the first and second NREM episodes (139% ± 9.34% and 125% ± 9.22% of mean across 4 NREM episodes, respectively), to the third and fourth episode (47% ± 4.59% and 53% ± 11.3%, respectively). Therefore, a significant decline was evident only when comparing the second and third NREM episodes (P = 0.0156, uncorrected nonparametric permutation test). The fact that the SWA decline between episodes was not exponential, but declined sharply when comparing early with late sleep, can be attributed to subject variability in a limited sample, and possibly to a first-night effect.

Figure 1.

A: Average power spectra in non-rapid eye movement (NREM) sleep during episodes 1 and 2 (early sleep, black) and episodes 3 and 4 (late sleep, gray) for Fp1 channel (mean ± SEM, n = 7). Triangles indicate significant bins based on SnPM (P < 0.05, single threshold corrected). B: Slow-wave activity (SWA; 0.5–4.0 Hz) profile in NREM sleep during the night for an individual subject (average 1-min values, % of the mean of 4 NREM episodes) rapid eye movement (REM) episodes are indicated by hatched areas. Early and late sleep (including REM episodes) are color-coded in black and gray, respectively. EEG refers to electroencephalogram.

Late Sleep is Associated with a Decreased Incidence of High-Amplitude Slow Waves

Slow waves were detected as negative deflections between consecutive zero crossings separated by 0.25 to 1 seconds (see Methods and Figure 2A). Based on the detections, changes in individual slow-wave parameters were examined between early and late sleep. For simplicity, we present, in detail, the results for a representative frontal channel (Fp1), but, as it will be discussed later, the multichannel analysis revealed similar findings across the entire cortical mantle (see Figure 6).

Figure 2.

A, top traces: representative 16-s electroencephalogram traces from the Fp1 channel during early and late sleep; bottom traces: corresponding band-pass filtered signal (0.5–4.0 Hz) with wave detections highlighted. Right panel: representative slow wave. The first (1) and second (2) segments, the negative peak (**), and consecutive zero crossings (*) are indicated. B: Distribution of the amplitude of slow waves during early and late sleep for Fp1. The number of waves was computed for groups of waves with logarithmically increasing amplitude. Mean values (± SEM, n = 7) are plotted as a percentage of the total number of waves within early (non-rapid eye movement [NREM] episodes 1 and 2, black) and late (NREM episodes 3 and 4, gray) sleep, respectively. Triangles indicate significance and direction of the nonparametric permutation test (P < 0.05, single threshold corrected). The inset shows mean incidence (number of waves/min of NREM sleep, ± SEM n = 7). C: Slow-wave incidence during early and late sleep for the Fp1 derivation. Slow waves were subdivided into 5 percentiles according to the amplitude of the negative peak. Boxplots show incidence values for all subjects. Notch indicates median value, the box represents the interquartile range, and whiskers extend to 1.5 times the interquartile range. Outliers (> 1.5 times the interquartile range) are plotted as circles. Triangles indicate significance and direction of the nonparametric permutation test (P < 0.05, single threshold corrected).

Figure 6.

Topographic distributions of slow-wave parameter changes during early and late sleep. Values were plotted at the corresponding position on the planar projection of the scalp surface and interpolated (biharmonic spline) between electrodes. Maximal and minimal values (± SEM, n = 7) are shown on the upper left corner of each topographic plot (the scale for color coding is on the right of E, row 1; n.s. refers to not significant). The units for each plot are indicated in the lower left corner. A: Average for early sleep (non-rapid eye movement [NREM] episodes 1 and 2). The channel used for single-channel analysis (Fp1) is indicated with a black dot in the top row. B: Average for late sleep (NREM episodes 3 and 4). Channels that are common to all subjects (n = 167) are indicated with black dots. C: Difference between early and late sleep shown as a percentage of the mean ([late-early]*200/[late+early]). The channels used for the regional comparison shown in E are indicated by colored dots. D: T-values for the comparisons between early and late sleep (2-tailed paired t-test). The minimum t-value for each map (indicated in black) is the criterion for significance (based on single threshold SnPM) at each channel. Gray is indicated only for nonsignificant channels. E: Regional comparison boxplots. The average percentage change for 2 representative regional channels (F=Fp1 and Fp2, black boxes; C=C3 and C4, gray boxes; O=O1 and O2, white boxes) are displayed. Asterisks indicate a significant difference based on nonparametric permutation tests between regions (P < 0.05). Black dots are outliers. Top row: EEG power density for slow-wave activity (0.5–4 Hz). Second row: Slow-wave incidence for high-amplitude waves (80^th-100^th percentile). Third and fourth rows: first- and second-segment average slow-wave slopes of all waves. Fifth and sixth rows: first- and second-segment maximum slow-wave slopes of all waves. Seventh row: Average number of peaks for all waves. Note that the higher average number of peaks is located posteriorly (A,B), but the relative change is more pronounced frontally. Note also that the direction of change between early and late sleep is opposite to that of all other parameters. For simplicity, however, the topographic distribution of t-values for the number of peaks comparison is shown as opposite to its actual sign.

The total number of slow waves was only marginally lower during late sleep compared to early sleep (35 ± 3.5 vs 32 ± 3.2 waves/min of NREM sleep, P = 0.0313 nonparametric permutation test, Figure 2B inset). However, a marked difference was observed in the proportion of high- and low-amplitude slow waves (Figure 2B). Slow waves with higher amplitude were more frequent during early sleep, compared with later, when sleep pressure had dissipated. Conversely, low-amplitude slow waves were more frequent during later NREM episodes.

Changes in slow-wave incidence were subsequently examined by sorting slow waves into 5 equally subdivided percentiles based on the amplitude of the negative peak. Percentiles were determined by pooling all slow waves for an individual subject and channel for the first 4 NREM sleep episodes. The incidence of slow waves was then computed within each percentile for each channel. When slow waves were sorted into amplitude percentiles, all but the intermediate amplitude percentiles were significantly different between the 2 conditions (Figure 2C, P = 0.0234 0–20^th, 60–80^th, 80–100^th percentiles, SnPM single threshold corrected). It should be noted, however, that high-amplitude slow waves were not entirely eliminated during late sleep (see individual examples in Figure 2A, and the histogram in Figure 2B). Also, for late sleep, the highest-amplitude waves were just as large as the largest waves in early sleep (only 0.05% of slow waves during early sleep exceeded the highest-amplitude wave during late sleep).

Late Sleep is Associated with Decreased Slow-Wave Slopes

Given that the distribution of slow-wave incidence during early and late sleep was dependent on amplitude as reported above, the change in slow-wave slopes was also examined by sorting waves into 5 equal amplitude ranges. When the slope was examined for waves of similar amplitude, the average first-segment slope decreased significantly for all but the largest amplitude waves between early and late sleep (Figure 3A left panel; P < 0.0391 for all percentiles except the 80^th–100^th; SnPM single threshold corrected). The second-segment average slope also decreased, but the change was significant for only 2 of the 5 percentiles (Figure 3A right panel, 20^th–40^th and 60^th −80^th percentiles P = 0.0156, a trend for all but the highest-amplitude waves to have less steep slopes was also evident; 0–20^th and 40^th −60^th percentiles P = 0.0703; 80^th −100^th percentile P = 0.6172; SnPM single threshold corrected).

Figure 3.

Slope changes between early and late sleep for Fp1. Slow waves were subdivided into 5 equal percentiles according to the amplitude of the negative peak. Boxplots show differences from the mean between early and late sleep expressed as a percentage ([late-early]*200/[late+early]) for each subject (n = 7). Notch indicates median value, the box represents the interquartile range, and whiskers extend to 1.5 times the interquartile range. Outliers (> 1.5 times the interquartile range) are plotted as circles. Triangles indicate significance and direction of the nonparametric permutation test (P < 0.05, single threshold corrected).

We then considered the maximum slopes of both the first and second segments of slow waves, a measure not directly dependent on amplitude or period. The maximum slope measurement was significant for all but the highest amplitude waves for both the first and second segments (Figure 3B, P ≤ 0.0313; SnPM single threshold corrected). The median decline for the first 4 amplitude percentile ranges across all slope measurements was approximately 19%. In general, the slopes of the first segment of slow waves differed significantly from that of the second segment (Supplementary Figure 1). The difference between slopes of the segments did not change from early to late sleep (P ≥ 0.14), and, therefore, slopes were averaged across this condition for this analysis. As amplitude increased (across percentiles), the steepness of the first-segment slope increased relative to the second-segment slope. For maximum slope, the first-segment slope was significantly steeper than the second segment across all amplitude percentage ranges (P = 0.0156 for all amplitude percentage ranges; SnPM single threshold corrected) but was maximally different for the highest-amplitude waves (54.0% ± 7.3% higher than the mean, 80^th −100^th percentile).

Slow-Wave Slopes are Steeper During Early Sleep than During Late Sleep Even for Epochs Equated for SWA and Wave Amplitude

Although early sleep was associated, on average, with a high proportion of high-amplitude slow waves, and late sleep with a high proportion of low-amplitude slow waves, we could identify individual early sleep epochs with few or no large-amplitude waves, as well as late sleep epochs with occasional high-amplitude waves. Typically, such epochs were nearly indistinguishable and could not be assigned correctly to early or late sleep conditions based on visual inspection (Figure 4A). Moreover, when we examined them in the frequency domain, we found that such visually indistinguishable epochs also had similar values of SWA.

We therefore asked whether the slope of the slow waves would reflect sleep pressure even when SWA values and wave amplitude were comparable. To investigate this possibility, we employed 2 complementary strategies.

First, we equated waves in early and late sleep based on their negative peak amplitude and power in the 0.5- to 2-Hz range (fast Fourier transform, 4-second Hanning window) of the band-pass filtered ear-referenced signal. The 2-Hz upper limit, which is used in standard visual scoring,⁹ was chosen to ensure that matched epochs would be as visually similar as possible. Specifically, for each NREM slow wave that occurred early in sleep and its corresponding 4-second epoch, we found the best matched epoch during late sleep that also contained a wave of similar amplitude (best match difference less than 5% of the mean, Figure 4A). Based on all the individual wave comparisons (average 2607 ± 327 comparisons, see Table 3), we created an average difference of the slopes for each subject. As shown in Figure 4B, after equating epochs in this manner (power difference 0.03%, amplitude difference −0.01%), slopes decreased on average by approximately 4% (Figure 4B, range −1.4% to 12.5%), and the difference in slope between early and late sleep were significant (P ≤ 0.0234; uncorrected nonparametric permutation tests).

Table 3.

Wave-Comparison Values

	NREM episodes: 1–2 v 3–4	SWS episodes: 1 v 2	NREM episode 1 1st 30% v last 30%	NREM episode 1: 1st 30% v 4: last 30%
Comparisons, no.	2607 ± 327	504 ± 146	159 ± 44	481 ± 62
Stage 2 only, %	59.7 ± 7.6	-	65.2 ± 10.6	79.5 ± 10.0
Stage 2/3, %	21.0 ± 3.2	-	22.0 ± 5.9	14.8 ± 6.8
Stage 3 only, %	11.4 ± 2.8	55.6 ± 9.7	9.1 ± 4.7	4.8 ± 3.6
Stage 3/4, %	5.1 ± 2.4	32.9 ± 6.0	3.0 ± 2.9	0.9 ± 0.9
Stage 4 only, %	2.9 ± 2.8	11.5 ± 4.3	0.7 ± 0.7	0 ± 0
Mean 0.5–2 Hz power, μV2/.25 Hz	386.2 ± 76.6	925.6 ± 102.3	254.0 ± 67.4	234.6 ± 46.2
Mean amplitude, μV	42.5 ± 4.3	71.7 ± 4.6	36.0 ± 5.5	31.0 ± 3.1
Mean average 1st slope	214 ± 21.9	364.5 ± 24.6	184.7 ± 26.6	170.4 ± 15.5
Mean maximum 1st slope	427.2 ± 37.4	687.5 ± 41.3	383.5 ± 48.1	346.8 ± 29.9
Mean average 2nd slope	206.4 ± 21.9	324.6 ± 25.9	190 ± 25.3	166.9 ± 15.5
Mean maximum 2nd slope	366.3 ± 32.1	542.6 ± 34.7	346.6 ± 44.2	309.3 ± 27.9

Data are expressed as mean ± SEM (n=7) for each of the 4 wave-comparison procedures. Percentage values are given as percentage of total number of comparisons for each subject. Note that sleep scoring was done on 20-s epochs, but waves were matched based on the corresponding 4-s epoch electroencephalogram power: for this reason some comparisons between early and late sleep differed in their sleep scoring and are labeled accordingly (e.g. Stage 2/3). Mean parameter values correspond to 0% in Figure 4B–E. NREM refers to non-rapid eye movement; SWS, slow-wave sleep.

To reduce epoch heterogeneity and evaluate sensitivity to changes during the first part of the night, we also equated slow waves occurring during slow-wave sleep only (Stages 3 and 4) when comparing NREM episode 1 with NREM episode 2 (504 ± 146 comparisons). The maximum first-segment slope and the average second-segment slope were significantly lower during the second sleep episode (Figure 4C, P = 0.0391 and P = 0.0156 respectively; uncorrected nonparametric permutation tests). Although the changes were not significant, 5 of 7 subjects had a decreased average first-segment slope and 6 of 7 subjects had a decreased maximum second-segment slope during the second sleep episode.

To evaluate whether slopes would be sensitive to changes within a NREM episode, we subdivided the first NREM episode into 10 percentiles based on the length of the episode as it has previously been done to investigate the within-episode time course.²² Again, we equated slow waves to compare the first 3 percentiles, presumably as the subjects transitioned to deeper sleep, with the last 3 percentiles, as they transitioned into the first REM episode. The average slopes of both the first and the second segments were significantly decreased (Figure 4D, P = 0.0469 and P = 0.0234 respectively; uncorrected nonparametric permutation tests). For the maximum slope measurement, first-segment slopes decreased in 5 of 7 subjects, and second-segment slopes decreased in 6 of 7 subjects, but the results were not significant.

Finally, we again used the first 3 percentiles of the first NREM episode, this time compared with the middle 3 percentiles of the fourth NREM episode, likely reflecting the deepest part of that episode. Here we found that all slopes decreased significantly (data not shown, P ≤ 0.0313). Remarkably, if we equated waves only by the best match in amplitude, removing the power-difference criteria, we found that both average and maximum slopes of the second segment still decreased (Figure 4E, P = 0.0156 for both slope measurements), whereas the difference in power for the 0.5- to 2-Hz range increased significantly (P = 0.0469). Four of 7 subjects had decreased average slope for the first segment, and 5 of 7 had a decrease in maximum first-segment slope.

Late Sleep is Associated with an Increased Proportion of Multipeak Waves

The proportion of waves with more than 1 negative peak was significantly higher during late sleep (Supplementary Figure 2, P ≤ 0.0156, nonparametric permutation test). Specifically, it was 59.1% (± 1.9%) during early sleep, and 68.4% (± 2.1%) for late sleep. The average number of peaks for a multipeak wave was 2.51 (± 0.024) during early sleep compared with 2.58 (± 0.012) during late sleep.

SWA and Slow-Wave Parameters Change Across Time in a Highly Correlated Manner

The level of SWA across NREM sleep episodes (average SWA for each of the first 4 NREM sleep episodes) showed a significant positive linear relationship with the incidence of high-amplitude slow waves (Figure 5A, 80^th −100^th percentile, r = 0.97 P < 0.001) and a negative correlation with the proportion of multipeak slow waves (Figure 5B, r = −0.89, P < 0.001). Strong positive correlations were evident between SWA and both slope measurements (average and maximum) of the first and second segment (average slope Figure 5C, first segment, r = 0.98, P < 0.001; second segment, r = 0.97, P < 0.001; maximum slope Figure 5D, first segment, r = 0.98, P < 0.001; second segment, r = 0.97, P < 0.001).

Figure 5.

Scatter plots of average slow-wave activity (SWA) values from each of the 4 non-rapid eye movement (NREM) episodes for each subject plotted against the average parameter values for each subject and episode. Incidence values are based on waves in the 80^th–100^th percentile. All other parameter values (percentage of multipeaks, first-segment slopes, and second-segment slopes) are computed from all waves. The data are presented as percentage of the mean across the 4 NREM episodes. A linear regression line has been fit to the data and is shown in black. Significant r-values of the Pearson correlation are shown (P values < 0.001).

Changes in Slow-Wave Parameters Show a Characteristic Topographic Distribution on the Scalp

The average (n = 7) scalp distribution of SWA (signal referenced to the average of all electrodes), high-amplitude slow-wave incidence, slow-waves slopes, and number of peaks for early sleep, late sleep, and the percentage decrease from early to late sleep relative to the mean are displayed in the first 3 columns of Figure 6. During early sleep, there was a clear SWA hotspot at the frontal pole (average maximum SWA 146 μV²± 23, corresponding approximately to the 10–20 channel Fp2), whereas SWA was relatively lower at symmetric bilateral locations over temporal and parietal cortices (Figure 6A, row 1). During late sleep, the topographic pattern of SWA did not change substantially (Figure 6B, row 1), as indicated by the comparison of the normalized values between early and late sleep, which showed no significant differences (data not shown). During late sleep, however, there was a striking global decrease in SWA compared with early sleep, as revealed in Figure 6C (row 1). At all channels, the average decrease in SWA, relative to the mean, was at least 49%, with the left posterior temporal lobe showing the greatest decrease (almost 115%), whereas channels located midway between Fz and Cz (according to the 10–20 locations) showed the least relative change. As indicated in Figure 6D (row 1), a more rigorous examination of the SWA values for each derivation between early and late sleep showed that, of the 167 channels that were common to all subjects, 156 significantly decreased from early to late sleep (93% of channels, P < 0.05; SnPM single threshold corrected). In order to quantify this difference, we took the average percentage change of frontal channels Fp1 and Fp2, central channels C3 and C4, and occipital channels O1 and O2 and compared the average change between fronto-central, fronto-occipital, and centro-occipital channels. As shown in Figure 6E (row 1), we found that the percentage change in SWA in the frontal channels was significantly larger (P = 0.0156; SnPM single threshold corrected) relative to the central channels.

A topographic analysis of the incidence of high-amplitude slow waves (80^th −100^th percentile) during early sleep revealed a hotspot near Fz but diffusely extended in all directions (Figure 6A, row 2). The existence of a hotspot was explained by the fact that the incidence of high-amplitude waves was within 10% of the maximum incidence (for this percentile) for all 7 subjects at Fz and at 2 adjacent channels. However, the hotspot was relatively diffuse. Derivations extending as posterior as Pz and laterally to C3 and C4 were within 25% of the maximum for all subjects (the results were similar when considering all waves). All channels had a high-amplitude slow-wave incidence during early sleep above 6 waves per minute of NREM sleep, and most (68%) were above 9 waves per minute. As was the case for SWA, an overall decrease of high-amplitude slow-wave incidence was evident during late sleep (155 of 167 channels, P < 0.05 SnPM single threshold corrected, Figure 6D, row 2), when there were fewer than 5 waves per minute for all channels (Figure 6B, row 2). The peak incidence also shifted posteriorly, was diffuse, and was more variable between subjects. Unlike the topographic pattern during early sleep, no channel locations had an incidence within 10% of the maximum for all subjects. Also, the 23 derivations that had a high-amplitude slow-wave incidence within 25% of the maximum for the 7 subjects were lateral or posterior to Cz. Correspondingly, the decrease of high-amplitude slow-wave incidence appeared most pronounced in frontal areas, as shown clearly in the percentage-change topoplot (Figure 6C, row 2). Comparison of the incidence change from early to late sleep between areas revealed that the change in the frontal area was significantly larger, compared with the central area (Figure 6E, row 2).

During early sleep, slow-waves slopes were steepest near and slightly posterior to Fz (Figure 6A, rows 3–6). The location of this hotspot did not change markedly during late sleep or between different slope measures (Figure 6A,B, rows 3–6). All measures of slow-wave slopes, however, decreased significantly for more than 92% of derivations from early to late sleep (Figure 6D, row 3–6). Again, the decrease of slow-wave slopes was most marked frontally, and the magnitude of change in slopes frontally was significantly larger than the change in the central and posterior channels (Figure 6E, rows 3–6) for all slope measures.

The topography of the number of peaks for slow waves revealed a clear anterior-to-posterior gradient during both early and late sleep (Figure 6A,B, row 7). In contrast to all other slow-wave parameters, there was a significant increase in the number of peaks, but this increase was significant for fewer (approximately 29% of channels), mostly frontal, channels (Figure 6D, row 7). Regionally, the increase from early to late sleep was again significantly larger in frontal channels (Figure 6E, row 7).

Multipeak Waves have Multiple Origins

Previous work using hd-EEG in humans has shown that sleep slow waves behave as traveling waves, with a distinct origin and propagation pattern across the scalp.¹⁷ For example, using a similar algorithm as in Massimini et al,¹⁷ the streamline analysis on a representative single-peak wave yielded a distinct right frontal origin with a predominant right-left propagation (Figure 7AB, column 1). On the basis of the computer simulations presented in the first companion paper,³ we asked whether slow waves having more than 1 peak might have distinct spatial origins and propagations. For the purpose of this analysis, we selected a number of waves having 2 peaks clearly separated in time. A representative multipeak wave is shown in Figure 7. The streamline analysis run on the individual peaks of multipeak waves typically revealed origins and/or propagations that were spatially unique for each peak. In the case illustrated in Figure 7A and B (columns 2 and 3), the first peak originated in a left temporal area with a left-right propagation, whereas the second peak, approximately 260 milliseconds later, has a right frontal origin and traveled primarily from right to left.

Figure 7.

Representative examples of traveling waves for single and multipeak waves. A: Butterfly plots showing electroencephalogram (EEG) traces overlapped for all the channels involved (see Methods) in an individual peak. Red dots show the negative peaks for each derivation. The blue line indicates the representative time for source localization depicted in C (70 ms after the maximum negative peak). B: Topographic display of the interpolated (100×100) delay gradient based on the corresponding time from the earliest channel detection for that peak (see corresponding red dots above). Individual channels are indicated as black dots. Streamlines along the gradient were computed for each channel, and the longest is highlighted in blue. The origin is indicated by the large red dot. C: Top, right, and left views of the minimum norm least squares source estimation 70 ms after the maximum negative peak (indicated by the corresponding vertical blue lines in A). Absolute values of the currents are displayed. Note the correspondence between the maximum current activation and the origin of the slow waves in B.

To confirm that each peak has a uniquely identifiable origin, we also performed source localization on representative single- and multipeak waves (Figure 7C). For the single-peak wave shown in Figure 7A and B, source localization confirmed that the maximum current activation right after the peak was located at the same location as the origin of the scalp-recorded traveling wave (see source localization 70 ms after peak, Figure 7C, column 1). Similarly, source localization of the first peak in the multipeak wave revealed a large maximal current activation near the origin of the first wave (see source localization 70 ms after the first peak, Figure 7C, column 2) and a later maximal activation near the origin of the second wave (see source localization 70 ms after the second peak, Figure 7C, column 3).

DISCUSSION

In this study, we used all-night hd-EEG recordings in humans to examine sleep slow-wave parameters during early and late sleep. We found that during NREM sleep episodes 1 and 2, when EEG SWA and presumably sleep pressure (the need to sleep) are high, there was a high proportion of large-amplitude slow waves and the slope of slow waves was steep. By contrast, during NREM episodes 3 and 4, when sleep pressure and SWA are low, the proportion of large-amplitude slow waves decreased and slow-wave slopes were reduced; instead, the proportion of multipeak waves increased. Further analysis showed that slow-wave slope decreased between early and late sleep even when waves were directly matched by epoch power and wave amplitude. The topographic analysis of hd-EEG data revealed that the observed changes in SWA, high-amplitude slow-wave incidence, and slow-wave slope were distributed characteristically across the scalp and that multipeak waves have multiple cortical origins.

Incidence of High-Amplitude Slow Waves

For the present analysis, we assessed all sleep slow waves, regardless of amplitude, based on a duration criterion (0.25 to 1 second negative-to-positive zero crossing). This method allowed us to demonstrate that, although the overall incidence of slow waves changes only modestly between early and late sleep, the distribution of slow-wave amplitudes changes markedly during the course of the night. These results are consistent with previously reported period-amplitude analyses.¹⁶ Specifically, the largest slow waves (top 20%) were at least 3 times more prevalent during early sleep, whereas, during later sleep, smaller waves dominated by a 3:1 ratio. Computer simulations³ suggest that 2 mechanisms may account for the reduction in the incidence of high-amplitude waves with decreasing sleep pressure: a smaller amplitude of the slow oscillation of the membrane potential of individual neurons and a poorer synchronization between neurons, where both mechanisms could result from a net reduction in cortical synaptic strength. Additional mechanisms, such as neuromodulatory changes and changes in local inhibition, may also play a role. Regardless of the specific mechanisms, the decrease in the number of large-amplitude waves with decreasing sleep pressure appears to be a robust phenomenon, as it is evident not only at the EEG level in humans, but also at the LFP level in rats.⁴

Changes in Slow-Wave Slopes

A marked change in slow-wave slope between early and late sleep is another feature that is seen both in the human EEG and in rat LFP recordings.⁴ As discussed in the companion papers,^3,4 the slope of evoked waves is traditionally used as an electrophysiologic measure of synaptic strength, particularly in studies of long-term potentiation and depression.^23–25 Although the slow waves of NREM sleep are not “evoked” in the classical sense, it is reasonable to assume that they are also to some extent “evoked” by spontaneous volleys of activity traveling within the cortex,¹⁷ and thus their slope could reflect synaptic strength.

More importantly, when the factors underlying slow-wave generation are considered, as in the companion modeling paper³, it appears that slow-wave slope is a direct measure of synaptic strength. In previous modeling work,²⁶ as well as in vivo,²⁷ it has been shown that, during slow-wave sleep, neurons tend to behave in somewhat synchronous fashion, such that they transition between the up state and the down state within about 100 milliseconds of one another. The rate at which this transition occurs across the population is determined by synaptic activity. Specifically, a population of neurons transitions into the up state with a rate based on the amount of synaptic activity added as neurons enter the up state 1 by 1, which is in turn determined by synaptic strength. Similarly, the rate at which a population of neurons leaves the up state is based on the rate at which synaptic activity is removed from the network as neurons 1 by 1 enter the down state (also determined by synaptic strength). Thus, the slope of slow waves may be the most direct reflection of synaptic strength available in the EEG signal for the following reasons: (1) EEG signals are predominantly the result of the synchronous synaptic activity of a population of cells²⁸ and (2) the rate of change of synaptic activity over time determines the slope of the slow wave.

Naturally, the change in slope we observed could also be explained in terms of traditional period-amplitude analysis.^13–16 When we compared waves of similar amplitude, then, the changes in slope would have to be interpreted as changes in period. Although the 2 results are consistent, we think that slope is a more direct measure of synaptic strength, for the reasons explained above. Conversely, the period is potentially sensitive to additional factors, such as the persistent Na⁺ current, the depolarization-activated K⁺ current, and synaptic depression,²⁶ and is therefore a more indirect measure. The fact that changes were also seen in maximum slope, a measure independent of period and amplitude, further corroborates this interpretation.

An intriguing finding was that the decrease in wave slopes during late sleep did not apply to slow waves of the highest-amplitude category (although their incidence did decrease). One possible explanation for this discrepancy is the following. It is well known that during sleep various kinds of stimuli can trigger slow waves with consistently high amplitude, commonly referred to as K-complexes (reviewed in ²⁹). It is possible that a substantial number of high-amplitude slow waves during late sleep may actually be triggered by external or internal stimuli on a background of lighter sleep. K-complexes, unlike slow waves of intrinsic cortical origin, are triggered through the involvement of ascending sensory pathways and the reticular activating system, with its diffuse action on the thalamocortical system. Thus, K-complexes may facilitate a near-synchronous recruitment of distant neuronal populations that is less dependent on cortico-cortical connection strength.

SWA and Slow Wave Slope

SWA is considered a reliable measure of sleep pressure because it increases after waking, increases further after sleep deprivation, and decreases during sleep (reviewed in⁸). The human EEG data presented in this paper, along with rat LFP data in a companion paper,⁴ indicate that the well-established changes in SWA with sleep pressure are associated with changes in several parameters of the individual slow waves: in fact, a strong linear correlation was found among SWA, incidence of high-amplitude slow waves, and slow-wave slopes. Thus, based on the present results, it can be hypothesized that the slope of the slow waves may also represent a reliable marker of sleep pressure. Both the human (this paper) and the rat⁴ data suggest, however, that slow-wave slope may be even more sensitive than SWA. In this study, when waves of the same amplitude and similar background EEG power were compared directly between early and late sleep (NREM episodes 1 and 2 vs. episodes 3 and 4), late sleep waves still showed a reduction in slope (Figure 4). This first comparison suggested that, as a measure, slope effects could be distinguished from SWA power and amplitude. However, one could also argue that this effect on slope could be attributable to circadian or neuromodulatory influences. Assuming that neuromodulatory effects, if they contributed to the observed changes in slope, would be roughly similar during the deepest part of the first 2 NREM episodes, we next compared only those waves occurring during slow-wave sleep NREM episodes 1 and 2 (again after they were equated by power and amplitude) and still observed a reduction in slope. We then took advantage of the known ultradian modulation of SWA during the course of a NREM episode to further examine the influence that mechanisms other than synaptic strength might have on slope. During the course of a NREM episode, SWA gradually increases, peaks somewhere near the middle of the episode, and then declines prior to the transition into REM.¹¹ Although virtually no experimental data exist, the most likely explanation for such a trajectory would be changes in the level of arousal-promoting neuromodulators. Given that, on average, slopes behave in a similar manner during a NREM episode (Supplementary Figure 3), we compared only the first part of NREM episode 1 with the last part. We reasoned that if the changes observed in slope were determined primarily by the level of neuromodulators, then, at similar points on the within-episode trajectory, slopes would not be different. However, slow-wave slopes still decreased. Additionally, this analysis argues against a circadian influence because it is unlikely that such factors would impact slope differentially on a time scale less than the length of a NREM episode. Finally, in direct comparison to what was done in the model, where synaptic strength and the level of neuromodulation could be independently controlled, we compared (1) the first part of NREM episode 1—when arousal-promoting neuromodulators would be relatively low but synaptic strength, according to our hypothesis, would be high—with (2) the middle part of NREM episode 4, during the peak of sleep depth, and presumably the nadir of arousing-promoting neuromodulators within the episode, but when synaptic strength was assumed to be low. Interestingly, although average power increased, slopes still declined. Such increased sensitivity would be expected if the slope of slow waves reflects a basic cellular phenomenon such as cortical synaptic strength.

Undoubtedly, synaptic strength is not the only factor that determines the slope of slow waves. The overall level of arousal-promoting neuromodulators, metabolic factors such as energy charge, adenosine levels, and the balance of excitation and inhibition are likely to affect the slope of slow waves. Such influences can be seen both in the time course of slope changes, as well as in the variable magnitude and sensitivity of different slope measures to our equating procedures. Regardless, the overall direction of the slope data in humans, together with the results from the other companion papers, provides substantial evidence to suggest that changes in synaptic strength can provide a parsimonious explanation for the homeostatic decrease of SWA during the course of sleep.

Finally, the change in slope offers a straightforward account for the shift in power to lower frequencies (< 1.5 Hz) during late sleep. In a companion paper, using an artificial signal designed to closely resemble LFP recordings in the rat, it was shown that a change in the incidence of high-amplitude slow waves was primarily responsible for the decline in absolute SWA (0.5–4 Hz) power.⁴ Furthermore, it was shown that a decrease in the slope of the slow waves resulted in a shift of the peak of the relative spectrum toward slower frequencies (< 1.5 Hz). This finding is relevant in terms of the suggested dissociation between slow (< 1 Hz) and fast (1–4 Hz) SWA (also called delta).^28–29 Such a shift could obscure the homeostatic decline of slow SWA frequencies. Instead of distinct rhythms, subject to different regulatory processes, the slower homeostatic decline of the EEG power below 1 Hz may simply reflect a redistribution of power density due to changes in the slope of the slow waves occurring between early and late sleep.

Topographic Analysis

In humans, the use of hd-EEG recordings also allowed us to investigate topographic changes in SWA and slow-wave parameters in the course of the night (Figure 6). The scalp distribution of SWA and its decline between early and late sleep was similar to what has been previously reported.³⁰ However, thanks to increased spatial sampling, we found that a substantial reduction of SWA occurred not only at frontal sites, but also at temporal scalp locations. The topographic analysis of slow-wave incidence and slow-wave slopes demonstrated that these parameters, too, showed a progressive decrease with decreasing sleep pressure at all scalp regions. Compared to SWA, however, the pattern of decrease of wave incidence and slope was more homogeneous and spatially graded from anterior to posterior cortical regions and did not show the relative sparing of SWA over the scalp area between and around Fz and Cz. This area, which showed the least relative change in SWA from early to late sleep, also showed the highest incidence of slow waves. Although this topographic correspondence may be coincidental, it may also be due to the preferential contribution of K-complexes, which tend to localize to this region (reviewed in ²⁹) and do not decrease in incidence with sleep pressure.

Multipeak Waves

In a companion paper, computer simulations also predicted that, to the extent that decreasing sleep pressure is associated with a decrease in cortical synaptic strength, there should be an increase in the number of waves with multiple peaks, due to reduced network synchronization and a slower rate of recruitment and decruitment.³ In a second companion paper, this prediction has been confirmed by LFP recordings in the rat⁴, and, as shown here, it also applies to human EEG recordings, in which the percentage of multipeak waves increased from 59% during early sleep to 68% during late sleep.

In addition, computer simulations predicted that distinct peaks in multipeak waves are associated with the emergence of distinct local clusters of synchronized neural activity.³ This topographic analysis of human hd-EEG sleep data indicates that the distinct peaks of multipeak waves most likely represent the asynchronous generation of slow waves within distant cortical sources, in accordance with the model's predictions. This was confirmed by analyzing the independent traveling of each of the peaks and by localizing their source using source modeling techniques. This finding raises the possibility that every peak observable in the EEG that contributes to the delta (SWA) range (0.5 - 4 Hz) may actually be due to spatially distinct cortical sources undergoing the typical slow oscillation. In this view, the so called “delta” activity would be due to the superimposition of spatially distinct slow oscillations, rather than to the superimposition of global oscillators resonating at different frequencies, thereby suggesting that, at the fundamental level, there may not be a distinction between slow (<1 Hz) and “delta” oscillations.

CONCLUSION

This is the last of 3 companion papers examining changes in sleep slow waves with decreasing sleep pressure. In the first paper, large-scale computer simulations showed that a decrease in cortico-cortical synaptic strength produced a decline in SWA that was accompanied by a decreased incidence of high-amplitude slow waves, decreased wave slopes, and an increased number of multipeak waves.³ In the second paper, the model's predictions were confirmed with LFP recordings in the rat brain.⁴ Moreover, the rat study showed that the results were not dependent on circadian effects but, rather, on homeostatic mechanisms triggered by sleep deprivation. In the current study, we further confirmed predictions from the model in humans using hd-EEG. We took advantage of the fact that short epochs of human sleep at very different times of the night are often indistinguishable from one another, in terms of amplitude and power, to show that the slope of slow waves, suggested by the model to be an EEG measure that is reflective of synaptic strength, may be an even more sensitive measure of homeostatic pressure. Moreover, we demonstrated that the predicted changes in slow-wave parameters, in particular slope, occur over the entire cortical mantle.

Taken together, results obtained at 3 different spatial scales—from the microscale of thalamocortical model neurons, to the mesoscale of LFP recordings of local neuronal populations, to the macroscale of hd-EEG recordings in humans—suggest that a reduction of cortical synaptic strength during sleep can provide a parsimonious account for the observed changes in SWA and slow-wave parameters with decreasing sleep pressure, although other mechanisms may certainly be involved. To the extent that this interpretation is correct, it also implies that the analysis of sleep slow waves might provide a noninvasive tool for measuring synaptic strength both in health and disease.

Supplementary Figure 1.

Difference between slopes of the .rst and second slow-wave segments for average (top) and maximum (bottom) slope measurements at Fp1. Slow waves were subdivided into 5 equal percentiles according to the amplitude as before. Box-plots show the slope difference from the mean expressed as a percentage ([1^st–^nd]*200/[1^st+2^nd]) for each subject (n = 7). Triangles indicate significance and direction of the nonparametric permutation test (p < 0.05, single threshold corrected).

Supplementary Figure 2.

Bar plots of the proportion of slow waves with more than 1 peak (% of the total number of waves) for early and late sleep for channel Fp1. Individual subject values are shown as white circles connected by lines.

Supplementary Figure 3.

Time course of slow-wave activity and slopes. Non-rapid eye movement (NREM) episodes were divided into 10 equal percentiles based on the length of each episode. Average values (± SEM, n = 7).