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.

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

Table 2 Sleep Measures by NREM Episode

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 < (more ...)

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 (more ...)

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 (more ...)

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).

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]) (more ...)

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).

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 (more ...)

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

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.

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.

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 (more ...)

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).

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 (more ...)

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).

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.

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.

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).

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.

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.

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.

We thank Chiara Cirelli and Sean Hill for helpful discussions and Adenauer Casali for assistance with source localization. Supported by NIH T90 DK070079 and NRSA T32 GM007507 to BAR, Swiss National Science Foundation PBZHB-106264 to VVV, and the NIH Director's Pioneer Award to GT.