Spectral Slope and Lempel-Ziv Complexity as Robust Markers of Brain States during Sleep and Wakefulness

Abstract

Nonoscillatory measures of brain activity such as the spectral slope and Lempel-Ziv complexity are affected by many neurological disorders and modulated by sleep. A multitude of frequency ranges, particularly a broadband (encompassing the full spectrum) and a narrowband approach, have been used especially for estimating the spectral slope. However, the effects of choosing different frequency ranges have not yet been explored in detail. Here, we evaluated the impact of sleep stage and task engagement (resting, attention, and memory) on slope and complexity in a narrowband (30-45 Hz) and broadband (1-45 Hz) frequency range in 28 healthy male human subjects (21.54 ± 1.90 years) using a within-subject design over 2 weeks with three recording nights and days per subject. We strived to determine how different brain states and frequency ranges affect slope and complexity and how the two measures perform in comparison. In the broadband range, the slope steepened, and complexity decreased continuously from wakefulness to N3 sleep. REM sleep, however, was best discriminated by the narrowband slope. Importantly, slope and complexity also differed between tasks during wakefulness. While narrowband complexity decreased with task engagement, the slope flattened in both frequency ranges. Interestingly, only the narrowband slope was positively correlated with task performance. Our results show that slope and complexity are sensitive indices of brain state variations during wakefulness and sleep. However, the spectral slope yields more information and could be used for a greater variety of research questions than Lempel-Ziv complexity, especially when a narrowband frequency range is used.

Keywords: EEG; Lempel–Ziv complexity; alertness; cognitive tasks; sleep; spectral slope.

Figure 1.

A, Overview of the experimental protocol. EEG was recorded throughout all tasks and during sleep (with full-night polysomnography) on the experimental days 7, 10, and 13 (see Extended Data Fig. 1-2 for the general sleep architecture on the different nights). The tasks, which are highlighted by a dashed, dark-green rectangle were primarily used to analyze the effects of engagement in different cognitive tasks during wakefulness. The adaptation night only served familiarization purposes and was not included in any of the analyses. An overview of the results from the screening entrance questionnaire is presented in Extended Data Figure 1-1. B, Example of the spectral slope estimation during N1 sleep. For illustration purposes, data are shown for the electrode Pz averaged over all subjects and sleep recordings. The spectral slope was fitted within 1–45 Hz (broadband, dashed green line) and 30–45 Hz (narrowband, dashed pink line). C, Schematic overview of the Lempel–Ziv complexity calculation based on a random 4 s epoch from electrode Pz of a subject during resting with closed eyes. First, the raw signal, filtered within a certain frequency range, is Hilbert transformed. Second, the resulting data is binarized around its median amplitude and stored as a vector of zeros and ones. Lastly, the Lempel–Ziv–Welch algorithm (Welch, 1984) is applied on this binary sequence in order to obtain a complexity value, which is driven by the number of unique repetitions of ones and zeros. The effect of signal regularity on Lempel–Ziv complexity and the spectral slope is further demonstrated in Extended Data Figure 1-4. For an overview of the number of epochs that were used for all analyses, see Extended Data Figure 1-3.

Figure 2.

Spectral slope (green, A) and Lempel–Ziv (LZ) complexity (purple, B) from 30 to 45 Hz across sleep, averaged over all lab-sessions per subject. Center figures show the data averaged over all electrodes and topographical maps are provided below (color-coding refers to z values of slope or complexity computed from the grand average across all sleep stages). In A, the log–log power spectra are provided for each sleep stage to illustrate the slope changes across different sleep stages. Classification accuracies are shown on the right side. A, The spectral slope decreases from wakefulness across all sleep stages to REM sleep with a small temporary increase during N3 sleep. B, Lempel–Ziv complexity increases from shallow N1 to light N2 sleep and is in general less modulated by sleep stage than the spectral slope. EMG activity did not confound the modulation of the spectral slope and Lempel–Ziv complexity during sleep (Extended Data Fig. 2-1) or wakefulness (Extended Data Fig. 2-2). ***p < 0.001, **p ≤ 0.010, *p ≤ 0.050, ^n.s.,p > 0.050; all p values are adjusted for multiple comparisons; error bars represent 95% confidence intervals (N = 27).

Figure 3.

Spectral slope (green, A) and Lempel–Ziv (LZ) complexity (purple, B) from 1 to 45 Hz across sleep, averaged over all lab-sessions per subject. Center figures show the data averaged over all electrodes and topographical maps are provided below (color-coding refers to z values of slope or complexity computed from the grand average across all sleep stages). In A, the log–log power spectra for each sleep stage are provided to illustrate the broadband slope differences across sleep stages. Classification accuracies are shown on the right side. A, Spectral slope steepens from wakefulness to N3 sleep but flattens to some extent in REM sleep. B, Lempel–Ziv complexity shows the same pattern as the spectral slope and likewise decreases from wakefulness to N3 with a subsequent increase in REM sleep. ***p < 0.001, **p ≤ 0.010, *p ≤ 0.050, ^n.s.p > 0.050; p values are adjusted for multiple comparisons; error bars represent 95% confidence intervals (N = 27).

Figure 4.

Spectral slope (green, A) and Lempel–Ziv (LZ) complexity (purple, B) from 30 to 45 Hz across tasks, averaged over all lab-sessions per subject (see Extended Data Fig. 4-1 for an analysis averaged over all timepoints per lab-session and Extended Data Fig. 4-2 for an analysis demonstrating similar results when using a different task order). Center figures show the data averaged over all channels and topographical maps are provided below (color-coding refers to z values of slope or complexity computed from the grand average across all tasks). In A, the log–log power spectra for each task are provided to illustrate narrowband slope differences across tasks. Classification accuracies are shown on the right side. A, The spectral slope flattens when engaging in cognitive tasks (Go/Nogo and learning) and is flattest during the retrieval session of the learning task. B, Lempel–Ziv complexity decreases with task engagement and reaches its minimum during the retrieval session. ***p < 0.001, **p ≤ 0.010, *p ≤ 0.050, ^n.s.p > 0.050; p values adjusted for multiple comparisons; error bars show 95% confidence intervals (N = 28).

Figure 5.

Spectral slope (green, A) and Lempel–Ziv (LZ) complexity (purple, B) from 1 to 45 Hz across tasks, averaged over all lab-sessions per subject (see Extended Data Figs. 5-1 and 5-2 for analyses averaged over all timepoints per session and for a different task order). Center figures show the data over all channels and topographical maps are provided below (color-coding refers to z values of slope or complexity computed from the grand average over all tasks). In A, the log–log power spectra for each sleep stage are provided to illustrate broadband slope differences across tasks. Classification accuracies are shown on the right side. A, The slope flattens from resting to the Go/Nogo task (see Extended Data Fig. 5-3 for an analysis of the effect of different epoch types and lengths for this task) and is flattest during retrieval. B, Complexity increases from resting with closed to open eyes and is further elevated in all active tasks, peaking during retrieval. ***p < 0.001, **p ≤ 0.010, *p ≤ 0.050, ^n.s.p > 0.050; p values adjusted for multiple comparisons; error bars show 95% confidence intervals (N = 28).

Figure 6.

A, Comparison of the multiclass classification accuracies within 30–45 Hz (see Extended Data Fig. 6-1 for all pairwise classification accuracies) for the spectral slope and Lempel–Ziv complexity regarding sleep stages (WAKE, N1, N2, N3, REM) and tasks during wakefulness (resting eyes closed, resting eyes open, auditory Go/Nogo, encoding, retrieval). Sleep stages and tasks could be decoded more precisely with the spectral slope. Overall classification accuracy was significantly higher for tasks than for sleep stages. B, Comparison of the classification accuracies across tasks and sleep stages for slope and complexity within 1–45 Hz (see Extended Data Fig. 6-2 for the pairwise classifications). The slope only yielded better decoding performance during sleep, whereas task classification worked better when using Lempel–Ziv complexity, which is arguably due to the difference in complexity between the two resting conditions that is not present in the slope. The dotted red lines represent chance level (20%). The correlation between slope and complexity within 30–45 Hz and 1–45 Hz is presented in Extended Data Figure 6-3. Extended Data Figures 6-4 and 6-5 demonstrate the robustness of the slope and complexity values across lab-visits and the correlation across frequency ranges. ***p < 0.001, ^n.s.p > 0.050 (N = 28).

Figure 7.

Relationship between Go/Nogo task performance and spectral slope (A) or Lempel–Ziv (LZ) complexity (B) within 30–45 Hz across different assessment times (see Extended Data Fig. 7-1 for the 1–45 Hz range). For the large scatterplots, data were averaged across all lab-sessions (small scatterplots show the relationship per lab-session). The topoplots depict the correlation strength for each electrode. Electrodes forming a significant cluster are highlighted with asterisks. Those showing a significant correlation after false discovery rate correction but did not from a cluster are marked with a cross. Only the narrowband spectral slope showed a consistent positive relationship with task performance (N = 26).

Figure 8.

Relationship between declarative memory recall performance and spectral slope (A) or Lempel–Ziv (LZ) complexity (B) within 30–45 Hz (see Extended Data Fig. 8-1 for the 1–45 Hz range). Results are shown for immediate recall in the evening and delayed recall on the next morning as well as for overnight change. For the large scatterplots, data was averaged across all lab-sessions (small scatterplots show the relationship per session). The topoplots represent the strength of the correlations on each electrode. Even though the spectral slope was consistently positively correlated with recall performance, no electrodes formed a significant cluster. Significant single electrodes that survived false discovery rate correction are highlighted with a cross (N = 28).