Spectral Slope and Lempel-Ziv complexity robustly differentiate brain states in sleep and wakefulness

Introduction:
Non-oscillatory measures of brain activity such as the spectral slope and Lempel-Ziv complexity are affected by multiple neurological disorders and are modulated during sleep. To date, a multitude of frequency ranges, particularly narrow- and broadband (encompassing the full spectrum) approaches, have been employed to estimate spectral slope and signal complexity. However, the effects of selecting different frequency ranges have not yet been explored in detail and little is known about the relationship between slope and complexity.
Method:
We evaluated the impact of sleep stage and task-engagement (resting, attention and memory) on the spectral slope and Lempel-Ziv complexity in a narrow- (30 – 45Hz) and broadband (1 – 45Hz) frequency range in 28 healthy male human subjects (21.54 ± 1.90 years) using a within-subject design over two weeks with three recordings per subject. Specifically, we determined how different brain states and frequency ranges affect slope and complexity and how the two measures perform in comparison, using semi-parametrical analyses of variance and multivariate pattern analyses.
Results:
In the broadband range, the slope steepened, and complexity decreased continuously from wakefulness to N3 sleep (slope: WTS4 = 1088.28; p < 0.001, complexity: WTS4 = 857.60; p < 0.001). REM sleep, however, was best discriminated by the narrowband slope. Importantly, slope and complexity also differentiated significantly between tasks during wakefulness (all p < 0.001). While the narrowband complexity decreased with task engagement (WTS4 = 199.55; p < 0.001), the slope flattened in both frequency ranges (narrowband: WTS4 = 56.64; p < 0.001, broadband: WTS4 = 40.45; p < 0.001). Critically, only the narrowband slope was consistently positively correlated with task performance (all r > 0.42; all p < 0.033).
Conclusion:
Our results show that slope and complexity are sensitive markers of brain state variations during wakefulness and sleep. Importantly, the spectral slope provides more information compared to Lempel-Ziv complexity and thus could be applicable to a wider array of research questions, particularly when focusing on a narrowband frequency range.