Brain entropy, fractal dimensions and predictability: A review of complexity measures for EEG in healthy and neuropsychiatric populations

Abstract

While electroencephalography (EEG) signals are commonly examined using conventional linear methods, there has been an increasing trend towards the use of complexity analysis in quantifying neural activity. On top of revealing complex neuronal processes of the brain that may not be possible with linear approaches, EEG complexity measures have also demonstrated their potential as biomarkers of psychopathology such as depression and schizophrenia. Unfortunately, the opacity of algorithms and descriptions originating from mathematical concepts have made it difficult to understand what complexity is and how to draw consistent conclusions when applied within psychology and neuropsychiatry research. In this review, we provide an overview and entry-level explanation of existing EEG complexity measures, which can be broadly categorized as measures of predictability and regularity. We then synthesize complexity findings across different areas of psychological science, namely in consciousness research, mood and anxiety disorders, schizophrenia, neurodevelopmental and neurodegenerative disorders, as well as changes across the lifespan, while addressing some theoretical and methodological issues underlying the discrepancies in the data. Finally, we present important considerations when choosing and interpreting these metrics.

Spectral slope and Lempel-Ziv complexity as robust markers of brain states during sleep and wakefulness

“…Mediano et al (2021) showed that in MEG within 0.5 – 30Hz, active tasks actually exhibited lower complexity values compared to rested wakefulness. In addition, a recent review from Lau et al (2022) discussed several studies that reported apparently contradicting modulations of neural complexity in different clinical conditions, where some report lower and others higher levels of complexity. Thus, the question whether higher neural complexity can always be clearly interpreted as more complex or irregular brain activity remains unclear.…”

“…Since REM sleep (sometimes called ‘paradoxical sleep’; Peigneux et al, 2001 or Siegel, 2011) is characterized by wake-like, but non-oscillatory brain activity (Blumberg et al, 2020; Peever & Fuller, 2017), these disparate results between the two frequency ranges suggest that the narrowband slope mainly measures non-oscillatory, aperiodic brain activity. The relative increase in broadband complexity during REM sleep has been attributed to higher levels of conscious content that accompany vivid dreaming and thus require more complex brain activity than deeper, mostly dreamless sleep stages (Lau et al, 2022; Mateos et al, 2018).…”

“…The copyright holder for this this version posted September 10, 2022. ; https://doi.org/10.1101/2022.09.10.507390 doi: bioRxiv preprint 2 Conceptually, the spectral exponent and neural complexity are regarded as two distinct measures as they are derived by different analytical approaches from the underlying electrophysiological signal. Neural complexity computed as Lempel-Ziv-Welch complexity (Welch, 1984) expresses the regularity and compressibility of a signal in time-domain (Lau et al, 2022) and is thought to be still strongly influenced by oscillatory activity (González et al, 2022;Tosun et al, 2019). In contrast, the spectral exponent reflects the absolute value of the slope (i.e., steepness) of a signal's power spectrum in the frequency-domain, which is thought to be mainly aperiodic (Donoghue et al, 2020).…”

Uncovering the Correlation between COVID-19 and Neurodegenerative Processes: Toward a New Approach Based on EEG Entropic Analysis

“…On the other hand, regularity measures investigate a lower level of details in the time-frequency domain, in favor of higher robustness. For this reason, they are applicable to noisier or smaller time series (which are typical of biosignals), for which predictability measures could not be reliably calculated [33]. Therefore, in recent years, new metrics for measuring regularity have been proposed.…”

“…Non-linear analyses (particularly among advanced EEG signal-processing techniques) investigate the complex emergent phenomena underlying chaotic dynamical systems, providing the possibility to analyze the strong complexity and irregularity of neuronal activities of the brain. These analyses are of extreme importance in order to identify the process of cognitive impairment [ 33 ]. Indeed, the complexity measures of EEG signals could enhance and provide more reliable results than traditional EEG analysis techniques (e.g., event-related potential, time, and frequency analysis) in the studies of psycho-pathological conditions [ 34 ] and the diagnosis of disorders [ 35 ].…”