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 (1) predictability and (2) 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.

Episodic long-term memory formation during slow-wave sleep

“…HFD provides a non-linear measure of the complexity, variability, and “randomness” of the EEG signal at each channel. Because high HFD values indicate the presence of cognitive processes (Lau et al, 2021; Parbat & Chakraborty, 2021), we wondered whether HFD values would be higher in the Trough condition, where sleep-learning occurred, than the Peak condition, where no significant sleep-learning occurred. We also examined whether HFD values would be higher for word-stimulated troughs/peaks versus non-stimulated troughs/peaks.…”

The Structure of Chaos: An Empirical Comparison of Fractal Physiology Complexity Indices Using NeuroKit2

“…Complexity is an umbrella term for concepts derived from information theory, chaos theory, and fractal mathematics, used to quantify unpredictability, entropy, and/or randomness. Using these approaches to characterize physiological signals (a subfield commonly referred to as “fractal physiology” [ 1 ]) has shown promising results in the assessment and diagnostic of the state and health of living systems [ 2 , 3 , 4 ].…”

“…Over the past few decades, there has been an important increase in the number of complexity indices [ 5 ]. Although these new procedures are usually mathematically well-defined and theoretically promising, limited empirical evidence is available to understand their similarities and differences [ 2 , 5 ]. Moreover, some of these methods are resource-intensive and require long computation times.…”

The Structure of Chaos: An Empirical Comparison of Fractal Physiology Complexity Indices using NeuroKit2

“…Complexity is an umbrella term for concepts derived from information theory, chaos theory, and fractal mathematics, used to quantify unpredictability, entropy, and/or randomness. Using these approaches to characterize physiological signals (a subfield commonly referred to as "fractal physiology" [1]) has shown promising results in the assessment and diagnostic of the state and health of living systems [2][3][4].…”

“…Over the past few decades, there has been an important increase in the number of complexity indices [5]. Although these new procedures are usually mathematically welldefined and theoretically promising, limited empirical evidence is available to understand their similarities and differences [2,5]. Moreover, some of these methods are resourceintensive and require long computation times.…”