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Specific patterns of brain activity during sleep and waking are recorded in the  electroencephalogram (EEG). Time-frequency analyses methods have been widely used to analyse  the EEG and identified characteristic oscillations for each vigilance state (VS) i.e., wakefulness,  rapid-eye movement (REM) and non-rapid-eye movement (NREM) sleep. However, other aspects  such as change of patterns associated with brain dynamics may not be captured unless a  non-linear-based analysis method is used. In this pilot study, Permutation Lempel-Ziv Complexity (PLZC), a novel symbolic dynamics analysis method, was used to characterise the changes in the  EEG in sleep and wakefulness during baseline and recovery from sleep deprivation. The results  obtained with PLZC were contrasted with a related non-linear method, Lempel-Ziv complexity  (LZC). Both measure the emergence of new patterns. However, LZC is dependent on the absolute  amplitude of the EEG, while PLZC is only dependent on the relative amplitude due to  symbolisation procedure and thus, more resistant to noise. We showed that PLZC discriminates  activated brain states associated with wakefulness and REM sleep, which both displayed higher  complexity, compared to NREM sleep. Additionally, significantly lower PLZC values were  measured in NREM sleep during the recovery period following SD compared to baseline, suggesting a reduced emergence of new activity patterns in the EEG. These findings were validated  using PLZC on surrogate data. By contrast, LZC was merely reflecting changes in the spectral  composition of the EEG. Overall, this study implies that PLZC is a robust non-linear complexity  measure, which is not dependent on amplitude variations in the signal, and which may be useful to further assess EEG alterations induced by environmental or pharmacological manipulations

Characterisation of the Effects of Sleep Deprivation on the Electroencephalogram Using Permutation Lempel–Ziv Complexity, a Non-Linear Analysis Tool