An in-depth analysis of parameter settings and probability distributions of specific ordinal patterns in the Shannon permutation entropy during different states of consciousness in humans

As electrical activity in the brain has complex and dynamic properties, the complexity measure permutation entropy (PeEn) has proven itself to reliably distinguish consciousness states recorded by the EEG. However, it has been shown that the focus on specific ordinal patterns instead of all of them produced similar results. Moreover, parameter settings influence the resulting PeEn value. We evaluated the impact of the embedding dimension m and the length of the EEG segment on the resulting PeEn. Moreover, we analysed the probability distributions of monotonous and non-occurring ordinal patterns in different parameter settings. We based our analyses on simulated data as well as on EEG recordings from volunteers, obtained during stable anaesthesia levels at defined, individualised concentrations. The results of the analysis on the simulated data show a dependence of PeEn on different influencing factors such as window length and embedding dimension. With the EEG data, we demonstrated that the probability P of monotonous patterns performs like PeEn in lower embedding dimension (m = 3, AUC = 0.88, [0.7, 1] in both), whereas the probability P of non-occurring patterns outperforms both methods in higher embedding dimensions (m = 5, PeEn: AUC = 0.91, [0.77, 1]; P(non-occurring patterns): AUC = 1, [1, 1]). We showed that the accuracy of PeEn in distinguishing consciousness states changes with different parameter settings. Furthermore, we demonstrated that for the purpose of separating wake from anaesthesia EEG solely pieces of information used for PeEn calculation, i.e., the probability of monotonous patterns or the number of non-occurring patterns may be equally functional.