Probing Intrinsic Neural Timescales in EEG with an Information-Theory Inspired Approach: Permutation Entropy Time Delay Estimation (PE-TD)

Time delays are a signature of many physical systems, including the brain, and considerably shape their dynamics; moreover, they play a key role in consciousness, as postulated by the temporo-spatial theory of consciousness (TTC). However, they are often not known a priori and need to be estimated from time series. In this study, we propose the use of permutation entropy (PE) to estimate time delays from neural time series as a more robust alternative to the widely used autocorrelation window (ACW). In the first part, we demonstrate the validity of this approach on synthetic neural data, and we show its resistance to regimes of nonstationarity in time series. Mirroring yet another example of comparable behavior between different nonlinear systems, permutation entropy-time delay estimation (PE-TD) is also able to measure intrinsic neural timescales (INTs) (temporal windows of neural activity at rest) from hd-EEG human data; additionally, this replication extends to the abnormal prolongation of INT values in disorders of consciousness (DoCs). Surprisingly, the correlation between ACW-0 and PE-TD decreases in a state-dependent manner when consciousness is lost, hinting at potential different regimes of nonstationarity and nonlinearity in conscious/unconscious states, consistent with many current theoretical frameworks on consciousness. In summary, we demonstrate the validity of PE-TD as a tool to extract relevant time scales from neural data; furthermore, given the divergence between ACW and PE-TD specific to DoC subjects, we hint at its potential use for the characterization of conscious states.