Measuring multivariate phase synchronization with symbolization and permutation

Abstract

Phase synchronization is an important mechanism for the information processing of neurons in the brain. Most of the current phase synchronization measures are bivariate and focus on the synchronization between pairs of time series. However, these methods do not provide a full picture of global interactions in neural systems. Considering the prevalence and importance of multivariate neural signal analysis, there is an urgent need to quantify global phase synchronization (GPS) in neural networks. Therefore, we propose a new measure named symbolic phase difference and permutation entropy (SPDPE), which symbolizes the phase difference in multivariate neural signals and estimates GPS according to the permutation patterns of the symbolic sequences. The performance of SPDPE was evaluated using simulated data generated by Kuramoto and Rössler model. The results demonstrate that SPDPE exhibits low sensitivity to data length and outperforms existing methods in accurately characterizing GPS and effectively resisting noise. Moreover, to validate the method with real data, it was applied to classify seizures and non-seizures by calculating the GPS of stereoelectroencephalography (SEEG) data recorded from the onset zones of ten epilepsy patients. We believe that SPDPE will improve the estimation of GPS in many applications, such as EEG-based brain–computer interfaces, brain modeling, and simultaneous EEG-fMRI analysis.