A time-frequency based approach for generalized phase synchrony assessment in nonstationary multivariate signals

This paper proposes a new approach to estimate the phase synchrony among nonstationary multivariate signals using the linear relationships between their instantaneous frequency (IF) laws. For cases where nonstationary signals are multi-component, a decomposition method like multi-channel empirical mode decomposition (MEMD) is used to simultaneously decompose the multi-channel signals into their intrinsic mode functions (IMFs). We then apply the Johansen method on the IF laws to assess the phase synchrony within multivariate nonstationary signals. The proposed approach is validated first using multi-channel synthetic signals. The method is then used for quantifying the inter-hemispheric EEG asynchrony during ictal and inter-ictal periods using a newborn EEG seizure/non-seizure database of five subjects. For this application, pair-wise phase synchrony measures may not be able to account for phase interactions between multiple channels. Furthermore, the classical definition of phase synchrony, which is based on the rational relationships between phases, may not reveal the hidden phase interdependencies caused by irrational long-run relationships. We evaluate the performance of the proposed method using the differentiation of unwrapped phase as well as other IF estimation techniques. The results obtained on newborn EEG signals confirm that the generalized phase synchrony within EEG channels increases significantly during ictal periods. A statistically consistent phase coupling is also observed within the non-seizure segments supporting the concept of constant inter-hemispheric connectivity in the newborn brain during inter-ictal periods.