Phase-compensated averaging for analyzing electroencephalography and magnetoencephalography epochs.

Stimulus-locked averaging for electroencephalography and/or megnetoencephalography (EEG/MEG) epochs cancels out ongoing spontaneous activities by treating them as noise. However, such spontaneous activities are the object of interest for EEG/MEG researchers who study phase-related phenomena, e.g., long-distance synchronization, phase-reset, and event-related synchronization/desynchronization (ERD/ERS). We propose a complex-weighted averaging method, called phase-compensated averaging, to investigate phase-related phenomena. In this method, any EEG/MEG channel is used as a trigger for averaging by setting the instantaneous phases at the trigger timings to 0 so that cross-channel averages are obtained. First, we evaluated the fundamental characteristics of this method by performing simulations. The results showed that this method could selectively average ongoing spontaneous activity phase-locked in each channel; that is, it evaluates the directional phase-synchronizing relationship between channels. We then analyzed flash evoked potentials. This method clarified the directional phase-synchronizing relationship from the frontal to occipital channels and recovered another piece of information, perhaps regarding the sequence of experiments, which is lost when using only conventional averaging. This method can also be used to reconstruct EEG/MEG time series to visualize long-distance synchronization and phase-reset directly, and on the basis of the potentials, ERS/ERD can be explained as a side effect of phase-reset.