Traveling waves and trial averaging: the nature of single-trial and averaged brain responses in large-scale cortical signals.

Analyzing single trial brain activity remains a challenging problem in the neurosciences. We gain purchase on this problem by focusing on globally synchronous fields in within-trial evoked brain activity, rather than on localized peaks in the trial-averaged evoked response (ER). We analyzed data from three measurement modalities, each with different spatial resolutions: magnetoencephalogram (MEG), electroencephalogram (EEG) and electrocorticogram (ECoG). We first characterized the ER in terms of summation of phase and amplitude components over trials. Both contributed to the ER, as expected, but the ER topography was dominated by the phase component. This means the observed topography of cross-trial phase will not necessarily reflect the phase topography within trials. To assess the organization of within-trial phase, traveling wave (TW) components were quantified by computing the phase gradient. TWs were intermittent but ubiquitous in the within-trial evoked brain activity. At most task-relevant times and frequencies, the within-trial phase topography was described better by a TW than by the trial-average of phase. The trial-average of the TW components also reproduced the topography of the ER; we suggest that the ER topography arises, in large part, as an average over TW behaviors. These findings were consistent across the three measurement modalities. We conclude that, while phase is critical to understanding the topography of event-related activity, the preliminary step of collating cortical signals across trials can obscure the TW components in brain activity and lead to an underestimation of the coherent motion of cortical fields.