Epoch averaging: induced responses across trials
Massive event-related cell synchronization is not guaranteed to take place with consistent temporal phase with respect to the onset of the event. It is therefore relatively easy to imagine that averaging trials when such phase jitters occurs across event repetitions would lead to decreased effect sensitivity. This assumption can be further elaborated in the theoretical and experimental framework of distributed, synchronized cell assemblies during perception and cognition (Varela et al.., 2001, Tallon-Baudry, 2009).
The seminal works by Gray and Singer in cat vision have shown that synchronization of oscillatory responses of spatially distributed cell ensembles is a way to establish relations between features in different parts of the visual field (Gray et al.., 1989). These authors evidenced that these phenomena take place in the gamma range ([40,60]Hz) – i.e., a upper frequency range – of the event-elated responses. These results have been confirmed by a large number of subsequent studies in animals and implanted electrodes in humans, which all demonstrated that these event-related responses could only be captured with an approach to epoch averaging that would be robust to phase jitters across trials (Tallon-Baudry, Bertrand, Delpuech, & Permier, 1997, Rodriguez et al.., 1999).
More evidence of gamma-range brain responses detected with EEG and MEG scalp techniques are being reported as analysis techniques are being refined and distributed to a greater community of investigators (Hoogenboom, Schoffelen, Oostenveld, Parkes, & Fries, 2006). It is striking to note that as a greater number of investigations are conducted, the frequency range of gamma responses of interest is constantly expanding and now reaches between [30,100]Hz and above. As a caveat, this frequency range is also most favorable to contamination from muscle activity, such as phasic contractions or micro-saccades, which may also happen to be task-related (Yuval-Greenberg & Deouell, 2009, Melloni, Schwiedrzik, Wibral, Rodriguez, & Singer, 2009). Therefore great precautions must be brought to rule out possible confounds in that matter.
An additional interesting feature of gamma responses for neuroimagers is that there is a growing body of evidence showing that they tend to be more specifically coupled to the hemodynamics responses captured in fMRI than other components of the electrophysiological responses (Niessing et al.., 2005, Lachaux et al.., 2007, Koch, Werner, Steinbrink, Fries, & Obrig, 2009).
Because induced responses are mostly characterized by phase jitters across trials, averaging MEG/EEG traces in the time domain would be detrimental to the extraction of induced signals from the ongoing brain activity (David & Friston, 2003). A typical approach to the detection of induced components once again builds on the hypothesis of systematic emission of event-related oscillatory bursts limited in time duration and frequency range. Time-frequency decomposition (TFD) is a methodology of choice in that respect, as it proceeds to the estimation of instantaneous power in the time-frequency domain of time series. TFD is insensitive to variations of the signal phase when computing the average signal power across trials. TFD is a very active field of signal processing and one of the core tools for TFD is wavelet signal decomposition. Wavelets feature the possibility to perform the spectral analysis of non-stationary signals, which spectral properties and contents are evolving with time (Mallat, 1998). This is typical of phasic electrophysiological responses for which Fourier spectral analysis is not adequate because it is based on signal stationarity assumptions (Kay, 1988).
Hence, even though the typical statistics of induced MEG/EEG signal analysis is the trial mean (i.e. sample average), it is performed with a different measure: the estimation of short-term signal power, decomposed in time and frequency bins. Several academic and commercial software solutions are now available to perform such analysis (and the associated inference statistics) on electrophysiological signals.