Objective: In neuroscience, time-frequency analysis has been used to get insight into brain rhythms from brain recordings. In event-related protocols, one applies it to investigate how the brain responds to a stimulation repeated over many trials. In this framework, three measures have been considered: the amplitude of the transform for each single trial averaged across trials, avgAMP; inter-trial phase coherence, ITC; and the power of the evoked potential transform, POWavg. These three measures are sensitive to different aspects of event-related responses, ITC and POWavg sharing a common sensitivity to phase resetting phenomena.
Methods: In the present manuscript, we further investigated the connection between ITC and POWavg using theoretical calculations, a simulation study and analysis of experimental data.
Results: We derived exact expressions for the relationship between POWavg and ITC in the particular case of the S-transform of an oscillatory signal. In the more general case, we showed that POWavg and ITC are connected through a relationship that roughly reads POWavg ≈ avgAMP2 × ITC2. This result was confirmed on simulations. We finally compared the theoretical prediction with results from real data.
Conclusion: We showed that POWavg and ITC are related through an approximate, simple relationship that also involves avgAMP.
Significance: The presented relationship between POWavg, ITC, and avgAMP confirms previous empirical evidence and provides a novel perspective to investigate evoked brain rhythms. It may provide a significant refinement to the neuroscientific toolbox for studying evoked oscillations.