The shaky ground truth of real-time phase estimation.

Instantaneous phase of brain oscillations in electroencephalography (EEG) is a measure of brain state that is relevant to neuronal processing and modulates evoked responses. However, determining phase at the time of a stimulus with standard signal processing methods is not possible due to the stimulus artifact masking the future part of the signal. Here, we quantify the degree to which signal-to-noise ratio and instantaneous amplitude of the signal affect the variance of phase estimation error and the precision with which "ground truth" phase is even defined, using both the variance of equivalent estimators and realistic simulated EEG data with known synthetic phase. Necessary experimental conditions are specified in which pre-stimulus phase estimation is meaningfully possible based on instantaneous amplitude and signal-to-noise ratio of the oscillation of interest. An open source toolbox is made available for causal (using pre-stimulus signal only) phase estimation along with a EEG dataset consisting of recordings from 140 participants and a best practices workflow for algorithm optimization and benchmarking. As an illustration, post-hoc sorting of open-loop transcranial magnetic stimulation (TMS) trials according to pre-stimulus sensorimotor μ-rhythm phase is performed to demonstrate modulation of corticospinal excitability, as indexed by the amplitude of motor evoked potentials.