Estimation of phase in EEG rhythms for real-time applications

Abstract

Objective. Estimating the ongoing phase of oscillations in electroencephalography (EEG) recordings is an important aspect of understanding brain function, as well as for the development of phase-dependent closed-loop real-time systems that deliver stimuli. Such stimuli may take the form of direct brain stimulation (for example transcranial magnetic stimulation), or sensory stimuli (for example presentation of an auditory stimulus). We identify two linked problems related to estimating the phase of EEG rhythms with a specific focus on the alpha-band: 1) when the signal after a specific stimulus is unknown (real-time case), or 2) when it is corrupted by the presence of the stimulus itself (offline analysis). We propose methods to estimate the phase at the presentation time of these stimuli. Approach. Machine learning methods are used to learn the causal mapping from an unprocessed EEG recording to a phase estimate generated with a non-causal signal processing chain. This mapping is then used to predict the phase causally where non-causal methods are inappropriate. Main results. We demonstrate the ability of these machine learning methods to estimate instantaneous phase from an EEG signal subjected to very minor pre-processing with higher accuracy than commonly used signal-processing methods. Significance. Neural oscillations have been implicated in a wide variety of sensory, cognitive and motor functions. The instantaneous phase of these rhythms may reflect specific processes of computation which can be acted upon if they can be estimated with sufficient accuracy. Such brain-state dependent paradigms are of increasing medical and scientific interest.