Detection and quantification of planar traveling waves in the EEG using spherical phase fitting

Recent years have seen an increasing interest in the spatiotemporal dynamics of oscillatory brain activity. Recordings at various scales have shown oscillations propagating as waves over cortical space, both at small and large scales. The most common waves observed in the EEG are planar waves, formed by a synchronized wavefront propagating in a consistent direction (e.g., posterior-anterior). These waves have been linked to diverse perceptual and cognitive measures. However, their quantification has faced issues due to the inherently noisy EEG signal and its ambiguous spatial localization. Existing methods employ restrictive windows of analysis (e.g., lines of electrodes) or rely on wave motifs extracted from the data. A specific algorithm for detecting planar waves is still lacking. Here, we present a comprehensive analysis pipeline for this purpose, comprising three steps: first, genuine oscillatory activity is extracted from the EEG as clusters. The spatial phase gradient is then fit using a spherical wave model. Finally, stable waves are extracted from the time series of fits. We validate our method using simulations over a physiological range of parameters. Using a forward model, we test EEG wave detection for propagation along different pathways at the source level. Lastly, we apply our analysis to real EEG recordings, targeting alpha oscillations during visual stimulation and at rest. In summary, our method provides a reliable algorithm for detecting planar waves in the EEG. Given the emerging functional roles of traveling waves in perception and cognition, this could potentially be utilized in a wide range of future studies.