Tracking propagating cortical activity in MEG/EEG with a bilinear state-space model

Magnetoencephalography (MEG) and electroencephalography (EEG) are ideal for studying macroscopic neural dynamics, but non-invasive tracking of cortical traveling waves remains a major methodological challenge. Traditional inverse solutions assume spatiotemporal separability, restricting sources to fixed spatial topographies. Consequently, they struggle to capture the continuous spatial migration of cortical traveling waves and often misinterpret phase-locked static sources as spurious propagation. To address this fundamental limitation, we propose a dynamic state-space framework that explicitly accommodates the spatiotemporal inseparability of propagating neural activity. Our approach models the sensor signal as a bilinear combination of two states that evolve together: a fast, narrowband stochastic oscillator carrying the electrical time course, and a slowly evolving spatial topography that drifts through a data-driven singular value decomposition subspace. Both the rhythmic electrical time series and the migrating source trajectory track jointly via an Unscented Kalman Filter. We evaluated the method on realistically simulated MEG data and empirical resting-state MEG and EEG recordings targeting the occipital alpha rhythm. In simulations, the approach accurately recovered electrical time courses and spatial trajectories across varying signal-to-noise ratios, spatial envelope velocities up to 0.1 m/s, and distinct cortical geometries (calcarine and central sulci), significantly outperforming traditional minimum norm estimation and dipole fitting. Crucially, the model resists fabricating spurious propagation trajectories when presented with stationary, coherent dipoles. Application to empirical MEG and EEG recordings of the occipital alpha rhythm yields anatomically plausible, temporally cohesive propagation paths that explain significantly more sensor-level variance than static baselines. By embedding the evolving source geometry directly into the inverse solution, this framework provides a robust, proof-of-concept tool for the non-invasive investigation of macroscopic propagating brain dynamics.