From state space oscillator model to oscillation component decomposition: (a) An illustrative example of a multichannel state space oscillation model: A single oscillation realized as an analytic signal xn is measured as two different projections having π/4 radian phase difference. (b) Graphical representation of the probabilistic generative model describing the oscillations as dynamic processes, that undergo mixing at the sensors and that are observed with additive Gaussian noise. (c) Graphical representation of the Variational Bayes’ approximation that allows iterative closed form inference. (d) Oscillation component analysis fitting and reconstruction pipeline for experimentally recorded neurophysiological data. The pipeline exposes a number of methods for ease of analysis, i.e., for fitting the OCA hyperparameters fit() method, that accepts the sensor recordings and an initial sensor noise covariance matrix as input, for extracting the oscillation time-courses get sources(), for reconstructing a multichannel signal from any arbitrary subset of oscillation components, apply(), for getting a final noise covariance estimate from the residuals of OCA fitting, get noise covariance() method etc.

Simulation Study: A. four neural sources carrying 3 oscillations, where the orange time-course is a lagged instance of blue time-course, red and green time courses are independent; B. power spectral density of the simulated EEG recording, and power distribution over the EEG sensors in different frequency bands; C. recovered oscillation components and their sensor level maps; D. sensor noise covariance for the simulation; E. estimated sensor noise covariance matrix; F. model structure selection via model structure posterior q(m).

OCA of the EEG from a healthy volunteer undergoing propofol-induced unconsciousness. Conditions of target effect site concentration of A. & D. 0 (i.e. baseline), B. & E. 2 µg mL−1 and C. & F. 4 µg mL−1 are analyzed. Panels A-C show the PSDs of reconstructed EEG activity within each canonical band. Panels D-F show the three dominant (in terms of sensor wide power) alpha component: the topographic maps show the magnitude (left) and phase (right) distribution of sensor level mixing, the time courses are 1 sec representative example of the extracted oscillations from the selected epochs. The black bars on the right display the coherency measure within alpha band. OCA correctly identifies that the spatial mixing sensor maps of the alpha waves (8 Hz to 12 Hz) are oriented posteriorly at baseline, but gradually become frontally-dominant under propofol. The sensor weights are scaled to have maximum value 1. So, the units of time series traces can be considered to be in µV (dB).

OCA of the EEG from a healthy young volunteer to compare between (A. & C.) wakeful resting state and (B. & D.) rapid eye movement sleep. Panels A-B show the PSDs of reconstructed EEG activity within each canonical band. Panels C-D show the three dominant (in terms of sensor wide power) alpha component: the topographic maps show the magnitude (left) and phase (right) distribution of sensor level mixing, the time courses are 1 sec representative example of the extracted oscillations from the selected epochs. The rightmost black bars display the coherency measure within alpha band. The contrasting topographic distribution of the alpha components (8–12 Hz), the shape of the oscillation power spectrum and alpha coherence hints at a distinct generating mechanism for alpha waves during stage–2 REM sleep compared to awake eyes closed alpha wave. The sensor weights are scaled to have a maximum value 1 so that the units of time series traces are in µV.

Cross–frequency phase–amplitude coupling in OCA components extracted from resting state MEG recording. The black traces show the conditional mean of a selected alpha component (8–12 Hz) amplitude given another selected slow/delta component (0–4 Hz) phase. The three slow oscillations and three alpha oscillations that explained the highest variance were selected for demonstration purposes. The topographic maps show the magnitude (left) and phase (right) distribution of sensor level mixing of the selected components.