Generalized cross-frequency decomposition: A method for the extraction of neuronal components coupled at different frequencies

Perceptual, motor and cognitive processes are based on rich interactions between remote regions in the human brain. Such interactions can be carried out through phase synchronization of oscillatory signals. Neuronal synchronization has been primarily studied within the same frequency range, e.g., within alpha or beta frequency bands. Yet, recent research shows that neuronal populations can also demonstrate phase synchronization between different frequency ranges. An extraction of such cross-frequency interactions in EEG/MEG recordings remains, however, methodologically challenging. Here we present a new method for the robust extraction of cross-frequency phase-to-phase synchronized components. Generalized Cross-Frequency Decomposition (GCFD) reconstructs the time courses of synchronized neuronal components, their spatial filters and patterns. Our method extends the previous state of the art, Cross-Frequency Decomposition (CFD), to the whole range of frequencies: it works for any f1 and f2 whenever f1:f2 is a rational number. GCFD gives a compact description of non-linearly interacting neuronal sources on the basis of their cross-frequency phase coupling. We successfully validated the new method in simulations and tested it with real EEG recordings including resting state data and steady state visually evoked potentials (SSVEP)