Cross-Frequency Decomposition: A novel technique for studying interactions between neuronal oscillations with different frequencies

Neuronal synchronization has been hypothesized as one mechanism allowing efficient communication between the neurons. In addition to interactions typically calculated at the same frequency range, phase synchronization between different frequency ranges has been demonstrated recently. Here, we present a novel method for the extraction of neuronal components showing cross-frequency phase synchronization. The method allows a compact representation of the sets of interacting components without the need to perform inverse modeling. In general it can be applied for the detection of phase interactions between components with frequencies f1 and f2, where f2=rf1 and r is some integer. This class of interactions includes alpha: beta and alpha: gamma synchronization frequently observed in EEG and MEG recordings. We refer to this method as Cross-Frequency Decomposition (CFD), which consists of the following steps: a) extraction of f1-oscillations with the spatio-spectral decomposition algorithm (SSD); b) frequency modification of the f1-oscillations obtained with SSD; and c) finding f2–oscillations synchronous with f1-oscillations using least-squares estimation. Our simulations showed that CFD was capable of recovering interacting components even when the signal-to-noise ratio was as low as 0.01. An application of CFD to real EEG data demonstrated that cross-frequency phase synchronization between alpha and beta oscillations can originate from the same or remote neuronal groups. While interactions occurring at the same spatial location can potentially indicate quasi-sinusoidal waveform of neuronal oscillations, any synchronization between spatially remote populations is likely to indicate genuine neurophysiological interactions between oscillations with different frequency content.