Nonlinear interaction decomposition (NID): A method for separation of cross-frequency coupled sources in human brain

Mina Jamshidi Idaji, Klaus Robert Müller, Guido Nolte, Burkhard Maess, Arno Villringer, Vadim V. Nikulin

Research output: Contribution to journalArticlepeer-review

4 Citations (Scopus)


Cross-frequency coupling (CFC) between neuronal oscillations reflects an integration of spatially and spectrally distributed information in the brain. Here, we propose a novel framework for detecting such interactions in Magneto- and Electroencephalography (MEG/EEG), which we refer to as Nonlinear Interaction Decomposition (NID). In contrast to all previous methods for separation of cross-frequency (CF) sources in the brain, we propose that the extraction of nonlinearly interacting oscillations can be based on the statistical properties of their linear mixtures. The main idea of NID is that nonlinearly coupled brain oscillations can be mixed in such a way that the resulting linear mixture has a non-Gaussian distribution. We evaluate this argument analytically for amplitude-modulated narrow-band oscillations which are either phase-phase or amplitude-amplitude CF coupled. We validated NID extensively with simulated EEG obtained with realistic head modelling. The method extracted nonlinearly interacting components reliably even at SNRs as small as −15 dB. Additionally, we applied NID to the resting-state EEG of 81 subjects to characterize CF phase-phase coupling between alpha and beta oscillations. The extracted sources were located in temporal, parietal and frontal areas, demonstrating the existence of diverse local and distant nonlinear interactions in resting-state EEG data. All codes are available publicly via GitHub.

Original languageEnglish
Article number116599
Publication statusPublished - 2020 May 1


  • Cross-frequency coupling
  • EEG
  • ICA
  • Independent component analysis
  • MEG
  • NID
  • Nonlinear interaction decomposition
  • Nonlinear neuronal interactions

ASJC Scopus subject areas

  • Neurology
  • Cognitive Neuroscience


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