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
Affiliations
Mina Jamshidi Idaji
Department of Neurology, Max Planck Institute for Human Cognitive and Brain Sciences, Leipzig, Germany; Machine Learning Group, Technical University of Berlin, Berlin, Germany; International Max Planck Research School NeuroCom, Leipzig, Germany
Klaus-Robert Müller
Machine Learning Group, Technical University of Berlin, Berlin, Germany; Department of Brain and Cognitive Engineering, Korea University, Anam-dong, Seongbuk-gu, Seoul, Republic of Korea; Max Planck Institute for Informatics, Stuhlsatzenhausweg, Saarbrücken, Germany
Guido Nolte
Department of Neurophysiology and Pathophysiology, University Medical Center Hamburg-Eppendorf, Hamburg, Germany
Burkhard Maess
MEG and Cortical Networks Group, Max Planck Institute for Human Cognitive and Brain Sciences, Leipzig, Germany
Arno Villringer
Department of Neurology, Max Planck Institute for Human Cognitive and Brain Sciences, Leipzig, Germany; Department of Cognitive Neurology, University Hospital Leipzig, Leipzig, Germany
Vadim V. Nikulin
Department of Neurology, Max Planck Institute for Human Cognitive and Brain Sciences, Leipzig, Germany; Centre for Cognition and Decision Making, Institute for Cognitive Neuroscience, National Research University Higher School of Economics, Moscow, Russia; Neurophysics Group, Department of Neurology, Charité-Universitätsmedizin Berlin, Berlin, Germany; Corresponding author. Max Planck Institute for Human Cognitive and Brain Sciences, Leipzig, Germany.
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.
