Nonlinear interaction decomposition (NID): A method for separation of crossfrequency coupled sources in human brain Abstract   Crossfrequency 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 (MEGEEG), which we refer to as Nonlinear Interaction Decomposition (NID). In contrast to all previous methods for separation of crossfrequency (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 nonGaussian distribution. We evaluate this argument analytically for amplitudemodulated narrowband oscillations which are either phasephase or amplitudeamplitude 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     xe2x88x92  15     (dB). Additionally, we applied NID to the restingstate EEG of 81 subjects to characterize CF phasephase 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 restingstate EEG data. All codes are available publicly via GitHub.

Neurocurrent response functions: A unified approach to MEG source analysis under the continuous stimuli paradigm Abstract   Characterizing the neural dynamics underlying sensory processing is one of the central areas of investigation in systems and cognitive neuroscience. Neuroimaging techniques such as magnetoencephalography (MEG) and Electroencephalography (EEG) have provided significant insights into the neural processing of continuous stimuli, such as speech, thanks to their high temporal resolution. Existing work in the context of auditory processing suggests that certain features of speech, such as the acoustic envelope, can be used as reliable linear predictors of the neural response manifested in MEEG. The corresponding linear filters are referred to as temporal response functions (TRFs). While the functional roles of specific components of the TRF are wellstudied and linked to behavioral attributes such as attention, the cortical origins of the underlying neural processes are not as well understood.  In this work, we address this issue by estimating a linear filter representation of cortical sources directly from neuroimaging data in the context of continuous speech processing. To this end, we introduce NeuroCurrent Response Functions (NCRFs), a set of linear filters, spatially distributed throughout the cortex, that predict the cortical currents giving rise to the observed ongoing MEG (or EEG) data in response to continuous speech. NCRF estimation is cast within a Bayesian framework, which allows unification of the TRF and source estimation problems, and also facilitates the incorporation of prior information on the structural properties of the NCRFs. To generalize this analysis to MEEG recordings which lack individual structural magnetic resonance (MR) scans, NCRFs are extended to freeorientation dipoles and a novel regularizing scheme is put forward to lessen reliance on finetuned coordinate coregistration. We present a fast estimation algorithm, which we refer to as the  ChampLasso  algorithm, by leveraging recent advances in optimization, and demonstrate its utility through application to simulated and experimentally recorded MEG data under auditory experiments. Our simulation studies reveal significant improvements over existing methods that typically operate in a twostage fashion, in terms of spatial resolution, response function reconstruction, and recovering dipole orientations. The analysis of experimentallyrecorded MEG data without MR scans corroborates existing findings, but also delineates the distinct cortical distribution of the underlying neural processes at high spatiotemporal resolution. In summary, we provide a principled modeling and estimation paradigm for MEG source analysis tailored to extracting the cortical origin of electrophysiological responses to continuous stimuli.