Localizing bicoherence from EEG and MEG.

We propose a new method for the localization of nonlinear cross-frequency coupling in EEG and MEG data analysis, based on the estimation of bicoherences at the source level. While for the analysis of rhythmic brain activity, source directions are commonly chosen to maximize power, we suggest to maximize bicoherence instead. The resulting nonlinear cost function can be minimized effectively using a gradient approach. We argue, that bicoherence is also a generally useful tool to analyze phase-amplitude coupling (PAC), by deriving formal relations between PAC and bispectra. This is illustrated in simulated and empirical LFP data. The localization method is applied to EEG resting state data, where the most prominent bicoherence signatures originate from the occipital alpha rhythm and the mu rhythm. While the latter is hardly visible using power analysis, we observe clear bicoherence peaks in the high alpha range of sensorymotor areas. We additionally apply our method to resting-state data of subjects with schizophrenia and healthy controls and observe significant bicoherence differences in motor areas which could not be found from analyzing power differences.

The LDA beamformer: Optimal estimation of ERP source time series using linear discriminant analysis.

We introduce a novel beamforming approach for estimating event-related potential (ERP) source time series based on regularized linear discriminant analysis (LDA). The optimization problems in LDA and linearly-constrained minimum-variance (LCMV) beamformers are formally equivalent. The approaches differ in that, in LCMV beamformers, the spatial patterns are derived from a source model, whereas in an LDA beamformer the spatial patterns are derived directly from the data (i.e., the ERP peak). Using a formal proof and MEG simulations, we show that the LDA beamformer is robust to correlated sources and offers a higher signal-to-noise ratio than the LCMV beamformer and PCA. As an application, we use EEG data from an oddball experiment to show how the LDA beamformer can be harnessed to detect single-trial ERP latencies and estimate connectivity between ERP sources. Concluding, the LDA beamformer optimally reconstructs ERP sources by maximizing the ERP signal-to-noise ratio. Hence, it is a highly suited tool for analyzing ERP source time series, particularly in EEG/MEG studies wherein a source model is not available.

Localizing true brain interactions from EEG and MEG data with subspace methods and modified beamformers.

To address the problem of mixing in EEG or MEG connectivity analysis we exploit that noninteracting brain sources do not contribute systematically to the imaginary part of the cross-spectrum. Firstly, we propose to apply the existing subspace method "RAP-MUSIC" to the subspace found from the dominant singular vectors of the imaginary part of the cross-spectrum rather than to the conventionally used covariance matrix. Secondly, to estimate the specific sources interacting with each other, we use a modified LCMV-beamformer approach in which the source direction for each voxel was determined by maximizing the imaginary coherence with respect to a given reference. These two methods are applicable in this form only if the number of interacting sources is even, because odd-dimensional subspaces collapse to even-dimensional ones. Simulations show that (a) RAP-MUSIC based on the imaginary part of the cross-spectrum accurately finds the correct source locations, that (b) conventional RAP-MUSIC fails to do so since it is highly influenced by noninteracting sources, and that (c) the second method correctly identifies those sources which are interacting with the reference. The methods are also applied to real data for a motor paradigm, resulting in the localization of four interacting sources presumably in sensory-motor areas.