Patricia Milz

1 The problem of interest here concerns electrophysiological signals from two cortical sites, acquired as invasive intracranial recordings, or from non-invasive estimates of cortical electric neuronal activity computed from EEG or MEG recordings (see e.g. https://doi.org/10.1101/269753 ). In the absence of other sources, these measured signals consist of an instantaneous linear mixture of the true, actual, unobserved local signals, due to low spatial resolution and volume conduction. A connectivity measure is unreliable as a true indicator of electrophysiological connectivity if it is not invariant to mixing, or if it reports a significant connection for a mixture of independent signals. In (Vinck et al 2011 Neuroimage 55:1548) it was shown that coherence, imaginary coherence, and phase locking value are not invariant to mixing, while the phase lag index (PLI) and the weighted version (wPLI) are invariant to mixing. Here we show that the lagged coherence (LagCoh) measure (2007, https://arxiv.org/abs/0711.1455 ), not studied in Vinck et al, is invariant to mixing. Additionally, we present here a new mixture-invariant connectivity statistic: the “standardized imaginary covariance” (sImCov). We also include in the comparisons the directed PLI (dPLI) by Stam et al (2012 Neuroimage 62:1415). Fourier coefficients for “N” trials are generated from a linear unidirectional causal time domain model with electrophysiological delay “k” and regression coefficient “b”. 1000 random data sets of “N” trials are simulated, and for each one, and for each connectivity measure, non-parametric randomization tests are performed. The “true positive detection rate” is calculated as the fraction of 1000 cases that have significant connectivity at p<0.05, 0.1, and 0.2. The connectivity methods were compared in terms of detection rates, under non-mixed and mixed conditions, for small and large sample sizes “N”, with and without jitter for “k”, and for different values of signal to noise. Under mixing, the results show that LagCoh outperforms wPLI, PLI, dPLI, and sImCov. Without mixing, LagCoh and sImCov outperform wPLI, PLI, and dPLI. Finally, it is shown that dPLI is an invalid estimator of flow direction, i.e. it reverses and “goes against the flow” by merely changing the sign of one of the time series, a fact that violates the basic definition of Granger causality. For the sake of reproducible research, the supplementary material includes Delphi Pascal source code and all detailed result files in human readable format.

1. EEG/MEG neuroimaging consists of estimating the cortical distribution of time varying signals of electric neuronal activity, for the study of functional localization and connectivity. Currently, many different imaging methods are being used, with very different capabilities of correct localization of activity and of correct localization of connectivity. The aim here is to provide a guideline for choosing the best (i.e. least bad) imaging method. This first study is limited to the comparison of the following methods for EEG signals: sLORETA and eLORETA (standardized and exact low resolution electromagnetic tomography), MNE (minimum norm estimate), dSPM (dynamic statistical parametric mapping), and LCMVBs (linearly constrained minimum variance beamformers). These methods are linear, except for the LCMVBs that make use of the quadratic EEG covariances. To achieve a fair comparison, it is assumed here that the generators are independent and widely distributed (i.e. not few in number), giving a well-defined theoretical population EEG covariance matrix for use with the LCMVBs. Measures of localization error, false positive activity, and false positive connectivity are defined and computed under ideal no-noise conditions. It is empirically shown with extensive simulations that: (1) MNE, dSPM, and all LCMVBs are in general incapable of correct localization, while sLORETA and eLORETA have exact (zero-error) localization; (2) the brain volume with false positive activity is significantly larger for MN, dSPM, and all LCMVBs, as compared to sLORETA and eLORETA; and (3) the number of false positive connections is significantly larger for MN, dSPM, all LCMVBs, and sLORETA, as compared to eLORETA. Non-vague and fully detailed equations are given. PASCAL program codes and data files are available. It is noted that the results reported here do not apply to the LCMVBs based on EEG covariance matrices generated from extremely few generators, such as only one or two independent point sources.

1. The sharing and the transmission of information between cortical brain regions is carried out by mechanisms that are still not fully understood. A deeper understanding should shed light on how consciousness and cognition are implemented in the brain. Research activity in this field has recently been focusing on the discovery of non-conventional coupling mechanisms, such as all forms of cross-frequency couplings between diverse combinations of amplitudes and phases, applied to measured or estimated cortical signals of electric neuronal activity. However, all coupling measures that involve phase computation have poor statistical properties. In this work, the conventional estimators for the well-known phase-phase (phase synchronization or locking), phase-amplitude, and phaseamplitude-amplitude couplings are generalized by means of the weighted multiple regression model. The choice of appropriate weights produces estimators that bypass the need for computing the complex-valued phase. In addition, a new coupling, denoted as the inhibitory coupling (InhCo), is introduced and defined as the dependence of one complex-valued variable on the inverse and on the conjugate inverse of another complex-valued variable. A weighted version denoted as wInhCo is also introduced, bypassing the need for computing the inverse of a complex variable, which has very poor statistical properties. The importance of this form of inhibitory coupling is that it may capture well- known processes, such as the observed inverse alpha/gamma relation within the same cortical region, or the inverse alpha/alpha relation between distant cortical regions.

1. The problem of interest here is the study of brain functional and effective connectivity based non-invasive EEG-MEG inverse solution time series. These signals generally have low spatial resolution, such that an estimated signal at any one site is an instantaneous linear mixture of the true, actual, unobserved signals across all cortical sites. False connectivity can result from analysis of these low-resolution signals. Recent efforts toward “unmixing” have been developed, under the name of “leakage correction”. One recent noteworthy approach is that by Colclough et al (2015 NeuroImage, 117:439-448), which forces the inverse solution signals to have zero cross-correlation at lag zero. One goal is to show that Colclough’s method produces false human connectomes under very broad conditions. The second major goal is to develop a new solution, that appropriately “unmixes” the inverse solution signals, based on innovations orthogonalization. The new method first fits a multivariate autoregression to the inverse solution signals, giving the mixed innovations. Second, the mixed innovations are orthogonalized. Third, the mixed and orthogonalized innovations allow the estimation of the “unmixing” matrix, which is then finally used to “unmix” the inverse solution signals. It is shown that under very broad conditions, the new method produces proper human connectomes, even when the signals are not generated by an autoregressive model.

1. In a seminal paper by von Stein and Sarnthein (2000), it was hypothesized that “bottom-up” information processing of “content” elicits local, high frequency (beta-gamma) oscillations, whereas “top-down” processing is “contextual”, characterized by large scale integration spanning distant cortical regions, and implemented by slower frequency (theta-alpha) oscillations. This corresponds to a mechanism of cortical information transactions, where synchronization of beta-gamma oscillations between distant cortical regions is mediated by widespread theta-alpha oscillations . It is the aim of this paper to express this hypothesis quantitatively, in terms of a model that will allow testing this type of information transaction mechanism. The basic methodology used here corresponds to statistical mediation analysis, originally developed by (Baron and Kenny 1986). We generalize the classical mediator model to the case of multivariate complex-valued data, consisting of the discrete Fourier transform coefficients of signals of electric neuronal activity, at different frequencies, and at different cortical locations. The “mediation effect” is quantified here in a novel way, as the product of “dual frequency RV-coupling coefficients”, that were introduced in (Pascual-Marqui et al 2016, http://arxiv.org/abs/1603.05343 ). Relevant statistical procedures are presented for testing the cross-frequency mediation mechanism in general, and in particular for testing the von Stein & Sarnthein hypothesis.

Functional states of the brain are constituted by the temporally attuned activity of spatially distributed neural networks. Such networks can be identified by independent component analysis (ICA) applied to frequency-dependent source-localized EEG data. This methodology allows the identification of networks at high temporal resolution in frequency bands of established location-specific physiological functions. EEG measurements are sensitive to neural activity changes in cortical areas of modality-specific processing. We tested effects of modality-specific processing on functional brain networks. Phasic modality-specific processing was induced via tasks (state effects) and tonic processing was assessed via modality-specific person parameters (trait effects). Modality-specific person parameters and 64-channel EEG were obtained from 70 male, right-handed students. Person parameters were obtained using cognitive style questionnaires, cognitive tests, and thinking modality self-reports. EEG was recorded during four conditions: spatial visualization, object visualization, verbalization, and resting. Twelve cross-frequency networks were extracted from source-localized EEG across six frequency bands using ICA. RMANOVAs, Pearson correlations, and path modelling examined effects of tasks and person parameters on networks. Results identified distinct state- and trait-dependent functional networks. State-dependent networks were characterized by decreased, trait-dependent networks by increased alpha activity in sub-regions of modality-specific pathways. Pathways of competing modalities showed opposing alpha changes. State- and trait-dependent alpha were associated with inhibitory and automated processing, respectively. Antagonistic alpha modulations in areas of competing modalities likely prevent intruding effects of modality-irrelevant processing. Considerable research suggested alpha modulations related to modality-specific states and traits. This study identified the distinct electrophysiological cortical frequency-dependent networks within which they operate.

Meditation is a self-induced and willfully initiated practice that alters the state of consciousness. The meditation practice of Zazen, like many other meditation practices, aims at disregarding intrusive thoughts while controlling body posture. It is an open monitoring meditation characterized by detached moment-to-moment awareness and reduced conceptual thinking and self-reference. Which brain areas differ in electric activity during Zazen compared to task-free resting? Since scalp electroencephalography (EEG) waveforms are reference-dependent, conclusions about the localization of active brain areas are ambiguous. Computing intracerebral source models from the scalp EEG data solves this problem. In the present study, we applied source modeling using low resolution brain electromagnetic tomography (LORETA) to 58-channel scalp EEG data recorded from 15 experienced Zen meditators during Zazen and no-task resting. Zazen compared to no-task resting showed increased alpha-1 and alpha-2 frequency activity in an exclusively right-lateralized cluster extending from prefrontal areas including the insula to parts of the somatosensory and motor cortices and temporal areas. Zazen also showed decreased alpha and beta-2 activity in the left angular gyrus and decreased beta-1 and beta-2 activity in a large bilateral posterior cluster comprising the visual cortex, the posterior cingulate cortex and the parietal cortex. The results include parts of the default mode network and suggest enhanced automatic memory and emotion processing, reduced conceptual thinking and self-reference on a less judgmental, i.e., more detached moment-to-moment basis during Zazen compared to no-task resting.