Interaction patterns of brain activity across space, time and frequency. Part I: methods

We consider exploratory methods for the discovery of cortical functional connectivity. Typically, data for the i-th subject (i=1...NS) is represented as an NVxNT matrix Xi, corresponding to brain activity sampled at NT moments in time from NV cortical voxels. A widely used method of analysis first concatenates all subjects along the temporal dimension, and then performs an independent component analysis (ICA) for estimating the common cortical patterns of functional connectivity. There exist many other interesting variations of this technique, as reviewed in [Calhoun et al. 2009 Neuroimage 45: S163-172]. We present methods for the more general problem of discovering functional connectivity occurring at all possible time lags. For this purpose, brain activity is viewed as a function of space and time, which allows the use of the relatively new techniques of functional data analysis [Ramsay & Silverman 2005: Functional data analysis. New York: Springer]. In essence, our method first vectorizes the data from each subject, which constitutes the natural discrete representation of a function of several variables, followed by concatenation of all subjects. The singular value decomposition (SVD), as well as the ICA of this new matrix of dimension [rows=(NT*NV); columns=NS] will reveal spatio-temporal patterns of connectivity. As a further example, in the case of EEG neuroimaging, Xi of size NVxNW may represent spectral density for electric neuronal activity at NW discrete frequencies from NV cortical voxels, from the i-th EEG epoch. In this case our functional data analysis approach would reveal coupling of brain regions at possibly different frequencies.Comment: Technical report 2011-March-15, The KEY Institute for Brain-Mind Research Zurich, KMU Osak

Lagged coherence: explicit and testable definition

Measures of association between cortical regions based on activity signals provide useful information for studying brain functional connectivity. Difficulties occur with signals of electric neuronal activity, where an observed signal is a mixture, i.e. an instantaneous weighted average of the true, unobserved signals from all regions, due to volume conduction and low spatial resolution. This is why measures of lagged association are of interest, since at least theoretically, "lagged association" is of physiological origin. In contrast, the actual physiological instantaneous zero-lag association is masked and confounded by the mixing artifact. A minimum requirement for a measure of lagged association is that it must not tend to zero with an increase of strength of true instantaneous physiological association. Such biased measures cannot tell apart if a change in its value is due to a change in lagged or a change in instantaneous association. An explicit testable definition for frequency domain lagged connectivity between two multivariate time series is proposed. It is endowed with two important properties: it is invariant to non-singular linear transformations of each vector time series separately, and it is invariant to instantaneous association. As a first sanity check: in the case of two univariate time series, the new definition leads back to the bivariate lagged coherence of 2007 (eqs 25 and 26 in this https URL). As a second stronger sanity check: in the case of a univariate and multivariate vector time series, the new measure presented here leads back to the original multivariate lagged coherence of 2007 (eq 31 in this https URL), which again trivially includes the bivariate case

Coherent intracerebral brain oscillations during learned continuous tracking movements

The aim of the present study was to assess changes in electroencephalogram (EEG) phase locking between fronto-parietal areas, including the frontal and parietal motor areas, during audiomotor learning of continuous tracking movements. Subjects learned to turn a steering wheel according to a given trajectory in order to minimise the discrepancy between a changing foreground stimulus (controllable by the subjects) and a constant background stimulus. The results of the present study show that increasing practice of continuous tracking movements that are continuously performed in the presence of auditory feedback is not accompanied by decrease in phase locking between areas involved. Moreover, the study confirms that internally produced movements show enhanced coherent activities compared to externally guided movements and therefore suggests that the motor-parietal network is more engaged during internally produced than externally produced movement

Biclustering of gene expression data by non-smooth non-negative matrix factorization

BACKGROUND: The extended use of microarray technologies has enabled the generation and accumulation of gene expression datasets that contain expression levels of thousands of genes across tens or hundreds of different experimental conditions. One of the major challenges in the analysis of such datasets is to discover local structures composed by sets of genes that show coherent expression patterns across subsets of experimental conditions. These patterns may provide clues about the main biological processes associated to different physiological states. RESULTS: In this work we present a methodology able to cluster genes and conditions highly related in sub-portions of the data. Our approach is based on a new data mining technique, Non-smooth Non-Negative Matrix Factorization (nsNMF), able to identify localized patterns in large datasets. We assessed the potential of this methodology analyzing several synthetic datasets as well as two large and heterogeneous sets of gene expression profiles. In all cases the method was able to identify localized features related to sets of genes that show consistent expression patterns across subsets of experimental conditions. The uncovered structures showed a clear biological meaning in terms of relationships among functional annotations of genes and the phenotypes or physiological states of the associated conditions. CONCLUSION: The proposed approach can be a useful tool to analyze large and heterogeneous gene expression datasets. The method is able to identify complex relationships among genes and conditions that are difficult to identify by standard clustering algorithms

Cortical electrical activity changes in healthy aging using EEG-eLORETA analysis

Brain aging causes loss of synaptic spines, neuronal apoptosis, and a reduction in neurotransmitter levels. These aging phenomena disturb cortical electrical activity and its synchronization with connected regions. Previous electroencephalography (EEG) studies reported an age-related decrease in electrical activity in the alpha frequency band at occipital, parietal, and temporal areas as well as a decrease in occipital delta activity. However, there is an ongoing debate about whether there is an increase or decrease of the activity in other frequency bands with aging due to inconsistent study findings. In this study, we aimed to detect age-related changes of cortical electrical activities in all five frequency bands (delta, theta, alpha, beta, and gamma) in a large sample of healthy subjects for the first time. Using eLORETA (exact low-resolution brain electromagnetic tomography) analysis, we applied an eLORETA source estimation method to resting-state EEG data in 147 healthy subjects (median age 55, IQR 26.5–67.0) to obtain cortical electrical activity and assessed age-related changes in this activity using correlation analysis with multiple comparison correction. The combination of the eLORETA source estimation method and correlation analysis implemented in eLORETA software detected age-related changes in specific cortical regions for each frequency band: (1) delta and theta cortical electrical activities decreased at the occipital area with age, (2) alpha cortical electrical activity decreased at the occipitoparietotemporal areas with age, (3) beta cortical electrical activity increased at the insula, sensorimotor area, supplementary motor area, premotor area, and right temporal areas with age (most significant correlation at the right insula), (4) gamma cortical electrical activity increased at the frontoparietal and left temporal areas with age. These findings extend previous EEG study findings and provide valuable information related to mechanisms of healthy aging. Overall, our findings revealed that even healthy aging greatly affects cortical electrical activities in a region-specific way

First Valence, Then Arousal: The Temporal Dynamics of Brain Electric Activity Evoked by Emotional Stimuli

The temporal dynamics of the neural activity that implements the dimensions valence and arousal during processing of emotional stimuli were studied in two multi-channel ERP experiments that used visually presented emotional words (experiment1) and emotional pictures (experiment2) as stimulus material. Thirty-two healthy subjects participated (mean age 26.8±6.4years, 24 women). The stimuli in both experiments were selected on the basis of verbal reports in such a way that we were able to map the temporal dynamics of one dimension while controlling for the other one. Words (pictures) were centrally presented for 450 (600) ms with interstimulus intervals of 1,550 (1,400) ms. ERP microstate analysis of the entire epochs of stimulus presentations parsed the data into sequential steps of information processing. The results revealed that in several microstates of both experiments, processing of pleasant and unpleasant valence (experiment1, microstate #3: 118-162ms, #6: 218-238ms, #7: 238-266ms, #8: 266-294ms; experiment2, microstate #5: 142-178ms, #6: 178-226ms, #7: 226-246ms, #9: 262-302ms, #10: 302-330ms) as well as of low and high arousal (experiment1, microstate #8: 266-294ms, #9: 294-346ms; experiment2, microstate #10: 302-330ms, #15: 562-600ms) involved different neural assemblies. The results revealed also that in both experiments, information about valence was extracted before information about arousal. The last microstate of valence extraction was identical with the first microstate of arousal extractio

The resting microstate networks (RMN): cortical distributions, dynamics, and frequency specific information flow

A brain microstate is characterized by a unique, fixed spatial distribution of electrically active neurons with time varying amplitude. It is hypothesized that a microstate implements a functional/physiological state of the brain during which specific neural computations are performed. Based on this hypothesis, brain electrical activity is modeled as a time sequence of non-overlapping microstates with variable, finite durations (Lehmann and Skrandies 1980, 1984; Lehmann et al 1987). In this study, EEG recordings from 109 participants during eyes closed resting condition are modeled with four microstates. In a first part, a new confirmatory statistics method is introduced for the determination of the cortical distributions of electric neuronal activity that generate each microstate. All microstates have common posterior cingulate generators, while three microstates additionally include activity in the left occipital/parietal, right occipital/parietal, and anterior cingulate cortices. This appears to be a fragmented version of the metabolically (PET/fMRI) computed default mode network (DMN), supporting the notion that these four regions activate sequentially at high time resolution, and that slow metabolic imaging corresponds to a low-pass filtered version. In the second part of this study, the microstate amplitude time series are used as the basis for estimating the strength, directionality, and spectral characteristics (i.e., which oscillations are preferentially transmitted) of the connections that are mediated by the microstate transitions. The results show that the posterior cingulate is an important hub, sending alpha and beta oscillatory information to all other microstate generator regions. Interestingly, beyond alpha, beta oscillations are essential in the maintenance of the brain during resting state.Comment: pre-print, technical report, The KEY Institute for Brain-Mind Research (Zurich), Kansai Medical University (Osaka

Innovations orthogonalization: a solution to the major pitfalls of EEG/MEG "leakage correction"

The problem of interest here is the study of brain functional and effective connectivity based on 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.Comment: preprint, technical report, under license "Attribution-NonCommercial-NoDerivatives 4.0 International (CC BY-NC-ND 4.0)", https://creativecommons.org/licenses/by-nc-nd/4.0