Isolated effective coherence (iCoh): causal information flow excluding indirect paths

A problem of great interest in real world systems, where multiple time series measurements are available, is the estimation of the intra-system causal relations. For instance, electric cortical signals are used for studying functional connectivity between brain areas, their directionality, the direct or indirect nature of the connections, and the spectral characteristics (e.g. which oscillations are preferentially transmitted). The earliest spectral measure of causality was Akaike's (1968) seminal work on the noise contribution ratio, reflecting direct and indirect connections. Later, a major breakthrough was the partial directed coherence of Baccala and Sameshima (2001) for direct connections. The simple aim of this study consists of two parts: (1) To expose a major problem with the partial directed coherence, where it is shown that it is affected by irrelevant connections to such an extent that it can misrepresent the frequency response, thus defeating the main purpose for which the measure was developed, and (2) To provide a solution to this problem, namely the "isolated effective coherence", which consists of estimating the partial coherence under a multivariate auto-regressive model, followed by setting all irrelevant associations to zero, other than the particular directional association of interest. Simple, realistic, toy examples illustrate the severity of the problem with the partial directed coherence, and the solution achieved by the isolated effective coherence. For the sake of reproducible research, the software code implementing the methods discussed here (using lazarus free-pascal "www.lazarus.freepascal.org"), including the test data as text files, are freely available at: https://sites.google.com/site/pascualmarqui/home/icoh-isolated-effective-coherenceComment: 2014-02-21 pre-print, technical report, KEY Institute for Brain-Mind Research, University of Zurich, et a

The cross-frequency mediation mechanism of intracortical information transactions

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.Comment: https://doi.org/10.1101/119362 licensed as CC-BY-NC-ND 4.0 International license: http://creativecommons.org/licenses/by-nc-nd/4.0

The dual frequency RV-coupling coefficient: a novel measure for quantifying cross-frequency information transactions in the brain

Identifying dynamic transactions between brain regions has become increasingly important. Measurements within and across brain structures, demonstrating the occurrence of bursts of beta/gamma oscillations only during one specific phase of each theta/alpha cycle, have motivated the need to advance beyond linear and stationary time series models. Here we offer a novel measure, namely, the "dual frequency RV-coupling coefficient", for assessing different types of frequency-frequency interactions that subserve information flow in the brain. This is a measure of coherence between two complex-valued vectors, consisting of the set of Fourier coefficients for two different frequency bands, within or across two brain regions. RV-coupling is expressed in terms of instantaneous and lagged components. Furthermore, by using normalized Fourier coefficients (unit modulus), phase-type couplings can also be measured. The dual frequency RV-coupling coefficient is based on previous work: the second order bispectrum, i.e. the dual-frequency coherence (Thomson 1982; Haykin & Thomson 1998); the RV-coefficient (Escoufier 1973); Gorrostieta et al (2012); and Pascual-Marqui et al (2011). This paper presents the new measure, and outlines relevant statistical tests. The novel aspects of the "dual frequency RV-coupling coefficient" are: (1) it can be applied to two multivariate time series; (2) the method is not limited to single discrete frequencies, and in addition, the frequency bands are treated by means of appropriate multivariate statistical methodology; (3) the method makes use of a novel generalization of the RV-coefficient for complex-valued multivariate data; (4) real and imaginary covariance contributions to the RV-coherence are obtained, allowing the definition of a "lagged-coupling" measure that is minimally affected by the low spatial resolution of estimated cortical electric neuronal activity.Comment: technical report, pre-print, 2016-03-1

Temporo-Spatial Dynamics of Event-Related EEG Beta Activity during the Initial Contingent Negative Variation

In the electroencephalogram (EEG), early anticipatory processes are accompanied by a slow negative potential, the initial contingent negative variation (iCNV), occurring between 500 and 1500 ms after cue onset over prefrontal cortical regions in tasks with cue-target intervals of about 3 s or longer. However, the temporal sequence of the distributed cortical activity contributing to iCNV generation remains unclear. During iCNV generation, selectively enhanced low-beta activity has been reported. Here we studied the temporal order of activation foci in cortical regions assumed to underlie iCNV generation using source reconstruction of low-beta (13–18 Hz) activity. During the iCNV, elicited by a cued simple reaction-time task, low-beta power peaked first (750 ms after cue onset) in anterior frontal and limbic regions and last (140 ms later) in posterior areas. This activity occurred 3300 ms before target onset and provides evidence for the temporally ordered involvement of both cognitive-control and motor-preparation processes already at early stages during the preparation for speeded action

Understanding Actions of Others: The Electrodynamics of the Left and Right Hemispheres. A High-Density EEG Neuroimaging Study

Background: When we observe an individual performing a motor act (e.g. grasping a cup) we get two types of information on the basis of how the motor act is done and the context: what the agent is doing (i.e. grasping) and the intention underlying it (i.e. grasping for drinking). Here we examined the temporal dynamics of the brain activations that follow the observation of a motor act and underlie the observer’s capacity to understand what the agent is doing and why. Methodology/Principal Findings: Volunteers were presented with two-frame video-clips. The first frame (T0) showed an object with or without context; the second frame (T1) showed a hand interacting with the object. The volunteers were instructed to understand the intention of the observed actions while their brain activity was recorded with a high-density 128-channel EEG system. Visual event-related potentials (VEPs) were recorded time-locked with the frame showing the hand-object interaction (T1). The data were analyzed by using electrical neuroimaging, which combines a cluster analysis performed on the group-averaged VEPs with the localization of the cortical sources that give rise to different spatiotemporal states of the global electrical field. Electrical neuroimaging results revealed four major steps: 1) bilateral posterior cortical activations; 2) a strong activation of the left posterior temporal and inferior parietal cortices with almost a complete disappearance of activations in the right hemisphere; 3) a significant increase of the activations of the right temporo-parieta

Tinnitus Intensity Dependent Gamma Oscillations of the Contralateral Auditory Cortex

Non-pulsatile tinnitus is considered a subjective auditory phantom phenomenon present in 10 to 15% of the population. Tinnitus as a phantom phenomenon is related to hyperactivity and reorganization of the auditory cortex. Magnetoencephalography studies demonstrate a correlation between gamma band activity in the contralateral auditory cortex and the presence of tinnitus. The present study aims to investigate the relation between objective gamma-band activity in the contralateral auditory cortex and subjective tinnitus loudness scores. In unilateral tinnitus patients (N = 15; 10 right, 5 left) source analysis of resting state electroencephalographic gamma band oscillations shows a strong positive correlation with Visual Analogue Scale loudness scores in the contralateral auditory cortex (max r = 0.73, p<0.05). Auditory phantom percepts thus show similar sound level dependent activation of the contralateral auditory cortex as observed in normal audition. In view of recent consciousness models and tinnitus network models these results suggest tinnitus loudness is coded by gamma band activity in the contralateral auditory cortex but might not, by itself, be responsible for tinnitus perception

The Moore-Penrose Pseudoinverse. A Tutorial Review of the Theory

In the last decades the Moore-Penrose pseudoinverse has found a wide range of applications in many areas of Science and became a useful tool for physicists dealing, for instance, with optimization problems, with data analysis, with the solution of linear integral equations, etc. The existence of such applications alone should attract the interest of students and researchers in the Moore-Penrose pseudoinverse and in related sub jects, like the singular values decomposition theorem for matrices. In this note we present a tutorial review of the theory of the Moore-Penrose pseudoinverse. We present the first definitions and some motivations and, after obtaining some basic results, we center our discussion on the Spectral Theorem and present an algorithmically simple expression for the computation of the Moore-Penrose pseudoinverse of a given matrix. We do not claim originality of the results. We rather intend to present a complete and self-contained tutorial review, useful for those more devoted to applications, for those more theoretically oriented and for those who already have some working knowledge of the sub ject.Comment: 23 page

Attention-induced deactivations in very low frequency EEG oscillations: differential localisation according to ADHD symptom status

Background: the default-mode network (DMN) is characterised by coherent very low frequency (VLF) brain oscillations. The cognitive significance of this VLF profile remains unclear, partly because of the temporally constrained nature of the blood oxygen-level dependent (BOLD) signal. Previously we have identified a VLF EEG network of scalp locations that shares many features of the DMN. Here we explore the intracranial sources of VLF EEG and examine their overlap with the DMN in adults with high and low ADHD ratings.Methodology/Principal Findings: DC-EEG was recorded using an equidistant 66 channel electrode montage in 25 adult participants with high- and 25 participants with low-ratings of ADHD symptoms during a rest condition and an attention demanding Eriksen task. VLF EEG power was calculated in the VLF band (0.02 to 0.2 Hz) for the rest and task condition and compared for high and low ADHD participants. sLORETA was used to identify brain sources associated with the attention-induced deactivation of VLF EEG power, and to examine these sources in relation to ADHD symptoms. There was significant deactivation of VLF EEG power between the rest and task condition for the whole sample. Using s-LORETA the sources of this deactivation were localised to medial prefrontal regions, posterior cingulate cortex/precuneus and temporal regions. However, deactivation sources were different for high and low ADHD groups: In the low ADHD group attention-induced VLF EEG deactivation was most significant in medial prefrontal regions while for the high ADHD group this deactivation was predominantly localised to the temporal lobes.Conclusions/Significance: attention-induced VLF EEG deactivations have intracranial sources that appear to overlap with those of the DMN. Furthermore, these seem to be related to ADHD symptom status, with high ADHD adults failing to significantly deactivate medial prefrontal regions while at the same time showing significant attenuation of VLF EEG power in temporal lobe

Brain function assessment in different conscious states

Background: The study of brain functioning is a major challenge in neuroscience fields as human brain has a dynamic and ever changing information processing. Case is worsened with conditions where brain undergoes major changes in so-called different conscious states. Even though the exact definition of consciousness is a hard one, there are certain conditions where the descriptions have reached a consensus. The sleep and the anesthesia are different conditions which are separable from each other and also from wakefulness. The aim of our group has been to tackle the issue of brain functioning with setting up similar research conditions for these three conscious states.Methods: In order to achieve this goal we have designed an auditory stimulation battery with changing conditions to be recorded during a 40 channel EEG polygraph (Nuamps) session. The stimuli (modified mismatch, auditory evoked etc.) have been administered both in the operation room and the sleep lab via Embedded Interactive Stimulus Unit which was developed in our lab. The overall study has provided some results for three domains of consciousness. In order to be able to monitor the changes we have incorporated Bispectral Index Monitoring to both sleep and anesthesia conditions.Results: The first stage results have provided a basic understanding in these altered states such that auditory stimuli have been successfully processed in both light and deep sleep stages. The anesthesia provides a sudden change in brain responsiveness; therefore a dosage dependent anesthetic administration has proved to be useful. The auditory processing was exemplified targeting N1 wave, with a thorough analysis from spectrogram to sLORETA. The frequency components were observed to be shifting throughout the stages. The propofol administration and the deeper sleep stages both resulted in the decreasing of N1 component. The sLORETA revealed similar activity at BA7 in sleep (BIS 70) and target propofol concentration of 1.2 μg/mL.Conclusions: The current study utilized similar stimulation and recording system and incorporated BIS dependent values to validate a common approach to sleep and anesthesia. Accordingly the brain has a complex behavior pattern, dynamically changing its responsiveness in accordance with stimulations and states. © 2010 Ozgoren et al; licensee BioMed Central Ltd