Dear Colleagues,
For those of you interested in this topic, I would like to point your
attention to two recently developed methods for connectivity analysis
based on time series of brain activity:

1. "The dual frequency RV-coupling coefficient: a novel measure for
quantifying cross-frequency information transactions in the brain"
http://arxiv.org/abs/1603.05343

2. "The isolated effective coherence"
http://journal.frontiersin.org/article/10.3389/fnhum.2014.00448/abstract

(abstracts below)
Cordially,
Roberto

...
Roberto D. Pascual-Marqui, PhD, PD ([log in to unmask])
The KEY Institute for Brain-Mind Research, University of Zurich
Visiting Professor at Neuropsychiatry, Kansai Medical University, Osaka
[www.keyinst.uzh.ch/loreta] [www.researcherid.com/rid/A-2012-2008]
[scholar.google.com/citations?user=pascualmarqui]

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ABSTRACT: dual frequency RV-coupling coefficient
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.

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ABSTRACT: isolated effective coherence
Functional connectivity is of central importance in understanding
brain function. For this purpose, multiple time series of electric
cortical activity can be used for assessing the properties of a
network: the strength, directionality, and spectral characteristics
(i.e., which oscillations are preferentially transmitted) of the
connections. The partial directed coherence (PDC) of Baccala and
Sameshima (2001) is a widely used method for this problem. The three
aims of this study are: (1) To show that the PDC can misrepresent the
frequency response under plausible realistic conditions, thus
defeating the main purpose for which the measure was developed; (2) To
provide a solution to this problem, namely the “isolated effective
coherence” (iCoh), which consists of estimating the partial coherence
under a multivariate autoregressive model, followed by setting all
irrelevant associations to zero, other than the particular directional
association of interest; and (3) To show that adequate iCoh estimators
can be obtained from non-invasively computed cortical signals based on
exact low resolution electromagnetic tomography (eLORETA) applied to
scalp EEG recordings. To illustrate the severity of the problem with
the PDC, and the solution achieved by the iCoh, three examples are
given, based on: (1) Simulated time series with known dynamics; (2)
Simulated cortical sources with known dynamics, used for generating
EEG recordings, which are then used for estimating (with eLORETA) the
source signals for the final connectivity assessment; and (3) EEG
recordings in rats. Lastly, real human recordings are analyzed, where
the iCoh between six cortical regions of interest are calculated and
compared under eyes open and closed conditions, using 61-channel EEG
recordings from 109 subjects. During eyes closed, the posterior
cingulate sends alpha activity to all other regions. During eyes open,
the anterior cingulate sends theta-alpha activity to other frontal
regions.
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