Generalized Partial Directed Coherence

Baccalá, Luiz Antonio; Sameshima, Koichi; Takahashi, Daniel Yasumasa

doi:10.1109/icdsp.2007.4288544

Cited by 233 publications

(228 citation statements)

References 10 publications

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“…Although PDC has proved to be an accurate tool for the detection of direct connectivities, both in cases of coupled oscillators (Baccalá and Sameshima 2001;Winterhalder et al 2005;Gourévitch et al 2006;Schelter et al 2006a) or simple neuronal models of interconnected neurons (Sameshima and Baccalá 1999;Kamiński et al 2001;Astolfi et al 2007), it has been shown that large differences in the variances of the modeled time series can yield distortions in the resulting PDC values (Winterhalder et al 2005;Baccala et al 2007). For example, a set of three uncorrelated white noise processes, where two of them have much larger variance than the third, will produce a distorted connectivity profile, since PDC wrongly detects connections from the low-variance process to the other two (Winterhalder et al 2005).…”

Section: Partial Directed Coherencementioning

confidence: 99%

Assessing cortico-hippocampal functional connectivity under anesthesia and kainic acid using generalized partial directed coherence

et al. 2010

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A significant challenge in modern neuroscience lies in determining the functional connectivity between discrete populations of neurones and brain regions. In this study, a variation of partial directed coherence, the generalized partial directed coherence (gPDC), along with a newly proposed critical value for gPDC, were applied on recorded local field potentials (LFPs) and single-unit activity, in order to assess information flow between medial prefrontal cortex (mPFC) and hippocampus and within the hippocampus of the rat brain, under isoflurane anesthesia and kainic acid-induced enhanced neuronal activity. Our findings suggest that, under anesthesia, there exists a continuous information flow from hippocampus towards mPFC, reversed mostly during activity bursts occurring in the mPFC. Moreover, there was a clear directional connection from the lateral towards medial dorsal hippocampus, most prominent in the beta frequency band (10-30 Hz). Kainic acid resulted in partially disrupting the reciprocal cortico-hippocampal connectivity and reversing the intra-hippocampal one. The biological implications of these findings on the effects of anesthesia and kainic acid in brain connectivity, along with implementation issues of gPDC analysis on field potentials and spike trains, are extensively discussed.

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Section: Partial Directed Coherencementioning

confidence: 99%

Assessing cortico-hippocampal functional connectivity under anesthesia and kainic acid using generalized partial directed coherence

et al. 2010

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“…eDC and ePDC constitute an extension of the well-known DC and PDC functions [6][7][8][9], the extension being in the fact that they are derived from the extended model (2.1), which describes instantaneous effects in addition to the commonly studied lagged effects. When we use the extended measures (2.2) and (2.3), the information that flows from one process to another is both lagged (k > 0) and instantaneous (k = 0), because it is measured in the frequency domain by the functionB(f ) = I − B(f ), which incorporates both B(0) and B(k) with k > 0, and by its inverse G(f ).…”

Section: (B) Extended Multivariate Autoregressive Processesmentioning

confidence: 99%

“…nDC and nPDC constitute a variant of the known DC and PDC functions [6][7][8][9], the variation being in the fact that they are derived from the MVAR model (2.1), including instantaneous effects, rather than from a classic strictly causal MVAR model. It can be shown that, because, in the absence of instantaneous causality, the eMVAR model reduces to a strictly causal model (see §3a), in this case, eDC and nDC amount to the DC, whereas ePDC and nPDC amount to the PDC.…”

Section: (B) Extended Multivariate Autoregressive Processesmentioning

confidence: 99%

“…A pioneering approach was that proposed by Akaike [5], who introduced a causality measure based on spectral decomposition, the so-called noise contribution ratio, which was named directed coherence (DC) by Saito & Harashima [6] for bivariate time series, and was used in the context of MV time series later on [7]. As a further step, partial directed coherence (PDC) was introduced by Baccala & Sameshima [8,9] as a straightforward frequency domain descriptor of Granger causality. DC and PDC are derived as factors in the decomposition of ordinary coherence and partial coherence and, as such, are able to elicit information on directionality from the spectral representation of multiple time series [10].…”

Section: Introductionmentioning

confidence: 99%

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A framework for assessing frequency domain causality in physiological time series with instantaneous effects

Faes

Erla

Porta

et al. 2013

Phil. Trans. R. Soc. A.

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We present an approach for the quantification of directional relations in multiple time series exhibiting significant zero-lag interactions. To overcome the limitations of the traditional multivariate autoregressive (MVAR) modelling of multiple series, we introduce an extended MVAR (eMVAR) framework allowing either exclusive consideration of time-lagged effects according to the classic notion of Granger causality, or consideration of combined instantaneous and lagged effects according to an extended causality definition. The spectral representation of the eMVAR model is exploited to derive novel frequency domain causality measures that generalize to the case of instantaneous effects the known directed coherence (DC) and partial DC measures. The new measures are illustrated in theoretical examples showing that they reduce to the known measures in the absence of instantaneous causality, and describe peculiar aspects of directional interaction among multiple series when instantaneous causality is non-negligible. Then, the issue of estimating eMVAR models from time-series data is faced, proposing two approaches for model identification and discussing problems related to the underlying model assumptions. Finally, applications of the framework on cardiovascular variability series and multichannel EEG recordings are presented, showing how it allows one to highlight patterns of frequency domain causality consistent with well-interpretable physiological interaction mechanisms.

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“…In • Partial directed coherence (PDC) was first proposed by [76] as a normalization of A(z) with the assumption that Σ is diagonal. The form has been renormalized in many ways: to include noise covariance in the normalization [79], or to provide meaningful connection strength [80]. The following description is proposed in [79] and described in [8].…”

Section: Therefore the Z Transform Of The Ar Equation Is A(z)y (Z) =mentioning

confidence: 99%

A Review on Dependence Measures in Exploring Brain Networks from fMRI Data

Pruttiakaravanich

Songsiri

2016

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Abstract. Functional magnetic resonance imaging (fMRI) technique allows us to capture activities occurring in a human brain via signals related to cerebral blood flow, oxygen metabolism and blood volume, known as BOLD (blood oxygen level-dependent) signals. Exploring relationships between brain regions inside human brains from fMRI data is an active and challenging research topic. Relationships or associations between brain regions are commonly referred to as brain connectivity or brain network. This connectivity can be divided into three groups; (i) structural connectivity representing physically anatomical connections between regions, (ii) the functional connectivity which describes the statistical information among brain regions and (iii) the effective connectivity which specifies how one region interacts with others by a causal model. This survey paper provides a review on learning brain connectivities via fMRI data where detailed mathematical definitions of dependence measures widely-used for functional and effective connectivities are described. These measures include correlation, partial correlation, coherence, partial coherence, directed coherence, partial directed coherence, Granger causality, and other concepts such as dynamical causal modeling or structural equation modeling. Interpretation and relations of these measures as well as relevant estimation techniques that are widely used in the problems of fMRI modeling are summarized in this paper.

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Generalized Partial Directed Coherence

Cited by 233 publications

References 10 publications

Assessing cortico-hippocampal functional connectivity under anesthesia and kainic acid using generalized partial directed coherence

Assessing cortico-hippocampal functional connectivity under anesthesia and kainic acid using generalized partial directed coherence

A framework for assessing frequency domain causality in physiological time series with instantaneous effects

A Review on Dependence Measures in Exploring Brain Networks from fMRI Data

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