Multivariate Granger causality: an estimation framework based on factorization of the spectral density matrix

Wen, Xiaotong; Rangarajan, Govindan; Ding, Mingzhou

doi:10.1098/rsta.2011.0610

Cited by 64 publications

(81 citation statements)

References 34 publications

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“…8c,d). Also, conditional GC influence analysis 21 left the pattern of results unchanged for gamma and beta, and suggested the involvement of larger networks for theta (Extended Data Fig. 9).…”

Section: Bastos Et Al Feedforward and Feedback Frequency Channelsmentioning

confidence: 99%

Visual areas exert feedforward and feedback influences through distinct frequency channels

Bastos

Vezoli

Bosman

et al. 2014

Preprint

178

284

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However, although these studies have revealed the anatomical paths and the neurophysiological consequences of influences in both directions, the neurophysiological mechanisms through which these influences are exerted remain largely elusive. Here we show that in the primate visual system, feedforward influences are carried by thetaband (~4 Hz) and gamma-band (~60-80 Hz) synchronization, and feedback influences by beta-band (~14-18 Hz) synchronization. These frequency-specific asymmetries in directed influences were revealed by simultaneous local field potential recordings from eight visual areas and an analysis of Granger-causal influences across all 28 pairs of areas. The asymmetries in directed influences correlated directly with asymmetries in anatomy and enabled us to build a visual cortical hierarchy from the influence asymmetries alone. Across different task periods, most areas stayed at their hierarchical position, whereas particularly frontal areas moved dynamically. Our results demonstrate that feedforward and feedback signalling use different frequency channels, which might subserve their differential communication requirements and lead to differential local consequences. The possibility to infer hierarchical relationships through functional data alone might make it possible to derive a cortical hierarchy in the living human brain.Many aspects of cognitive performance can only be explained through the concept of feedback influences. For example, reaction times are shortened when stimulus locations are pre-cued and attention can be pre-directed, an effect that cannot be explained if only constant feedforward input is considered 3 . Numerous neurophysiological studies have demonstrated the effects of feedback influences on neuronal activity 2 , yet the mechanisms through which feedback influences are exerted remain elusive. Anatomical studies have revealed that structural connections in the feedforward direction, i.e. from the primary sensory areas to higher order areas, are complemented by connections in the feedback direction 1,4 . In addition, it is well established that feedforward and feedback connections follow a characteristic pattern with regard to cortical layers: Feedforward connections target the granular layer 1 ; they originate preferentially in supragranular layers, and this preference is stronger for projections traversing more hierarchical levels, i.e. it is quantitatively related to the hierarchical distance 4 .Feedback connections avoid targeting the granular layer 1 ; they originate preferentially in the infragranular layers, and again, this preference is stronger for projections traversing more hierarchical levels and is thereby quantitatively related to hierarchical distance 4 . These asymmetries have been used to arrange the visual cortical areas into a hierarchy 1,4 , which has influenced many theories of cognition and brain function 5,6 .Recent studies have documented a neurophysiological asymmetry between cortical layers in visual cortex: While supragranular layers show local gam...

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Section: Bastos Et Al Feedforward and Feedback Frequency Channelsmentioning

confidence: 99%

Visual areas exert feedforward and feedback influences through distinct frequency channels

Bastos

Vezoli

Bosman

et al. 2014

Preprint

178

284

View full text Add to dashboard Cite

show abstract

“…A limitation on the use of bivariate Granger causality is that if the process in question contains more than two variables, then a conclusion of having an influence from one to another variable could come from the other mediate variables [81,82]. Therefore, in the estimation formulation, we should regress out the effect from other variables, here denoted by z(t ).…”

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

confidence: 99%

“…It is clear that once we compute the regression estimates of model parameters, if y has an influence on x, it should help predict x and the variance of the residual error on the second model should be decreased. It is stated in [81,82] that the bivariate Granger causality from y to x is quantified by the log-likelihood ratio…”

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

confidence: 99%

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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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“…Faes et al [18] address in the frequency domain the theoretically challenging issue of the dependence of causality on the canonical form of the multivariate model necessary to interpret instantaneous links resulting from the inadequate temporal resolution in relation to the latencies among signals. Wen et al [19] propose an efficient method for estimating Granger causality among a subgroup of signals present in Ω starting from the spectral density matrix describing all the causal interactions in Ω. Finally, Ramb et al [20] examine in the frequency domain the effects of the latent confounders on the renormalized partial directed coherence.…”

mentioning

confidence: 99%