Granger causality and information flow in multivariate processes

Blinowska, Katarzyna J.; Kuś, Rafał; Kamiński, Maciej

doi:10.1103/physreve.70.050902

Cited by 238 publications

(180 citation statements)

References 22 publications

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“…In contrast, EEG studies in healthy controls have revealed a front-to-back pattern of directed connectivity, particularly in the alpha band (17)(18)(19)(20)(21)(22), consistent with modeling studies that have shown that such patterns may arise due to differences in the number of anatomical connections (the degree) of anterior and posterior regions (22,23). However, modeled patterns of information flow depend on the assumed strength of the underlying structural connections (22)(23)(24), and the observed EEG patterns strongly depend on the choice of reference (25), which may explain why, controversially, the reverse back-tofront pattern has also been observed in EEG (26)(27)(28). An important advantage of MEG over EEG in this context is that it is referencefree.…”

supporting

confidence: 56%

“…17-22, but see refs. [26][27][28] is that the patterns of directionality in EEG strongly depend on the choice of reference (25). MEG, in contrast, is reference-free.…”

Section: Discussionmentioning

confidence: 99%

“…From these time series, the first 20 artifact-free epochs, containing 4,096 samples (3.2768 s), were selected to obtain stable results (70). These time series were then filtered in classical EEG/MEG frequency bands [delta (0.5-4 Hz), theta (4-8 Hz), alpha1 (8-10 Hz), alpha2 (10-13 Hz), beta (13)(14)(15)(16)(17)(18)(19)(20)(21)(22)(23)(24)(25)(26)(27)(28)(29)(30), and lower gamma (30-48 Hz)], using an offline discrete fast Fourier transform filter that does not distort the phases (BrainWave, version 0.9.150.6; home.kpn.nl/stam7883/brainwave.html). Subsequently, the instantaneous phase for each time series was computed by taking the argument of the analytic signal as computed using the Hilbert transform (see e.g., ref.…”

Section: Methodsmentioning

confidence: 99%

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Direction of information flow in large-scale resting-state networks is frequency-dependent

Hillebrand

Tewarie

Dellen

et al. 2016

Proc. Natl. Acad. Sci. U.S.A.

332

366

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Normal brain function requires interactions between spatially separated, and functionally specialized, macroscopic regions, yet the directionality of these interactions in large-scale functional networks is unknown. Magnetoencephalography was used to determine the directionality of these interactions, where directionality was inferred from time series of beamformer-reconstructed estimates of neuronal activation, using a recently proposed measure of phase transfer entropy. We observed well-organized posterior-to-anterior patterns of information flow in the higher-frequency bands (alpha1, alpha2, and beta band), dominated by regions in the visual cortex and posterior default mode network. Opposite patterns of anterior-toposterior flow were found in the theta band, involving mainly regions in the frontal lobe that were sending information to a more distributed network. Many strong information senders in the theta band were also frequent receivers in the alpha2 band, and vice versa. Our results provide evidence that large-scale resting-state patterns of information flow in the human brain form frequencydependent reentry loops that are dominated by flow from parietooccipital cortex to integrative frontal areas in the higher-frequency bands, which is mirrored by a theta band anterior-to-posterior flow.information flow | phase transfer entropy | resting-state networks | magnetoencephalography | atlas-based beamforming T he brain is an extremely complex system (1-3) containing, at the macroscopic scale, interconnected functional units (4) with more-or-less specific information processing capabilities (5). However, cognitive functions require the coordinated activity of these spatially separated units, where the oscillatory nature of neuronal activity may provide a possible mechanism (6-9). A complete description of these interactions, in terms of both strength and directionality, is therefore necessary for the understanding of both normal and abnormal brain functioning.Functional interactions may be inferred from statistical dependencies between the time series of neuronal activity at different sites, so-called functional connectivity (10). Indeed, interactions in large-scale functional networks have been observed using Electroencephalography, Magnetoencephalography (EEG/MEG) and functional Magnetic Resonance Imaging (fMRI) (e.g., refs. 11-14). However, as yet, little is known about the directionality of these interactions in large-scale functional networks during the resting state. Estimating directionality from fMRI is challenging due to its limited temporal resolution and indirect relation to neuronal activity (15, 16). In contrast, EEG studies in healthy controls have revealed a front-to-back pattern of directed connectivity, particularly in the alpha band (17-22), consistent with modeling studies that have shown that such patterns may arise due to differences in the number of anatomical connections (the degree) of anterior and posterior regions (22, 23). However, modeled patterns of information flow depend on the a...

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supporting

confidence: 56%

“…17-22, but see refs. [26][27][28] is that the patterns of directionality in EEG strongly depend on the choice of reference (25). MEG, in contrast, is reference-free.…”

Section: Discussionmentioning

confidence: 99%

Section: Methodsmentioning

confidence: 99%

See 1 more Smart Citation

Direction of information flow in large-scale resting-state networks is frequency-dependent

Hillebrand

Tewarie

Dellen

et al. 2016

Proc. Natl. Acad. Sci. U.S.A.

332

366

View full text Add to dashboard Cite

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“…They are due to: (i) unrobust methods of connectivity estimation, and, even more important, (ii) application of bivariate methods. The mechanism of generation of false connections in the case of bivariate networks was elucidated in [9,10].…”

Section: Discussionmentioning

confidence: 99%

Application of directed transfer function and network formalism for the assessment of functional connectivity in working memory task

Blinowska

Kamiński

Brzezicka

et al. 2013

Phil. Trans. R. Soc. A.

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The dynamic pattern of functional connectivity during a working memory task was investigated by means of the short-time directed transfer function. A clear-cut picture of transmissions was observed with the main centres of propagation located in the frontal and parietal regions, in agreement with imaging studies and neurophysiological hypotheses concerning the mechanisms of working memory. The study of the time evolution revealed that most of the time short-range interactions prevailed, whereas the communication between the main centres of activity occurred more sparsely and changed dynamically in time. The patterns of connectivity were quantified by means of a network formalism based on assortative mixing-an approach novel in the field of brain networks study. By means of application of the above method, we have demonstrated the existence of a modular structure of brain networks. The strength of interaction inside the modules was higher than between modules. The obtained results are compatible with theories concerning metabolic energy saving and efficient wiring in the brain, which showed that preferred organization includes modular structure with dense connectivity inside the modules and more sparse connections between the modules.

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“…Granger causality 2 refers to a family of synchrony measures that are derived from linear stochastic models of time series; as the above linear interdependence measures, they quantify to which extent different signals are linearly interdependent (see (Granger , 1969;Kamiński et al, 1991Kamiński et al, , 2005Gourévitch et al, 2006;Korzeniewska et al, 2003;Eichler, 2006;Blinowska et al, 2004;Ancona et al, 2004;Astolfi et al, 2004Astolfi et al, , 2005Schelter et al, 2005;Chen et al, 2006) for detailed information about Granger causality). Whereas the linear interdependence measures of Section 2.1 to 2.4 are bivariate, i.e., they can only be applied to pairs of signals, Granger causality measures are multivariate, they can be applied to multiple signals simultaneously.…”

Section: Granger Causalitymentioning

confidence: 99%

A comparative study of synchrony measures for the early diagnosis of Alzheimer's disease based on EEG

Dauwels

Vialatte

Musha³

et al. 2010

NeuroImage

371

384

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It is well known that EEG signals of Alzheimer's disease (AD) patients are generally less synchronous than in age-matched control subjects. However, this effect is not always easily detectable. This is especially the case for patients in the pre-symptomatic phase, commonly referred to as Mild Cognitive Impairment (MCI), during which neuronal degeneration is occurring prior to the clinical symptoms appearance. In this paper, various synchrony measures are studied in the context of AD diagnosis, including the correlation coefficient, mean-square and phase coherence, Granger causality, phase synchrony indices, information-theoretic divergence measures, state space based measures, and the recently proposed stochastic event synchrony measures. Experiments with EEG data show that many of those measures are strongly correlated (or anti-correlated) with the correlation coefficient, and hence, provide little complementary information about EEG synchrony. Measures that are only weakly correlated with the correlation coefficient include the phase synchrony indices, Granger causality measures, and stochastic-event synchrony measures. In addition, those three families of synchrony measures are mutually uncorrelated, and therefore, they each seem to capture a specific kind of interdependence. For the data set at hand, only two synchrony measures are able to convincingly distinguish AD patients from age-matched control patients, i.e., Granger causality (in particular, full-frequency directed transfer function) and stochastic event synchrony. Those two measures are used as features to distinguish MCI patients from age-matched control subjects, yielding a leave-one-out classification rate of 83%. The classification performance may be further improved by adding complementary features from EEG; this approach may eventually lead to a reliable EEG-based diagnostic tool for MCI and AD.

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Granger causality and information flow in multivariate processes

Cited by 238 publications

References 22 publications

Direction of information flow in large-scale resting-state networks is frequency-dependent

Direction of information flow in large-scale resting-state networks is frequency-dependent

Application of directed transfer function and network formalism for the assessment of functional connectivity in working memory task

A comparative study of synchrony measures for the early diagnosis of Alzheimer's disease based on EEG

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