Analysing connectivity with Granger causality and dynamic causal modelling

Friston, Karl J.; Moran, Rosalyn J.; Seth, Anil K.

doi:10.1016/j.conb.2012.11.010

Cited by 569 publications

(437 citation statements)

References 57 publications

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“…The determination of a VAR model (1) should not be taken to imply that the time series data modelled by the stochastic process U t was actually generated by a linear autoregressive scheme. In comparison to effective connectivity techniques like dynamic causal modelling [DCM] (Friston et al, 2003), which make very explicit assumptions about the generative mechanism underlying the observed data (Friston et al, 2013), the VAR models underlying G-causality are "generic", in the sense that they make no assumptions about the mechanism that produced the data, beyond that a VAR model actually exists. Standard theory (Anderson, 1971) yields that a rather general class of covariance-stationary multivariate process-including many nonlinear processes-may be modelled as VARs, albeit of theoretically infinite order (see also the next Section).…”

Section: G-causality: Theory Estimation and Inferencementioning

confidence: 99%

“…Methodological development in this application domain is rapidly advancing and a full review is beyond the present scope (see, for example, Deshpande and Hu, 2012;Friston et al, 2013;Bressler and Seth, 2011;Ding et al, 2006). This section summarises some of the main issues involved in application of G-causality (as implemented by the MVGC toolbox) to some of the more common varieties of neuroscience time-series data.…”

Section: Application To Neuroscience Time Series Datamentioning

confidence: 99%

“…Alternative promising approaches include estimation of state-space models which jointly parameterize functional connectivity and hemodynamic responses (Ryali et al, 2011) or blind deconvolution of the HRF to retrieve the underlying neuronal processes (Havlicek et al, 2011;Wu et al, 2013). In general, G-causality of fMRI BOLD data should be treated with caution and may best be interpreted as exploratory (Friston et al, 2013). See Seth et al (2013) for further discussion of this important application domain.…”

Section: Application To Fmri Bold Datamentioning

confidence: 99%

“…Importantly, G-causality is a measure of directed functional connectivity in terms of providing a statistical description of observed responses. In contrast, methods for identifying effective connectivity aim to elucidate the "the simplest possible circuit diagram explaining observed responses" (ValdesSosa et al, 2011;Aertsen and Preißl, 1991;Friston et al, 2003Friston et al, , 2013.…”

Section: Introductionmentioning

confidence: 99%

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The MVGC multivariate Granger causality toolbox: A new approach to Granger-causal inference

Barnett

Seth

2014

Journal of Neuroscience Methods

805

840

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Background: Wiener-Granger causality ("G-causality") is a statistical notion of causality applicable to time series data, whereby cause precedes, and helps predict, effect. It is defined in both time and frequency domains, and allows for the conditioning out of common causal influences. Originally developed in the context of econometric theory, it has since achieved broad application in the neurosciences and beyond. Prediction in the G-causality formalism is based on VAR (Vector AutoRegressive) modelling.New Method: The MVGC Matlab c Toolbox approach to G-causal inference is based on multiple equivalent representations of a VAR model by (i) regression parameters, (ii) the autocovariance sequence and (iii) the cross-power spectral density of the underlying process. It features a variety of algorithms for moving between these representations, enabling selection of the most suitable algorithms with regard to computational efficiency and numerical accuracy.Results: In this paper we explain the theoretical basis, computational strategy and application to empirical G-causal inference of the MVGC Toolbox. We also show via numerical simulations the advantages of our Toolbox over previous methods in terms of computational accuracy and statistical inference. Comparison with Existing Method(s):The standard method of computing G-causality involves estimation of parameters for both a full and a nested (reduced) VAR model. The MVGC approach, by contrast, avoids explicit estimation of the reduced model, thus eliminating a source of estimation error and improving statistical power, and in addition facilitates fast and accurate estimation of the computationally awkward case of conditional G-causality in the frequency domain. Conclusions:The MVGC Toolbox implements a flexible, powerful and efficient approach to G-causal inference.

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Section: G-causality: Theory Estimation and Inferencementioning

confidence: 99%

Section: Application To Neuroscience Time Series Datamentioning

confidence: 99%

Section: Application To Fmri Bold Datamentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

The MVGC multivariate Granger causality toolbox: A new approach to Granger-causal inference

Barnett

Seth

2014

Journal of Neuroscience Methods

805

840

View full text Add to dashboard Cite

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“…Therefore, the analysis of effective connectivity requires two important concepts; a selection of causal model and model parameter estimation. Common techniques of exploring the effective connectivity includes dynamic causal modeling (DCM) [39,6,13,40,41,42], Granger causal modeling (GCM) [42,43,41,13,44] and structural equation modeling (SEM) [45,46,47,20,48].…”

Section: Effective Connectivitymentioning

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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Association of Seizure Spread With Surgical Failure in Epilepsy

et al. 2019

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IMPORTANCE Seizures recur in as many as half of patients who undergo surgery for drug-resistant temporal lobe epilepsy (TLE). Understanding why TLE is resistant to surgery in some patients may reveal insights into epileptogenic networks and direct new therapies to improve outcomes. OBJECTIVE To characterize features of surgically refractory TLE. DESIGN, SETTING, AND PARTICIPANTS Medical records from a comprehensive epilepsy center were retrospectively reviewed for 131 patients who received a standard anteromedial temporal resection by a single surgeon from January 1, 2000, to December 31, 2015. Thirteen patients were excluded for having less than 1 year of follow-up. Patients at the highest risk for seizure recurrence were identified. Intracranial electroencephalogram (iEEG) analyses generated 3-dimensional seizure spread representations and quantified rapid seizure spread. The final analyses of seizure outcome and follow-up data were performed in June 2017. MAIN OUTCOMES AND MEASURES The Engel class seizure outcome following surgery was evaluated for all patients, defining seizure recurrence as Engel class II or greater. Intracranial recordings of neocortical grids/strips and depth electrodes were analyzed visually for seizure spread. Fast β power was projected onto reconstructions of patients' brain magnetic resonance imaging scans to visualize spread patterns and was quantified to compare power within vs outside resective margins. RESULTS Of 118 patients with 1 year of follow-up or more (mean [SD], 6.5 [4.6] years), 66 (55.9%) were women and 52 (44.1%) were men (median age, 39 years [range, 4-66 years]). The cumulative probability of continuous Engel class I seizure freedom since surgery at postoperative year 10 and afterward was 65.6%, with 92% of recurrences in years 1 to 3. Multivariable statistical analyses found that the selection for iEEG study was the most reliable predictor of seizure recurrence, with a mixed-effects model estimating that the Engel score in the iEEG cohort was higher by a mean (SD) of 1.1 (0.33) (P = .001). In patients with iEEG results, rapid seizure spread in less than 10 seconds was associated with recurrence (hazard ratio, 5.99; 95% CI, 1.7-21.1; P < .01). In the first 10 seconds of seizures, fast β power activity outside the resective margins in the lateral temporal cortex was significantly greater in patients whose seizures recurred compared with patients who were seizure-free (mean [SEM], 137.5% [16.8%] vs 93.4% [4.6%]; P < .05). CONCLUSIONS AND SIGNIFICANCE Rapid seizure spread outside anteromedial temporal resection resective margins plays a significant role in the surgical failure of drug-resistant TLE. Seizure control after epilepsy surgery might be improved by investigating areas of early spread as candidates for resection or neuromodulation.

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Analysing connectivity with Granger causality and dynamic causal modelling

Abstract: Highlights► A brief introduction to the analysis of directed connectivity in brain networks. ► An overview of advances in Granger causality and dynamic causal modelling. ► A comparative evaluation of both approaches in terms of their pros and cons.

Cited by 569 publications

References 57 publications

The MVGC multivariate Granger causality toolbox: A new approach to Granger-causal inference

The MVGC multivariate Granger causality toolbox: A new approach to Granger-causal inference

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

Association of Seizure Spread With Surgical Failure in Epilepsy

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