Linear and nonlinear causality between signals: methods, examples and neurophysiological applications

Gourévitch, Boris; Jeannès, Régine Le Bouquin; Faucon, G.

doi:10.1007/s00422-006-0098-0

Cited by 210 publications

(146 citation statements)

References 66 publications

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“…Geweke [13] was the first to propose a linear bivariate time-series approach assessing linear Granger causality (LGC) based on the prediction error variance of the time series associated with a statistical test for causality [12]. If process X 2 has no causal influence on process X 1 , then LGC X 2 →X 1 becomes close to zero, which means that the knowledge of past values of X 2 does not improve the prediction of X 1 , but if LGC Bassani et al [15] estimated the direct causal coupling by applying two GC approaches (the F-test and the Wald test) along the baroreflex in two anaesthesiological procedures.…”

Section: (I) Linear Methodsmentioning

confidence: 99%

“…This is associated with various delays and is able to determine whether the causal relation between two nonlinear signals (x, y) is coupled directly or mediated by another process [12]. Here, the extended Granger causality index (EGCI) y→x was introduced as a function of δ (neighbourhood size).…”

Section: (I) Linear Methodsmentioning

confidence: 99%

“…Today, this concept is known as GC. GC for two processes X 1 (t) and X 2 (t) is defined as: X 1 (t) has causal influence on X 2 (t); (X 1 (t) → X 2 (t)) if the knowledge of the past of both X 1 (t) and X 2 (t) reduces the variance of the prediction error of X 2 (t) in comparison with the knowledge of the past of X 2 (t) alone (the past and the present cause the future but not vice versa) [7,12]. GC can be assessed by linear and nonlinear methods as described below.…”

Section: (A) Granger Causalitymentioning

confidence: 99%

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Cardiovascular and cardiorespiratory coupling analyses: a review

Schulz

Adochiei

Edu

et al. 2013

Phil. Trans. R. Soc. A.

145

127

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Recently, methods have been developed to analyse couplings in dynamic systems. In the field of medical analysis of complex cardiovascular and cardiorespiratory systems, there is growing interest in how insights may be gained into the interaction between regulatory mechanisms in healthy and diseased persons. The couplings within and between these systems can be linear or nonlinear. However, the complex mechanisms involved in cardiovascular and cardiorespiratory regulation very likely interact with each other in a nonlinear way. Recent advances in nonlinear dynamics and information theory have allowed the multivariate study of information transfer between time series. They therefore might be able to provide additional diagnostic and prognostic information in medicine and might, in particular, be able to complement traditional linear coupling analysis techniques. In this review, we describe the approaches (Granger causality, nonlinear prediction, entropy, symbolization, phase synchronization) most commonly applied to detect direct and indirect couplings between time series, especially focusing on nonlinear approaches. We will discuss their capacity to quantify direct and indirect couplings and the direction (driver–response relationship) of the considered interaction between different biological time series. We also give their basic theoretical background, their basic requirements for application, their main features and demonstrate their usefulness in different applications in the field of cardiovascular and cardiorespiratory coupling analyses.

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Section: (I) Linear Methodsmentioning

confidence: 99%

Section: (I) Linear Methodsmentioning

confidence: 99%

Section: (A) Granger Causalitymentioning

confidence: 99%

See 1 more Smart Citation

Cardiovascular and cardiorespiratory coupling analyses: a review

Schulz

Adochiei

Edu

et al. 2013

Phil. Trans. R. Soc. A.

145

127

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show abstract

“…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

366

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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“…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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Linear and nonlinear causality between signals: methods, examples and neurophysiological applications

Abstract: Definition of Granger Causality Coefficients. The two signals x(t i), i.e. ipsi-lateral LFP) and y(t i), i.e.contra-lateral LFP, (sampled at t i = 0, ∆t, ..., (N − 1)∆t, where N = 3.6 × 10 5) are modelled by a

Cited by 210 publications

References 66 publications

Cardiovascular and cardiorespiratory coupling analyses: a review

Cardiovascular and cardiorespiratory coupling analyses: a review

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

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

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