Conceived and designed the experiments: ABB AKS. Performed the experiments: ABB. Analyzed the data: ABB. Contributed reagents/materials/analysis tools: MM MAB QN MB SL AKS. Wrote the paper: ABB AKS.
The authors have declared that no competing interests exist.
Changes in conscious level have been associated with changes in dynamical integration and segregation among distributed brain regions. Recent theoretical developments emphasize changes in directed functional (i.e., causal) connectivity as reflected in quantities such as ‘integrated information’ and ‘causal density’. Here we develop and illustrate a rigorous methodology for assessing causal connectivity from electroencephalographic (EEG) signals using Granger causality (GC). Our method addresses the challenges of nonstationarity and bias by dividing data into short segments and applying permutation analysis. We apply the method to EEG data obtained from subjects undergoing propofolinduced anaesthesia, with signals sourcelocalized to the anterior and posterior cingulate cortices. We found significant increases in bidirectional GC in most subjects during lossofconsciousness, especially in the beta and gamma frequency ranges. Corroborating a previous analysis we also found increases in synchrony in these ranges; importantly, the Granger causality analysis showed higher intersubject consistency than the synchrony analysis. Finally, we validate our method using simulated data generated from a model for which GC values can be analytically derived. In summary, our findings advance the methodology of Granger causality analysis of EEG data and carry implications for integrated information and causal density theories of consciousness.
An important challenge for cognitive neuroscience is to characterize directed functional (i.e., causal) connectivity between brain regions, either in the absence of identifiable behaviour or during task performance. In particular, characterizing causal connectivity patterns across different conscious levels (e.g., sleep, anaesthesia, normal wakefulness) is likely to shed important new light on the neural mechanisms underlying consciousness, and may also provide new clinical methods for assessment of intraoperative anaesthetic depth
One powerful approach to identifying causal connectivity from time series data, originally developed in the 1960s by Norbert Wiener and Clive Granger, is ‘Granger causality’ (GC)
We illustrate our method by application to highdensity, steadystate, sourcelocalized EEG data acquired from subjects during wakeful resting (WR) and when undergoing propofolinduced general anaesthesia (lossofconsciousness, LOC). Extending a previous analysis, we focused on time series localized to the anterior and posterior cingulate cortices (ACC and PCC respectively), see
The frontal region (left) is a portion of the anterior cingulate cortex (with extension to the mesiofrontal cortex) and the posterior region (right) is a portion of the posterior cingulate cortex (with extension to the precuneus). Reproduced with permission from Ref.
The data analysed in this study were obtained from a previous study
We reanalyzed a subset of the data comprising 5 min of spontaneous highdensity EEG recordings sampled at 1000 Hz from each of 7 subjects during both WR and LOC, with LOC defined as clinical unconsciousness (no response to command, Ramsay scale score 5)
In this section we rehearse the formalism of Granger causality in the time and frequency domains. Given two widesense stationary time series
Importantly, GC has a spectral decomposition that can be used to restrict inferences about causal influence to particular frequency bands
To obtain the ‘bandlimited’ GC for a frequency band defined by the range
To validate our GC methodology, we simulated data from a multivariate autoregressive model with white noise error terms, a model for which we were able to derive true GC values analytically. The general such system is specified by:
GC analysis was conducted on artifactfree epoched time series, following notch filtering and downsampling, reflecting mean EEG activity within two sourcelocalized brain areas, the ACC and the PCC, recorded from subjects during normal wakeful resting (WR) and under propofol sedation (LOC).
The data have been notch filtered at 50 Hz and 100 Hz and downsampled to 250 Hz.
Vertical lines indicate segment boundaries. The time series shown for each segment have been preprocessed to remove the linear trend and renormalized to each have mean of 0 and standard deviation of 1.
We next computed, for each segment, the recommended model order (
We next carried out the following GC analysis method for each subject, condition (WR or LOC), direction, and frequency band (delta, theta, alpha, beta, gamma). First, for each 2 sec segment we calculated numerical estimates of GC using Eqs. (1), (2), (8) and (10), using the model order
Numerical GC values obtained directly from finite data yield biased estimates of the true GC of the underlying process. In our next step we estimated and removed the bias by applying the following permutation procedure. For each subject, condition, direction and frequency band, we selected 1000 random pairs of 2 sec segments from the ACC with (noncorresponding) 2 sec segments from the PCC. We then computed the numerical GC for each pair,
Finally, for each subject, condition, direction and frequency band, we obtained an estimate of the mean GC,
We repeated the above procedure for the timedomain, with timedomain GC values computed in approximation by taking the mean over frequencies from 0.5–40 Hz (Eq. (10)). We avoided the explicit timedomain GC (3) because that was found to sometimes contain residual spurious contributions from the line noise at 50 Hz
To confirm validity of application of linear regression models of order
Left column shows the mean spectral GC in the direction PCC
Subject  1  2  3  4  5  6  7 

n/s  (+)  n/s  [+]  n/s  [+]  n/s 

[+]  +  n/s  n/s  +  n/s  n/s 

n/s  [+]  n/s  n/s  [+]  n/s  n/s 

n/s  +  n/s  n/s  +  n/s  n/s 

(+)  n/s  [−]  n/s  n/s  n/s  (+) 
time domain  (+)  +  n/s  n/s  +  n/s  [+] 
Subject  1  2  3  4  5  6  7 

n/s  n/s  n/s  n/s  n/s  n/s  n/s 

n/s  n/s  n/s  (+)  n/s  n/s  n/s 

n/s  n/s  n/s  [+]  n/s  n/s  n/s 

n/s  +  n/s  [+]  n/s  (+)  (+) 

[+]  (+)  n/s  [+]  [+]  +  + 
time domain  n/s  +  n/s  [+]  n/s  +  (+) 
To validate the GC analysis of the EEG data, we applied the same procedure to the simulation model described in the section ‘Simulation model’, for which analytical GC values could be computed. The model we simulated had the following nonzero regression matrices
(a) Mean spectral GC obtained from 200 sec of simulated data, obtained from the model described by Eqs. (12) and (18), implementing bidirectional causality between two variables
We next compared the results of our GC analysis of the EEG data with a phase synchrony analysis of the same data. Unlike GC, phase synchrony provides an
As described in the
For each subject and condition we divided the synchrony data into 10 sec nonoverlapping windows. For each window we calculated the proportion of timepoints with abovethreshold (i.e.,
Each panel shows a different frequency band. Error bars show standard error. Mean and standard error computed across 10 sec windows of data, see main text.
Subject  1  2  3  4  5  6  7 

−  n/s  +  n/s  n/s  n/s  n/s 

n/s  −  n/s  +  +  +  + 

(−)  n/s  n/s  +  n/s  +  + 

−  −  +  +  +  +  + 

n/s  −  +  +  −  +  + 
To examine changes in spectral power on a subjectbysubject basis, we applied a fast Fourier transform to each of the 10 sec windows identified in the previous synchrony analysis. For each subject and frequency band we computed the mean power spectral density (PSD) across all windows, in both the ACC (
Each panel shows a different frequency band. Error bars show standard error. Mean and standard error computed across 10 sec windows of data, see main text.
Logarithms are to base 10.
Subject  1  2  3  4  5  6  7 







































We have presented a method for applying GC analysis to steady state EEG data, that (i) accommodates nonstationarity by dividing the data into short approximatelystationary segments, and (ii) systematically removes bias by permutation analysis. Our method is generally applicable in neuroimaging contexts that generate continuous time series data at sampling rates reflecting neural interactions (magneto/electroencephalographic signals, intracranial recordings, electrocorticographic signals, other localfieldpotential signals). We demonstrated the efficacy of our method via a rigorous set of simulations for which GC could be solved analytically. We illustrated its value by application to sourcelocalized steadystate highdensity EEG data obtained from healthy human subjects undergoing propofolinduced anaesthesia, examining changes in bidirectional GC between the ACC and PCC as subjects transitioned from wakeful resting (WR) to lossofconsciousness (LOC). We found an increase in bidirectional GC during LOC that was most pronounced in the beta (12–25 Hz) and gamma (25–40 Hz) frequency bands and which was observed consistently across subjects. A comparison with a phase synchrony analysis (following
The increasing focus on functional brain networks underlying cognition
Remove any linenoise artifact via notch filtering; avoid bandpass filtering.
Choose a minimum timescale for interactions within the system under consideration; downsample the data to a rate reflecting this timescale.
Choose a segment length over which the data remain approximately stationary, reflecting a tradeoff between increased stationarity (better for short segments) and parameter estimation (better for long segments); partition the data into nonoverlapping segments of the chosen length, removing the linear trend and mean from each segment. Exclude segments containing artifacts.
For each segment, estimate the model order (e.g., using the Akaike or Bayesian information criterion
Using this model order, compute GC in both directions for all pairs of variables and for all frequencies of interest. For bandlimited GC, integrate spectral GC across the relevant frequencies; for timedomain GC, integrate across all frequencies (up to the Nyquist frequency), omitting any frequencies contaminated by linenoise removal.
To estimate the bias in GC values for a particular connection and frequency, compute the mean numerical GC at this frequency between
Subtract the estimated bias from each raw GC value to obtain an approximately unbiased estimate.
Assess significance using a Wilcoxon rank sum test on the distribution of approximately unbiased GC estimates across segments.
Elements of the above method have been proposed previously. Analysis of short timewindows was advocated by Hesse
The context of spectral bidirectional GC between two variables is deliberately simple. The method is however readily extensible to more complicated situations including conditional GC (in which the GC between each pair is conditioned on the common causal influence of other variables, see
The neurophysiological changes accompanying propofolinduced LOC have been extensively studied. Alkire and colleagues found using positron emission tomography a reduction in global brain metabolism of about 50
Addressing this need, a variety of theoretical interpretations have been offered to account for the sedative effects of anaesthetics, including impaired thalamocortical connectivity
The ability to detect directed functional brain networks during anaesthetic LOC is therefore key to refining, as well as differentiating between, the above theories. To our knowledge, only one previous neuroimaging study has attempted this. Lee and colleagues
Stepping back, most theoretical views share the notion that anaesthetic LOC is associated with decreased functional (or effective) connectivity, whether directed or undirected. On the face of it, these views contrast with our results which showed increased GC and phase synchrony during LOC, as well as increased power. However, increased functional connectivity could be consistent with overall reduction of causal density and/or information integration under at least two scenarios. First, high values of some measures (synchrony, bivariate GC) could reflect pathologically increased integration at the expense of differentiation. This view aligns with the increased corticalsubcortical synchrony observed during LOC associated with generalized epilepsy
We have described a methodological pipeline for GC analysis of steadystate EEG signals, accommodating nonstationarity, eliminating bias, and validated against an analytically solvable model. This pipeline represents a contribution towards the general problem of identifying directed functional connectivity in brain networks
We are grateful to Lionel Barnett for useful discussions. We acknowledge Pierre Boveroux and JeanFrancois Brichant for also having a role in the original data collection.