Tutorial 28: Connectivity

[TUTORIAL UNDER DEVELOPMENT: NOT READY FOR PUBLIC USE]

Authors: Hossein Shahabi, Mansoureh Fahimi, Francois Tadel, Esther Florin, Sergul Aydore, Syed Ashrafulla, Takfarinas Medani, Elizabeth Bock, Sylvain Baillet

Introduction

During the past few years, the research focus in brain imaging moved from localizing functional regions to understanding how different regions interact together. It is now widely accepted that some of the brain functions are not supported by isolated regions but rather by a dense network of nodes interacting in various ways.

Brain networks (connectivity) is a recently developed field of neuroscience which investigates interactions among regions of this vital organ. These networks can be identified using a wide range of connectivity measures applied on neurophysiological signals, either in time or frequency domain. The knowledge provides a comprehensive view of brain functions and mechanisms.

This module of Brainstorm tries to facilitate the computation of brain networks and the representation of their corresponding graphs. Figure 1 illustrates a general framework to analyze brain networks. Preprocessing and source localization tasks for neural data are thoroughly described in previous sections of this tutorial. The connectivity module is designed to carry out remained steps, including the computation of connectivity measures, and statistical analysis and visualizations of networks.

GeneralFlowConn.png

General terms/considerations for a connectivity analysis

Sensors vs sources: The connectivity analysis can be performed either on sensor data (like EEG, MEG signals) or on reconstructed sources (voxels/scouts).

Nature of the signals: The selection of connectivity method depends on the nature of the data. Some approaches are more suitable for spontaneous data (resting state) while others work better with task data (trials).

Point-based connectivity vs. full network: Most of the connectivity functions in this toolbox have the option to either compute the connectivity between one point (channel) and the rest of the network (1 x N) or the entire network (N x N). While the later calculates the graph thoroughly, the first option enjoys a faster computation and it is more useful when you are interested in the connectivity of an ROI with the other regions of the brain.

Temporal resolution: Connectivity networks can be computed in two ways; static and dynamic. Time-varying networks can present the dynamics of brain networks. In contrast, the static graphs illustrate a general perspective of brain connectivity which is helpful in specific conditions. Users need to decide which type of network is more informative for their study.

Time-frequency transformation: Many connectivity measures use a time-frequency transformation to transfer the data to the frequency domain. These approaches include short time Fourier transform, Hilbert transform, and Morlet wavelet.

Output data structure: Consequently, computed connectivity matrices in this toolbox have up to four dimensions; channels x channels x frequency bands x time. Also, when dealing with trials and several files, each file has that 4-D structure.

Simulated data (AR model)

In order to compare different connectivity measures, we use simulated data with known ground truth. Consider three channels constructed using the following AR process.

\begin{eqnarray*}
x_{1}(n) & = & a_{11}x_{1}(n-1) + \cdots + a_{1k}x_{1}(n-k) + e_{1}(n) \\
x_{2}(n) & = & a_{21}x_{2}(n-1) + \cdots + a_{2k}x_{2}(n-k) + e_{2}(n) \\
x_{3}(n) & = & a_{31}x_{3}(n-1) + \cdots + a_{3k}x_{3}(n-k) + b_{1}x_{1}(n-1) + \cdots + b_{r}x_{1}(n-r) + e_{3}(n) \\
\end{eqnarray*}

where aij and bi are coefficients of 4th order all-pole filters. These coefficients were calculated in a way that the first channel has a dominant peak in the Beta band (25 Hz), the second channel shows the highest power in the Alpha band (10 Hz), and a similar level of energy in both bands in the third signal. bi describe the transfer function from channel 1 to channel 3 and values are selected where it should have a peak in the Beta band.

Using these coefficients, we simulate signals (Fs = 100). The connectivity measures will be tested by this dataset, which is available here.

SimSignals1.PNG

One can take the Fourier transform from the AR equations and rearrange them in a matrix form.

\begin{eqnarray*}
A(f)X(f)  & = & E(f)  \\
define \quad H(f) & = & A^{-1}(f) \quad Transfer \quad function\\
X(f) & = & H(f)E(f) \\
\end{eqnarray*}

By calculating the H(f), we will have:

TransferMatrix3_AR3.png

In this figure, the diagonal elements show the auto transfer function, which in our specific case the spectrum of the signals. The off-diagonal terms represent the interactions between different signals. Here, we see the transfer function from channel 1 to channel 3.

Besides the original transfer function, we can compute the directed transfer function (DTF) and partial directed coherence (PDC). Details about those measures can be found in ref.

Directed transfer function_AR3.png

Partial Directed Coherence_AR3.png

Coherence (FFT-based)

The coherence is a statistical measure which computes the relation between two signals, like x(t) and y(t), in the frequency domain. The magnitiude-squared coherence is,

\begin{eqnarray*}
C_{xy}(f) &=& \frac{\left |S_{xy}(f)  \right |^{2}}{S_{xx}(f)S_{yy}(f)}  \\
S_{xy}(f) &:& Cross-spectral \quad density \\
S_{xx}(f) \quad and \quad S_{yy}(f) &:& Auto-spectral \quad density \\
\end{eqnarray*}

The coherence function uses the Fourier transform to compute the spectral densities. Two related measures, which alleviate the problem of volume conduction, are imaginary and lagged coherence. More information regarding these measures can be found here. The formulas for computing the two values are as follows:

Imaginary Coherence:

\begin{eqnarray*}
IC_{xy}(f) = \frac{Im \left (S_{xy}(f)  \right )}{\sqrt{ S_{xx}(f)S_{yy}(f)  }} \\
\end{eqnarray*}

Lagged Coherence:

\begin{eqnarray*}
LC_{xy}(f) = \frac{Im \left (S_{xy}(f)  \right )}{\sqrt{ S_{xx}(f)S_{yy}(f) - \left [ Re\left ( S_{xy}(f) \right ) \right ]^{2} }} \\
\end{eqnarray*}

where Im() and Re() describe the imaginary and real parts of the spectral densities.

To calculate coherence values in Brainstorm:

CohProcess_Aug19.PNG

In general, after running the connectivity processes, you can find a multi-dimensional matrix of connectivity in the database. In order to represent this matrix, there are several options.

Right-click on the file and select Power spectrum and Display as image. These two figures are plotted here. The left figure shows the Coherence values in all analyzed frequencies. Another figure displays the Transfer matrix between channels for the selected frequency bin.

CohResults1_Aug19.PNG


Similarly, we can run this process and select "imaginary coherence", which gives us the following representation,

StatCoherence_Process_lc.PNG

And finally, "lagged coherence": StatCoherence-Results_lc.PNG

We see the last two measures are similar but have different values in several frequencies. However, both imaginary and lagged coherence are more accurate than coherence.

Granger Causality

Granger Causality (GC) is a method of functional connectivity, adapted by Clive Granger in the 1960s, but later refined by John Geweke in the form that is used today. Granger Causality is originally formulated in economics but has caught the attention of the neuroscience community in recent years. Before this, neuroscience traditionally relied on stimulation or lesioning a part of the nervous system to study its effect on another part. However, Granger Causality made it possible to estimate the statistical influence without requiring direct intervention (ref: wiener-granger causality a well-established methodology).

Granger Causality is a measure of linear dependence, which tests whether the variance of error for a linear autoregressive model estimation of a signal (A) can be reduced when adding a linear model estimation of a second signal (B). If this is true, signal B has a Granger Causal effect on the first signal A, i.e., independent information of the past of B improves the prediction of A above and beyond the information contained in the past of A alone. The term independent is emphasized because it creates some interesting properties for GC, such as that it is invariant under rescaling of A and B, as well as the addition of a multiple of A to B. The measure of Granger Causality is nonnegative, and zero when there is no Granger causality(Geweke, 1982).

The main advantage of Granger Causality is that it is an asymmetrical measure, in that it can dissociate between A->B versus B->A. It is important to note however that though the directionality of Granger Causality is a step closer towards measuring effective connectivity compared to symmetrical measures, it should still not be confused with “true causality”. Effective connectivity estimates the effective mechanism generating the observed data (model-based approach), whereas GC is a measure of causal effect based on prediction, i.e., how well the model is improved when taking variables into account that are interacting (data-driven approach) (Barrett and Barnett, 2013). The difference with causality is best illustrated when there are more variables interacting in a system than those considered in the model. For example, if a variable C is causing both A and B, but with a smaller delay for B than for A, then a GC measure between A and B would show a non-zero GC for B->A, even though B is not truly causing A (Bressler and Seth, 2011).

The complete formulation of this method is discussed in the advanced section. Here, we apply the Granger causality and its spectral version on the simulated data.

StatGranger_Process.PNG

Input options:

Estimator options:

Output options:

By running the process function, the Granger causality can be displayed in a matrix.



GrangerMatrixRes2.png



The upper right element of this matrix shows there is a signal flow from channel 1 to channel 3. However, the Granger function by itself cannot represent the transfer function (frequency spectrum).

To do that, we need to run the Spectral Granger causality. GrangerSpecProcess3.png

Here, is that process similar to the previous function with two extra options. These include the frequency resolution and maximum frequency of interest which was discussed previously in the Coherence process. As a result, the power spectrum of the transfer function is depicted:



SpecResultGranger2.png



It shows a clear peak at 25 Hz, as expected.

Coherence and envelope Correlation by Hilbert transform and Morlet wavelets

In chapter 24, the Morlet wavelets and Hilbert transform were fully introduced and examined as tools to decompose signals in the time-frequency domain. This representation can be used for computing the coherence and related measures as well.

Besides the lagged and Imaginary Coherence, which were discussed earlier in this tutorial, a measure named "envelope correlation" was found in 2010 (ref). This method work based on the pairwise orthogonalization of signals, removing their real part of coherence, and computing the correlation between the orthogonalized parts. The entire process alleviates the effect of volume conduction in MEEG signals. This method has shown to work well on resting-state MEG.

In late 2019, we launched our newly designed process called "HCoh". This process and its corresponding functions compute the Coherence, lagged-coherence, and envelope correlation using the Hilbert transform and Morlet wavelets. By splitting the signals and employing the Parallel processing toolbox (if applicable and available), it is capable of analyzing long recordings and a high number of channels in an efficient time.

The complete mathematical background about this process is presented in the "advanced" section. The general framework can be simplified as

FlowChartHCorr.png

Now, we are ready to start working with this process.

DynHCorr_Process.PNG

Phase locking value

An alternative class of measures considers only the relative phase through the computation of a phase locking value between the two signals (Tass et al., 1998). Phase locking is a fundamental concept in dynamical systems that has been used in control systems (the phase-locked loop) and in the analysis of nonlinear, chaotic and non-stationary systems. Since the brain is a nonlinear dynamical system, phase locking is an appropriate approach to quantifying interaction. A more pragmatic argument for its use in studies of LFPs (local field potentials), EEG and MEG is that it is robust to fluctuations in amplitude that may contain less information about interactions than does the relative phase (Lachaux et al., 1999; Mormann et al., 2000).

The most commonly used phase interaction measure is the Phase Locking Value (PLV), the absolute value of the mean phase difference between the two signals expressed as a complex unit-length vector (Lachaux et al., 1999; Mormann et al., 2000). If the marginal distributions for the two signals are uniform and the signals are independent then the relative phase will also have a uniform distribution and the will be zero. Conversely, if the phases of the two signals are strongly coupled then the PLV will approach unity. For event-related studies, we would expect the marginal to be uniform across trials unless the phase is locked to a stimulus. In that case, we may have nonuniform marginals which could in principle lead to false indications of phase locking.

Phase synchronization between two narrow-band signals is frequently characterized by the Phase Locking Value (PLV). Consider a pair of real signals s1(t) and s2(t), that have been band-pass filtered to a frequency range of interest. Analytic signals can be obtained from s1(t) and s2(t) using the Hilbert transform:

\begin{eqnarray*}
z_{i}(t)= s_{i}(t) + j HT\left ( s_{i}(t) \right ) \\
\end{eqnarray*}

Using analytical signals, the relative phase between z1(t) and z2(t) can be computed as,

\begin{eqnarray*}
\Delta \phi (t)= arg\left ( \frac{z_{1}(t)z_{2}^{*}(t)}{\left | z_{1}(t) \right |\left | z_{2}(t) \right |} \right ) \\
\end{eqnarray*}

The instantaneous PLV is

\begin{eqnarray*}
PLV(t)= \left | E\left [ e^{j\Delta \phi (t)} \right ] \right | \\
\end{eqnarray*}


Correlation

The correlation is the basic approach to show the dependence or association among two random variables or MEG/EEG signals. While this method has been widely used in electrophysiology, it should not be considered as the best technique for finding the connectivity matrices. The correlation by its nature fails to alleviate the problem of volume conduction and cannot explain the association in different frequency bands. However, it still can provide valuable information in case we deal with a few narrow-banded signals.

StatCorrelation_Process.PNG

Method selection and comparison

We can have a comparison between different connectivity functions. The following table briefly does this job.

TableComparison.PNG

Comparing different approaches with the ground truth we find out that the HCorr function works slightly better than other coherence functions.

Coh13_AR3.png

Connectivity measures on real data : LFP data

In this section we will show how to use the Brainstorm connectivity tools on real data.

LFP data recorded on monkey

Experimental Setup and data recording:

For this part we will use the Local Field Potential (LFP) monkey data described in Bresslers et al (1993), these data are widely used over the last past years in many studies.

The original data could be found in this link, more information on the data organization is explained here and also here.

These recordings were made using 15 surface-to-depth bipolar electrodes, separated by 2.5mm, implanted in the cerebral hemisphere contralateral to the monkey's prefered hand.For our analysis in this tutorial, we have selected the monkey named GE.

The data are recorded from 6 main areas of the right cortex (Straite, Prestriate, Parietal, Somato, Motor, and frontal cortex). The approximative locations of the 15 electrodes are shown in this figure. The are digitazed at 200sample per second (200Hz).

GE_brain.png GE_electrodePosition.png

On the left, a scheme of the monkey brain area, on the right, the locations of 15 electrode pairs in the right hemisphere (reproduced from Aydore et al (2013) and Bresslers et al (1993)).

In these experiments, the monkey was trained to depress a lever and wait for a visual stimulus that informs the monkey to either let go the lever (release/GO) or keep the lever down (not release/NOGO). The visual stimulus is presented with four dots arranged as a left (or right) slanted line or diamand on a display screen. (The dots form either a shape of a diagonal line or a shape of a diamond.)

For our analysis in this tutorial, we select a dataset with a diagonal line as the 'NOGO' stimulus and the diamond as the 'GO'.

For more details about the experiment please refer to Bresslers et al (1993) and to this page.

Importing and analyzing data within brainstorm:

For our case, we imported and adapted the data to the brainstorm format, you can download a sample of the data here. (todo >this sample contains only 50 epochs per condition, the full data should uploaded asap)

Voltage is in uV and was recorded at 200Hz sampling rate. After pooling and ordering the dataset together, we randomly select 480 trials for each condition (GO and NOGO) with only one conctingency for condition (only one kind of stimulation for each condition).

Timeline explanation

Defining the lever initial descent to be at time t = 0ms. Each trial lasts 600ms, the stimulus was given 100ms after the lever was depressed, and last for 100ms. On GO trials, a water reward was provided 500 ms after stimulus onset only if the hand was lifted within the 500ms. On the NOGO trials, the lever was depressed for 500ms.

In the following figure, we show the time line of the averaged response for the 480 epochs for the GO condition. The blue line is at t = 0ms begening of the recording, the green line is the stimulus onset at t = 100ms, the orange line is the mean time of the response onset in the case of the GO condition (release the lever), the red line is the time cursor, set at t = 250ms, time that we choose to separate between early response and late response in this tutorial.


lfpTimeLine.png


In this analysis, we will focus mainly on two windows. The early response for t ϵ[100, 250 ms] in which we expect a visual activation on the occipital area (striate and prestriate areas, group of electrodes 1 to 6). We will also show some analysis on the late response, for t ϵ [250, 450 ms] in which we expect an activation/connectivity between the striate and motor cortex in the GO condition and no or less activation for the NOGO condition.

Process of computation:

For most of the connectivity measures, we will use the following steps :

First we compute the the connectivity value between one pair of electrode (or scouts) for each trial (time serie), in this case we have 480 trials for each condition, therefore we will compute 480 values for each pair of electrods. After that we will average the connectivity over all the trails and we will get the average value for the pair of electrodes. As explained in the previous sections, Brainstorm offers two options, the NxN (matrix) or 1xN (vector) measures, whre N is the number of channel.

Remove intermediate data :

To free space in your hard disc and in order to be able to compute other connectivity meaure, you can/should remove the previous individual connectivity for each trial. To do so, keep the 'time freq' in process1, click Run and choose : File>Delete File>Delete selected Files and then click on run. This process will delet the individual data for each trial.

DeleteFiles.png

Phase Locking Value (PLV)

We select the two groupes of files in the the process 1 (drag and drop), then hit Run, select Connectivity then Phase Locking Value NxN. Choose time window between 100 to 250ms (for early analysis and later 250 to 450 ms for the late response). 

For Hilbert transform, we select bands from 12 to 60 Hz as shown in the fugure. The PLV is more accurate on short frequency band and to pretend for significant value we recommend to use time windows with more than 100 samples (it's not the cqse in this data).

For the remaining, keep the other options as they are, select the Magnitude and choose the option 'Save individual results (one file per input file)' and finaly click on Run.

PLV_EarlyAnswerWithERP.png

This could take some times according to your computer and the size of your data.

Now, in order to have one measure for each condition, we need to average all the connectivity measure across trials. We do this from the Brainstorm Process1 window, select 'Process time-freq' (the third icone). Then click on run and select : Average->Average Files, select the option : By trial group (folder average) with the function Arithmetic average. This will compute the average connectivity PLV matrix for the Go and NoGo stimulus.

In order to represent this matrix, there are several options.

Right click on the connectivity file and select the first option > Display as graph [NxN]. We display both figures for the GO (left figure) and NOGO (right figure) conditions.

As explained above, we will focus on the early response in which we expect high connectivity measures on the striate and prestriate areas. For the late response, we expect high measures on/between the occipital and motor cortex du to the eventual hand movements..

Early response t ϵ [100-250 ms]:

The first option to display the results is: select the connectivity file in the database, right-click and then choose the first option "Display as a graph" From the brainstorm control panel "Display", we can tune the value of the frequency band from the cursor. Same options are available for the connectivity threshold and for the distance filtring.

For these data we don't have the exact location of the electrode on the cortex, we build an approximation of the location, therefore we will set the distance filtering to zero in this case.

For the following figure, we choose 0mm, band1, threshold 0.844.

plv_early_go_band1.PNG plv_early_nogo_band1.PNG

As we expected, the results show high connectivity value (PLV) between the striate and prestriate area. The strength of the measures is almost the same for both conditions, however, we observe some difference on the electrodes between the Line and the Diamond, this is probably due to the difference on the shape (patern) of the visual stimuli.

We will also display the connectivity matrix as an image, either by selecting the measure and press 'Enter' or Right-click on the connectivity file and select the first option > Display as an image [NxN]

plv_early_go_band1_image_ncm.PNG plv_early_nogo_band1_image_ncm.PNG

As we saw before, the highest values are between the electrodes 2, 3, 4, 5, and 6 which are in the occipital cortex.

To highlight the difference between the two conditions, we can use the Process2 and compute the difference between the two images. (Further methods for statistics are under development)

From the Process2 bar, we can compute the difference between the images in order to highlight the main difference between the two condition. To do that, you jus drag the associated connectivity file for the condition one to the Files A and the condition two to the files B, then click on run, select Difference, then one of the proposed options, in this tutorial we selected the 'Normalized: A-B/A+B'. plv_early_go_band1_image-plv_early_nogo_band1_image_ncm.PNG

The resulted image shows the highest difference in the connectivity is between the electrodes (2,6) and (3,6), this is exactely the difference that we observed in the previous graphes, which is mainly the difference between the two conditions. There is also diference in the paires (1,14), (8,14) and (11,14), which involves the visuql, the motor and the frontal cortexes, probably due to the preparation to the decision making, and prepare to activate or inhibite the action of the hand.

Late response t ϵ [250-450 ms] :

distance filtering : 0mm, band1, threshold 0.644

plv_late_go_band1.PNG plv_late_nogo_band1.PNG

In this late response, also as we expected, we see higher value in the GO condition then the NOGO condition. Also we observe a connexion between the striate to motot cortex, this connection is related to the mouvmenet of the hand to release the lever.

These results show also the connection between the striat/prestiriate to the frontal regions since this later is involved in the selection of actions based on perceptual cues and reward values as shown in this paper.

These connectivity results are highly correlated to the ones observed within the previous publications Aydore et al. (2013) and Bresslers et al (1993). We should also notice that is in this process, the difference in the result is related to the implementation methods, the selected time windows and the sample data size and choice (here we picked randomly 480 samples from each condition).

As in previous, we will visualize the results as an image for the difference between the two conditions.

Of course, ultimately statistical analysis of these maps is required to make scientific inferences from your data.

plv_late_go_band1_image-plv_late_nogo_band1_image_ncm.PNG

From this matrix, we can check pixels by pixels the different values and combinations of electrodes, we notice a slight difference between the electrodes (1,4), (2,4), (1,8), (2,9), (2,10), (4,8), (7,8) but also it shows the highest value between (3,9) and (9,14) wich is related to the connection between the visual cortex to the motor cortex and to the frontal cortex.

Remove the ERP from the signal:

As explained in the previous sections, some connectivity measures can be estimated without the the ERP, this option brings the signals to a slightly more stationary state [Wang and al]

If we choose the option that remove the ERP from each trial before computing the connectivity, we end up with these results (todo : remove the erp is not available on bst for plv for now) :

Early response t ϵ [100-250 ms] :

Parameters : 0mm, band1, threshold 0.75

PLVnoERP_early_go_band1.PNG PLVnoERP_early_nogo_band1.PNG

Late response t ϵ [250-450 ms] :

Parameters : 0mm, band1, threshold 0.666

PLVnoERP_late_go_band1_bis.PNG PLVnoERP_late_nogo_band1.PNG

We observe coherent results with this option. For the early response, a new connextion in the cortex motor between the node (10,11) is highlighted. For the late response, more connextion value are visible in the cas of GO condition.

Coherence (COH)

We use the same data as previous, and we will compute the coherence. We will try to show similar results as shown in the Bresslers et al (1993) in which high value of coherence are observed between the striate and motor cortex areas for the GO condition within the freauency band 12-25 Hz.

Early response t ϵ [100-250 ms] :

Parameters : 0mm, band2, threshold 0.5, with the ERP

COH_early_go_band2.PNG COH_early_nogo_band2.PNG

For both conditions, we observe similar value.

Late response t ϵ [250-450 ms] :

Parameters : 0mm, band2, threshold 0.35, with the ERP

COH_late_go_band2.PNG COH_late_nogo_band2.PNG

As expected, in this case, high value of the coherence are observed for the GO condition (>0,6) wherease for the NOGO condition this value is less than 0,4. We noticed also connection between the visual striate and prestriate to the motor cortex in the GO condition.

Results without the ERP :

Early respinse t ϵ [100-250 ms] :

Parameters : 0mm, band1, threshold 0.35,

COHnoERP_early_go_band1.PNG COHnoERP_early_nogo_band1.PNG

Late response t ϵ [250-450 ms] :

Parameters : 0mm, band1, threshold 0.66

COHnoERP_late_go_band1.PNG COHnoERP_late_nogo_band1.PNG

Correlation (COR)

We use the same data as previous, and we will compute the correlation. As explained before, the correlation is the basic and simple method to observe interaction between region.

Late response t ϵ [250-450 ms] :

Parameters : 0mm, threshold 0.7, with the ERP

CORR_late_go_band1.PNG CORR_late_nogo_band1.PNG

Parameters : 0mm, threshold 0.63, without the ERP

CORRnoERP_late_go_band1.PNG CORRnoERP_late_nogo_band1.PNG

Spectral Granger Causality (SGC)

Early response t ϵ [100-250 ms] :

Parameters : 0mm, threshold 2.5, band1 12.5, with the ERP

SGC_early_go_band1.PNG SGC_early_nogo_band1.PNG

In this example, we see that reciprocal causal influences existe between the electrodes of the striate (1,2,3) and the prestriate(4,5,6). We can also see that the the channel 1 initiates the exchange, and physiologically, the striate cortex precedes prestriate cortex in the anatomical organisation of the visual system.

Late response t ϵ [250-450 ms] :

Parameters : 0mm, threshold 0.315, band1 12.5, with ERP

SGC_late_go_band1.PNG SGC_late_nogo_band1.PNG

Early response t ϵ [100-250 ms] :

Parameters : 0mm, threshold 2.5, band1 12.5, without ERP

SGC_early_go_band1.PNG SGC_early_nogo_band1.PNG

Late response t ϵ [250-400 ms] :

Parameters : 0mm, threshold 0.315, band1 12.5

SGC_late_go_band1.PNG SGC_late_nogo_band1.PNG

Early response: without ERP


SGCnoERP_early_go_band1.PNG SGCnoERP_early_nogo_band1.PNG


Late response: without ERP


SGC_late_go_band1.PNG SGC_late_nogo_band1.PNG

Early response: without ERP

SGCnoERP_early_go_band1.PNG SGCnoERP_early_nogo_band1.PNG

Late response: without ERP


SGCnoERP_late_go_band1.PNG SGCnoERP_late_nogo_band1.PNG

Phase Transfer Entropy (PTE)

early with erp 0,1, b1. 0mm ...not relevant > recheck


TODO : Connectivity measure on real data : MEG/EEG data

SGCnoERP_early_go_band1.PNG SGCnoERP_early_nogo_band1.PNG

Late response: without ERP

SGCnoERP_late_go_band1.PNG SGCnoERP_late_nogo_band1.PNG

Phase Transfer Entropy (PTE)

early with erp 0,1, b1. 0mm ...not relevant > recheck

TODO : Connectivity measure on real data : MEG/EEG data

For all the brain imaging experiments, it is highly recommended to have a clear hypothesis to test before starting the analysis of the recordings. With this auditory oddball experiment, we would like to explore the temporal dynamics of the auditory network, the deviant detection, and the motor response. According to the literature, we expect to observe at least the following effects:

For this data we select three main time windows to compute the connectivity:

time 1 : 0-150 ms : we expect the bilateral response in the primary auditory cortex (P50, N100), in both experimental conditions (standard and deviant beeps).

time 2 : 100-300 ms: Bilateral activity in the inferior frontal gyrus and the auditory cortex corresponding to the detection of an abnormality (latency: 150-250ms) for the deviant beeps only.

time 3 : 300-550 ms : Frontal regions activation related to the decision making and motorpreparation, for the deviant beeps only (after 300ms).

The computation are done here only for the second recording.

Sources level

Connectivity is computed at the source points (dipole) or at a defined brain region also called scouts. The signal used art this level is obtained from the inverse problem process, in which each source-level node (dipole) is assigned with an activation value at each time point.

Therefore, we can compute the connectivity matrix between all pairs of the node. This process is possible only of the inverse problem is computed (ref to tuto here).

To run this in brainstorm, you need to drag and drop the source files within the process1 tab, select the option 'source process' click on the Run button, then you can select the connectivity measure that you want to perform.

As in the previous section, we can compute the source connectivity matrix for each trail, then average overall trial. However, this process is time and memory consuming. For each trial, a matrix of 15002x15002 elements is computed and saved in the hard disc (~0.9 Go per trial). In the case of the unconstrained source, the size is 45006x45006.

connectivitySourceSpace.png

This is obviously a very large number and it does not really make sense. Therefore, the strategy is to reduce the dimensionality of the source space and adopt a parcellation scheme, in other terms we will use the scouts. Instead, to compute the connectivity value values between two dipoles, we will use a set of dipoles pairs that belong to a given area in the cortex.

Although the choice of the optimal parcellation scheme for the source space is not easy. The optimal choice is to choose a parcellation based on anatomy, for example the Brodmann parcellation here. In brainstorm these atlases are imported in Brainstorm as scouts (cortical regions of interest), and saved directly in the surface files as explained in this tutorial here.

In this tutorial, we will use the scouts " Destrieux atlas" (following figure) destrieuxScouts.png

To select this atlas, from the connectivity menu, you have to check the box 'use scouts', select the scout function 'mean' and apply the function 'Before', save individual results.

In this tutorial, we select the correlation as example, the same process is expected for the other methods.

processConnectivityScouts.png

For more detail for these options please refer to this thread

The following matrix is the solution that we obtain with these scouts with the size of 148x148 for this atlas (~400 Ko)

connectivityScoutDistrieux.png

For this data we select three main time windows to compute the connectivity:

time 1 : 0-150 ms : we expect the bilateral response in the primary auditory cortex (P50, N100), in both experimental conditions (standard and deviant beeps).

time 2 : 100-300 ms : Bilateral activity in the inferior frontal gyrus and the auditory cortex corresponding to the detection of an abnormality (latency: 150-250ms) for the deviant beeps only.

time 3 : 300-550 ms : Frontal regions activation related to the decision making and motor preparation, for the deviant beeps only (after 300ms).

The computation are done here only for the second recording.


Coherence

Correlation

For this data we select three main time windows to compute the connectivity:

time 1 : 0-150 ms : we expect the bilateral response in the primary auditory cortex (P50, N100), in both experimental conditions (standard and deviant beeps).

time 2 : 100-300 ms : Bilateral activity in the inferior frontal gyrus and the auditory cortex corresponding to the detection of an abnormality (latency: 150-250ms) for the deviant beeps only.

time 3 : 300-550 ms : Frontal regions activation related to the decision making and motor preparation, for the deviant beeps only (after 300ms).

The computation are done here only for the second recording.


For the time 1, We find high correlation value in both hemisphere on the temporal areas.

This connectivity is observed between the area 99 and 41 and between the 42 and 100 areas.

Corresponding to the name of the areas here

time 3 : 300-550 ms : Frontal regions activation related to the decision making and motor preparation, for the deviant beeps only (after 300ms).

The computation are done here only for the second recording.

Coherence

Correlation

For the time 1, We find high correlation value in both hemisphere on the temporal areas.

This connectivity is observed between the area 99 and 41 and between the 42 and 100 areas.

Corresponding to: name of the areas here

Similar results are observed either for the deviant and standard sounds.

MatrixDeviantCorDestrieuxTime1.PNG GraphDeviantCorDestrieuxTime1.PNG

For the time 3,


PLV

This connectivity is observed between the area 99 and 41 and between the 42 and 100 areas.

Corresponding to: name of the areas here

Similar results are observed either for the deviant and standard sounds.

MatrixDeviantCorDestrieuxTime1.PNG GraphDeviantCorDestrieuxTime1.PNG

For the time 3,

PLV


GraphStandardPlvDestrieuxBandbetaHzTime3_all.PNG GraphDeviantPlvDestrieuxBandbetaHzTime3_all.PNG

Using the option > right-click on figure> Graphic Options > Display Region max M or just use from the keyboard with M key.

GraphStandardPlvDestrieuxBandbetaHzTime3_Max.PNG } GraphDevianPlvDestrieuxBandbetaHzTime3_Max.PNG

TODO : Sensors level

Connectivity is computed at the sensors or the electrodes levels from the recorded time series.

PLV

GraphStandardPlvDestrieuxBandbetaHzTime3_all.PNG GraphDeviantPlvDestrieuxBandbetaHzTime3_all.PNG

Using the option > right-click on figure> Graphic Options > Display Region max M or just use from the keyboard with M key.


GraphStandardPlvDestrieuxBandbetaHzTime3_Max.PNG } GraphDevianPlvDestrieuxBandbetaHzTime3_Max.PNG

TODO : Sensors level

Connectivity is computed at the sensors or the electrodes levels from the recorded time series.

PLV

GraphStandardPlvMEGBandbetaHzTime3_All.PNG GraphDevianPlvMEGBandbetaHzTime3_all.PNG

Using the option > right-click on figure> Graphic Options > Display Region max M or just use from the keyboard with M key.


GraphStandardPlvMEGBandbetaHzTime3_Max.PNG GraphDevianPlvMEGBandbetaHzTime3_Max.PNG

Advanced

TODO : discuss

- Explain or give more information about the methods and how to choose the best parameters

ex: plv better with 100 samples & narrow bands

Using the option > right-click on figure> Graphic Options > Display Region max M or just use from the keyboard with M key.

GraphStandardPlvMEGBandbetaHzTime3_Max.PNG GraphDevianPlvMEGBandbetaHzTime3_Max.PNG

TODO : discuss

- Explain or give more information about the methods and how to choose the best parameters

ex : plv better with 100 samples & narrow bands

- Explain the choice either with ERP or without, and why (link to the cited paper, can't find it)

- Show/add other relevant measures of statistics to separate the two conditions

- Add the option : checkbox remove the erp for PLV and CORR and PTE

- ...

Advanced

Granger Causality - Mathematical Background

GC_Math_Time2.PNG



Practical issues about GC:

Temporal resolution: the high time resolution offered by MEG/EEG and intracranial EEG allows for a very powerful application of GC and also offers the important advantage of spectral analysis.

Stationarity: the GC methods described so far are all based on AR models, and therefore assume stationarity of the signal (constant auto-correlation over time). However, neuroscience data, especially task-based data such as event-related potentials are mostly nonstationary. There are two possible approaches to solve this problem. The first is to apply methods such as differencing, filtering, and smoothing to make the data stationary (see a recommendation for time domain GC). Dynamical changes in the connectivity profile cannot be detected with the first approach. The second approach is to turn to versions of GC that have been adapted for nonstationary data, either by using a non-parametric estimation of GC or through measures of time-varying GC, which estimate dynamic parameters with adaptive or short-time window methods (Bressler and Seth, 2011).

Number of variables: Granger causality is very time-consuming in the multivariate case for many variables (O(m^2) where m represents the number of variables). Since each connection pair results in two values, there will also be a large number of statistical comparisons that need to be controlled for. When performing GC in the spectral domain, this number increases even more as statistical tests have to be performed per frequency. Therefore, it is usually recommended to select a limited number of ROIs or electrodes based on some hypothesis found in previous literature, or on some initial processing with a more simple and less computationally heavy measure of connectivity.

Pre-processing: The influence of pre-processing steps such as filtering and smoothing on GC estimates is a crucial issue. Studies have generally suggested to limit filtering only for artifact removal or to improve the stationarity of the data but cautioned against band-pass filtering to isolate causal influence within a specific frequency band (Barnett and Seth, 2011).

Volume Conduction: Granger causality can be performed both in the scalp domain or in the source domain. Though spectral domain GC generally does not incorporate present values of the signals in the model, it is still not immune from spurious connectivity measures due to volume conduction (for a discussion see (Steen et al., 2016)). Therefore, it is recommended to reduce the problem of signal mixing using additional processing steps such as performing source localization and doing connectivity in the source domain.

Data length: because of the extent of parameters that need to be estimated, the number of data points should be sufficient for a good fit of the model. This is especially true for windowing approaches, where data is cut into smaller epochs. A rule of thumb is that the number of estimated parameters should be at least (~10) several times smaller than the number of data points.

Additional documentation

References

Articles

Forum discussions

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Tutorials/Connectivity (last edited 2020-04-01 06:01:22 by TakfarinasMedani)