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

Cognitive and perceptual functions are the result of coordinated activity of functionally specialized regions in the brain. Brain connectivity investigates how these different regions (or nodes) interact as a network, with the goal of having a better understanding of how the brain processes information. Depending on which connectivity characteristic is studied, a distinction is made between structural (fiber pathways), functional (non-directed statistical dependency) and effective (causal interaction) connectivity between regions. Effective connectivity is often referred as directed functional connectivity. In this tutorial we will see how to compute different connectivity metrics for non-directed and directed functional analyses in Brainstorm, first with simulated data and later with real data.

Contents

  1. General considerations in connectivity analysis
  2. Simulated data (MAR model)
  3. Correlation
  4. Coherence
  5. Granger Causality
  6. Coherence and envelope Correlation by Hilbert transform and Morlet wavelets
  7. Phase locking value
  8. Correlation
  9. Method selection and comparison
  10. Connectivity measures on real data : LFP data
  11. TODO : Connectivity measure on real data : MEG/EEG data
  12. TODO : Connectivity measure on real data : MEG/EEG data
  13. Sections to add
  14. On the hard drive
  15. Additional documentation

General considerations in connectivity analysis

Sensors or sources: Connectivity analysis can be performed on sensor data (EEG/MEG signals) or on reconstructed sources (voxels or scouts).

Recording condition: While connectivity analysis can be performed on resting-state (spontaneous) and event-related (trials) recordings, the appropriate connectivity method depends on the recording condition.

Point-based connectivity vs. full network: Connectivity can be computed between one node (aka seed) and the rest of the nodes in the network (1×N approach), or between all the possible node pairs in the network (N×N approach). While the later calculates the detailed connectivity graph, the 1×N approach is faster to compute and it is more useful when you are interested in the connectivity of a specific ROI wrt 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 methods rely on the time-frequency representation of the data. These approaches include short time Fourier transform, Hilbert transform, and Morlet wavelet.

Simulated data (MAR model)

To compare different connectivity metrics, we use simulated data with known ground truth. Consider three channels constructed using the following multivariate autoregressive (MAR) process of 4th order.

\begin{eqnarray*} x_1(n) & = & \sum_{k=1}^{4} A_{(1,1,k)}x_1(n-k) + e_1(n) \\ x_2(n) & = & \sum_{k=1}^{4} A_{(2,2,k)}x_2(n-k) + e_2(n) \\ x_3(n) & = & \sum_{k=1}^{4} A_{(3,3,k)}x_3(n-k) + \sum_{k=1}^{d} A_{(1,3,k)}x_1(n-k) + e_3(n)\\ \end{eqnarray*}

where $$A_{(i,i,:)}$$ with $$i = 1, 2 \textrm{ and } 3$$ 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 the third channel a similar level of energy in both bands. Additionally, the signal in the third channel is influenced by the signal in first channel by the filter $$A_{(1,3,:)}$$. For a MAR model, the transfer function (or frequency response) is defined as:

$$H_{i,j}(f) = \frac{1}{A_{i,j}(f)}$$\\

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The diagonal elements show the auto-transfer function, which in our specific case is 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. These transfer functions are our connectivity ground of truth.

The simulated data and scripts to generate it can be found here.

Correlation

Correlation is a non-directed connectivity metric that can be used to show similarity, dependence or association among two random variables or MEG/EEG signals. While this metric has been widely used in electrophysiology, it should not be considered the best technique to evaluate connectivity. The correlation metric 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.

For non-directed connectivity metrics, the metric value " from Signal $$i$$ to Signal $$j$$ " is equal to the metric value " from Signal $$j$$ to Signal $$i$$ ".

In Display as image, the value of the connectivity metric between a signal and itself plotted as zero so that it doesn't force scaling the colormap to 1 if the other values are much smaller.

Coherence

Coherency or complex coherence, $$C_{xy}(f)$$, is a complex-valued metric that measures of the linear relationship of two signals in the frequency domain. And, its magnitude square coherence (MSC), $$C^2_{xy}(f)$$, often referred to as coherence, measures the covariance of two signals in the frequency domain. For a pair of signals $$x(t)$$ and $$y(t)$$, with spectra $$X(f)$$ and $$Y(f)$$, the MSC is defined as:

Two related measures, which alleviate the problem of volume conduction, are ?imaginary coherence, $IC_{xy}(f)$, and the ?lagged coherence, $LC_{xy}(f)$, which are defined as:

where $$\mathrm{Im}$$ and $$\mathrm{Re}$$ describe the imaginary and real parts of the cross spectrum.

To calculate coherence values in Brainstorm:

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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.

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Similarly, we can compute the "imaginary coherence":

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And the "lagged coherence": [ATTACH]

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.

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Input options:

Estimator options:

Output options:

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



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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. [ATTACH]

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:



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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

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

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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: 

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


 


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. 
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Method selection and comparison


We can have a comparison between different connectivity functions. The following table briefly does this job. 
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Comparing different approaches with the ground truth we find out that the HCorr function works slightly better than other coherence functions. 
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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). 
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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. 
 
 
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. 
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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. 
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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. 
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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] 
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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'. [ATTACH] 
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 
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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. 
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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 
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Late response t ϵ [250-450 ms] : 
Parameters :0mm, band1, threshold 0.666 
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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 
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For both conditions, we observe similar value. 
Late response t ϵ [250-450 ms] : 
Parameters : 0mm, band2, threshold 0.35, with the ERP 
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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, 
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Late response t ϵ [250-450 ms] : 
Parameters : 0mm, band1, threshold 0.66 
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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 
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Parameters : 0mm, threshold 0.63, without the ERP 
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Spectral Granger Causality (SGC)


Early response t ϵ [100-250 ms] :  
Parameters : 0mm, threshold 2.5, band1 12.5, with the ERP 
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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 
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Early response t ϵ [100-250 ms] :  
Parameters : 0mm, threshold 2.5, band1 12.5, without ERP 
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Late response t ϵ [250-400 ms] :  
Parameters : 0mm, threshold 0.315, band1 12.5 
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Early response: without ERP 
 
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Early response: without ERP 
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Late response: without ERP 
 
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Phase Transfer Entropy (PTE)


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


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


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Late response: without ERP 
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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. 
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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) [ATTACH] 
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. 
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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) 
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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. 
 
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. 
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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. 
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For the time 3,  


PLV


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


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


PLV


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


TODO : Sensors level


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


PLV


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


Sections to add




On the hard drive


TODO: Document data storage. 


Additional documentation




References




Articles




Forum discussions


 






 
















    
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Tutorials/Connectivity  (last edited 2021-03-26 00:32:29 by RaymundoCassani)