# Connectivity Tutorial and Methods Development on BST

Hello BST-ers;
I was checking the connectivity tutorials online and couldn't really get a hang on the various things that we can do with BST.

Specifically, I have a few points that might be of interest to other members:

1. I created some scouts with BST and thought about running some granger causality analyses; however, I see that not everybody agrees with GC anymore, so I wanted to have your opinion on this;

2. do we have an expected date for the release of online documentation regarding the connectivity? IMHO, BST is so clear up until the source level that I am sure a lot of us are hitting against this cap;

3. irrespectively of BST current development, how would you conduct statistical comparisons of connectivity matrices across participants (kind of in the Process A vs Process B fashion?). I am interested in comparing the connectivity between two conditions, but I am not sure what the suggested way of doing this could be.

Thanks again for the ginormous work y'all are doing.
Best,
Alfredo

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Dear Alfredo,

1. Granger causality is a good approach to differentiate between the source and the sink of information flow. The performance of GC depends on how accurate is the underlying model and assumptions. Also, the interpretation is not very easy when we have more than two signals in our model. That is why we only have bi-variate functions. However, If you have few sources it should have satisfactory results.

2. We are working on documentation for the connectivity section and try to generate examples for sources as well. You can check the progress on the designated page. Hopefully, it will be available by the end of summer.

3. There are a couple of approaches for that. Sometimes you can find features from connectivity matrices (like network measures) and then compare those features between two groups. Another approach is to subtract one matrix from another one (if there are dependent groups like two conditions of a cognitive task) and compare the difference with a null hypothesis distribution to find out the connections with significant differences between groups.

• Hossein

Hello Hossein,
This is great, thanks!

Just to push forward the convo meanwhile the Tutorials are out, let me try to ask a couple more Qs that might be helpful to all of us:

1. Granger causality is a good approach to differentiate between the source and the sink of information flow. The performance of GC depends on how accurate is the underlying model and assumptions. Also, the interpretation is not very easy when we have more than two signals in our model. That is why we only have bi-variate functions. However, If you have few sources it should have satisfactory results.

If I understand this correctly, then GC is better suited for testing the influence of one region to another (2 signals) or of a few ROIs on each other. Am I correct?

3. There are a couple of approaches for that. Sometimes you can find features from connectivity matrices (like network measures) and then compare those features between two groups. Another approach is to subtract one matrix from another one (if there are dependent groups like two conditions of a cognitive task) and compare the difference with a null hypothesis distribution to find out the connections with significant differences between groups.

Cool! My design is a within-subject, therefore I believe that this second scenario could fit my needs. Trying to implement it into BST, would you run a Process 2 A(Condition 1) - B (Condition 2) difference and then test the result on Process 1 --> test --> Parametric Test Against zero?

Cheers;

Maybe a non-parametric paired test?

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Thanks @Francois ;

Yet, if I subtract the connectivity matrix from condition A - B (Process 2), and then use the resulting N images (one difference file per subject) in Process 1 I can only use Test --> Parametric Test Against Zero.
I can't seem to be able to find a non-parametric option.

Am I getting this right @hossein27en ?

Yet, if I subtract the connectivity matrix from condition A - B (Process 2), and then use the resulting N images (one difference file per subject) in Process 1 I can only use Test --> Parametric Test Against Zero.

Using parametric tests requires values that are following a normal distributions:
https://neuroimage.usc.edu/brainstorm/Tutorials/Statistics#Parametric_Student.27s_t-test
You have to validate carefully for this normality hypothesis first:
https://neuroimage.usc.edu/brainstorm/Tutorials/Statistics#Histograms

I can't seem to be able to find a non-parametric option.

Indeed, there are no permutation statistics we can compute from one single set of samples. We need two sets of samples to permute between them:
https://neuroimage.usc.edu/brainstorm/Tutorials/Statistics#Nonparametric_permutation_tests

Cool; now that makes more sense.

So, a good option seems to have the individual connectivity matrices in Process 2 (A - B) and then run a Test --> Perm t-test paired.

Is there a way to implement a sliding window for the test (e.g., running the connectivity analyses on 10ms windows rather than on the entire file - and not manually changing the "time window" option?).

Shall that be scripted?

Time windows? You have a time dimension in you Granger causality matrices?

Not sure what you can do with these files, but in general, if you want to compute something on averages over a short time window, you can call the process "Frequency > Group in time or frequency bands" first. But I have no idea if this behaves well in the case of connectivity matrices, or if it is related to what you are asking...

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I forgot to mention that the second part of the question was about the Amplitude Envelope Correlation connectivity option...

and here some info about the difference between various methods (see Table 1)
O'Neill, G. C., Tewarie, P., Vidaurre, D., Liuzzi, L., Woolrich, M. W., & Brookes, M. J. (2018). Dynamics of large-scale electrophysiological networks: a technical review. Neuroimage , 180, 559-576.

Yeah. It is good to use the non-parametric tests most of the time so you don't need to be concerned about the distribution of your data.
However, if you want to do it for multiple time windows and obviously each element of the matrix, you need to do correct multiple comparisons.

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Thanks @hossein27en;
I went a little bit further with this, and used the AEC method to estimate (leakage controlled) amplitude correlation between a few ROIs across different conditions. Then computed non-parametric testing as you suggested.

I am still trying to wrap my head around the directed measures of connectivity;
I have followed the same procedure but estimated Granger Causality (maximum default order = 10) between the same two regions to investigate the direction of the flow (A to B or vice versa). Yet, with this method the two ROIs were not significantly related to each other.