Hello,

I am a newbie with gPPI so I apologize if this is trivial. Consider two seed regions of interests (e.g. two spheres in two different parts of the brain). I run gPPI for both of them. I have noticed that the value reported in the seed1 t-results at location of seed2, is different from the value reported in seed2 results at location seed1: i.e. the gPPI results are not symmetric. Since I am trying to build a connectivity (adjacency) matrix between multiple ROIs, the adjacency matrix is not symmetric and I am not sure how to proceed with graph theoretical measures.

Is there an error in my analysis or is it correct that the results are not symmetric? The top triangle of the adjacency matrix is strongly correlated with the bottom triangle, but since they are not identical I am not sure which value to consider as "task connectivity" link weight between the two ROIs.

Thank you!
Enrico

Enrico,

You are correct that the gPPI is not symmetrical. A few possible reasons are: (1) The deconvolution process; (2) A might influence B, but B might not influence A; (3) difference in neurovascular coupling; (4) differences in the timing of the neural activity or BOLD signal. For example, the activity in B is due to the task effect plus some influence from A, while the activity in A is purely due to activity from the task. There will likely be some residual correlations in actual data, which directionality can't be determined from the results. However, if you had the anatomical pathways, you could then infer direction.

For graph theory, you generally use the entire row, not just the upper or lower triangle.

There is no clear consensus as to whether you should use the top or bottom triangle or to average the top and bottom triangle. Keep in mind that if you change the order of the seeds, then the upper and lower triangles would change. For example, if you switch the top and bottom rows, then most of the matrix stays the same, but the outside rows and columns will change.

To complicate matters further with gPPI, you might have 3 or more conditions, so it is unclear, unless you are using the difference of only 2 conditions, how to apply graph theory to multiple values for each edge.

Hope this doesn't confuse you too much and hopefully it will generate some discussion about how to apply graph theory to PPI.

Dear Donald

thank you for the quick reply. This is fascinating. I was asking because I am trying to replicate the same analysis as in http://www.colelab.org/pubs/2013_Cole_NatNeurosci.pdf, specifically their comparison between gPPI and correlation/covariance approach (they mention that they obtained similar results although PPI was better in their case). Maybe I'll ask dr Cole how he dealt with the non symmetrical nature of the adjacency matrix. In theory one could think it as a directed graph... did anyone ever studied gPPI and directed connectivity e.g. using simulated networks? I also like dr Cole's point of regressing out the task to avoid looking at simple co-activations (important especially in block design)

Anyway, I also hope that this will generate some discussion about gPPI and graph theory!

all the best
Enrico

If I recall correctly, he used the upper triangle of the connectivity matrix.

I am not aware of anyone who has used simulated networks and looked at directed connectivity. 

I don't think regressing out the task works particularly well as you are only regressing out the mean effect across all blocks, there will still be residual differences on a block by block basis that is in the data.

The WB option in the gPPI toolbox dramatically speeds up the estimation process, so you can loop through many seeds quickly.