How to compute a projection matrix?

[Nadezhda Chaplinskaia]

Hello,

Could you please tell me what is the correct way to compute a Projection Matrix to monitor the activity with scalp EEG in TVB? 

I have obtained all other necessary files (connectivity matrix, tracked length matrix, centers coordinates, average region orientations, region mapping, sensors) and also I have computed the leadfield matrix, but I have doubts of how to use leadfield matrix to compute projection matrix.

Thanks!

Best,

Nadezhda

[WOODMAN Michael]

hi,

the lead field matrix is the projection matrix, so you likely already have it and are just confused by the confusing naming scheme.

cheers

Marmaduke

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[Nadezhda Chaplinskaia]

Hi,

Thank you for the quick reply! 

My leadfield matrix has the shape of (n_nodes, n_channels, 3), but the projection matrix should be with the shape (n_nodes, n_channels). Could you please tell me how to obtain the leadfield matrix with the right shape?

My idea was that the projection matrix is the projection of average region orientations to the leadfield, so that knowing the leadfield and average normal vectors I could compute the projection matrix. Am I wrong? 

Thank you very much for the help!

Nadezhda

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[WOODMAN Michael]

hi

Yes you can apply the average normals to the 3 orthogonal dipoles to get the correct shape.  

cheers,

Marmaduke

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Sent: Wednesday, February 26, 2025 5:35:39 PM
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Subject: [RESEAUX SOCIAUX] Re: [RESEAUX SOCIAUX] [TVB] How to compute a projection matrix?

 

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[Michelangelo Fabbrizzi]

Hi Nadezhda,

I think it can help you read here https://neuroimage.usc.edu/brainstorm/Tutorials/HeadModel (Gain Matrix). You have to convert from "unconstrained" (3 orthogonal directions in the space) to "constrained" (1 direction, normal to the cortex surface in the point of the dipole).  Of course, it works properly only if you have the surface of your subject (not an average surface).

If you calculated the Gain (or Leadfield, or Projection) Matrix with Brainstorm, you can use the bst_gain_orient command. If you used SimNIBS you can read the gifti surfaces, concatenate and then project to normal.

Hope it helps,

Miche