Dear SPM experts

I am making a new post because I realized my original question has changed.

I m trying to find the neuronal signal from VOIs which I want to use in a separate analysis. Below are my questions

1. I was told that DCM.qU.x gives me the neuronal signal of my VOIs. However I m looking for specific equations that can give me the transformation from fMRI signal to the neuronal signal (conditional expectations of the hidden neuronal states)

2. I did a quick test with 3 regions (VOIs), 500 time points., so each region was 1x500. When I applied DCM to it, and looked at the neuronal states, it was as follows

size(DCM.qU.x{1,1})

ans =

15 500

The question is, why this 3 changed to 15 ?

The size of the S matrix is 15x15 which makes sense if x is 15. However I m not sure why these 3 regions were changed to 15

size(DCM.qU.S{1,1})

ans =

15 15

3. Does adopting a mean field assumption for estimating the signal in each node mean these nodes cannot be considered independent of each other ? And would that also induce some correlation between these nodes due to this assumption ? Are we here referring to each voxel in a VOI as a node, or each VOI as a node.

Thanks a lot and best
Qasim