Dear Zach

I hope you don’t mind me CC’ing the SPM mailing list so others can benefit.

You asked how to interpret the self-connections in SPM. In brief, writing out the DCM for fMRI neural model (ordinary differential equation) for a self-connection:

dz/dt = (-0.5 * exp[A + Bu(t)] ) * z + CU

Where u(t)>0 at times when the modulatory input is switched on and u(t)=0 at other times. Details of the terms of the equation are in the DCM tutorial paper (https://doi.org/10.1016/j.neuroimage.2019.06.031) . Equivalently this can be written as:

dz/dt = (-0.5 * exp(A) * exp(Bu(t))) * z + Cu

So you can see the default connection strength is -0.5Hz, which is scaled by the exponential of the A matrix, and by the exponential of the B matrix (at times when modulation is switched on).

To answer your direct question, you are correct, and you can confirm this by plugging in numbers to the formula. E.g. if the modulatory input is on, so u(t)=1, and if A=0 and B=0, then the self-connection is -0.5 * exp(0) * exp(0) = -0.5Hz (the default value for a self-connection). If you increase the B parameter from zero to two, then it’s -0.5 * exp(0) * exp(2) = -3.7Hz, so much more inhibitory.

I hope that helps

Peter

Subject: Inquiry regarding interpretation of self-connection in one-state fMRI DCM

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Dear Professor Zeidman,

I apologize for reaching out once again, but I've been grappling with the interpretation of self-connection in one-state DCM for quite some time.

There is the equation:

So, large 'a' parameter will cause faster neural decay than a small 'a' parameter.

For one-state fMRI DCM, the relationship between the values on the diagonal of matrix A and 'a' is:

So large values on the diagonal of matrix A (DCM.Ep.A) will cause slower decay than small values on the diagonal of matrix A. 

However, the values on the diagonal of matrix of B matrices are NOT log scaling parameters.

So larger values on the diagonal of matrix of B matrices (DCM.Ep.B) indicate the corresponding experimental effects faster decay than small values on the diagonal of matrix of B.

Am I correct?

Thank you!

Best,

Zach