1) With respect to FIR modelling, did I understand you correctly in that what you said was that the FIR model has no neural basis or underpinnings, as it uses only the BOLD signal, from which to derive the underlying neural or synaptic response is an ill-posed inverse problem? In contrast, the canonical hrf as a basis function is rooted in knowledge about neural hemodynamics and therefore allows inference with respect to the underlying neural causes. Is that a fair reflection of what you said, or did I misunderstand you?

 

This is nearly right – when you estimate a hemodynamic response function (using a single canonical basis function or FIR basis functions) you are estimating the hemodynamic response (not the neuronal response).  In the special case that you use a canonical function, there is only one parameter and any condition specific differences can be attributed to differences in the amount of neuronal activity. When there are many parameters, a difference in the shape of the HRF cannot be interpreted as the difference in the shape of the neuronal input, because - as  you say - this is an ill-posed inverse (deconvolution) problem.

 

2) Also, is the temporal confound not similarly a problem when using the canonical hrf together with a parametric modulator as basis functions, simply because of the overlap/sluggishness of neural hemodynamics?

 

No – because you are forcing the same temporal shape on all the responses - so that they can only differ in their amplitude (which is modulated with the parametric regressor).

 

With very best wishes,

 

Karl