Dr. Friston,
The second, smoothing convolution may not, theoretically, introduce a second
delay, but when I compared fitted response plots with and without the first hrf
convolution, I found what appeared to be a more "delayed" waveform when both
convolutions were done (approximate delay: 2 scans or 6 sec). In fact, it
appears that this additional "delay" was the reason my activations "disappeared"
when both convolutions were done. In support of this conclusion, the activations
"reappeared" when I added the temporal derivative to the doubly convolved
boxcar!
Best Regards,
Aaron Field, MD, PhD
Department of Radiology
Wake Forest University School of Medicine
Winston-Salem, NC 27104
Voice: 336-716-9349 Fax: 336-716-2029
Karl Friston wrote:
> Dear Aaron,
>
> > > During an fMRI analysis in SPM99b, using a standard boxcar paradigm,
> > > there are two occasions when the user must decide whether to convolve
> > > with the hemodynamic response function. The first occurs during setup of
> > > the design matrix, when the option to convolve the boxcar with the hrf
> > > is offered. The second occurs during the estimation step, when the hrf
> > > is offered as an alternative to a Gaussian kernel for temporal smoothing
> > > of (I believe) the data as well as the entire design matrix, which I
> > > understand to be necessary due to the nature of serially correlated
> > > regression. If I select both of these options, does the boxcar get
> > > convolved with the hrf twice? If so, this seems inappropriate, as once
> > > should be enough.
> >
> > I can not answer your question regarding what the SPM program does, but
> > indeed it is theoretically correct to convolve the boxcar with the HRF
> > twice. This is because the underlying neural activity has been convolved
> > twice (given the assumptions one makes): once by physiology (which
> > one could heuristically associated with your "1st" HRF convolution)
> > and once by the matrix operations peformed in the SPM program.
> >
> > Sincerely,
> > Eric
>
> Eric is absolutely right. The box-car convolution with the hrf emulates
> the causes of the observed data (specifically the endogenous
> convolution of changes in neuronal activity by the hrf) to provide a
> better model of the responses. The second time the hrf can enter is in
> terms of filtering (i.e. smoothing). This is unrelated to modeling the
> causes but allows for a better model of the temporal correlations. A
> critical point to note here is that the second convolution uses a
> symmetric kernel that has the same frequency structure as the hrf but
> is not the actual hrf. This means that filtering does not implement a
> second 'delay'.
>
> Best wishes - Karl
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