Hi all,
im not the expert here, but have used this in a couple of studies. So a
few pointers below. Rik' s indeed the real expert, you probably rad his
papers on the topic (if not, see f.e.:
http://www.ncbi.nlm.nih.gov/pubmed/11771976).
Good luck,
Bas
Op 04-05-10 14:28, cyril pernet schreef:
> Hi Josee
>> I have read several threads (and a couple papers) on the use of
>> temporal and dispersion derivatives, but would like to clarify how
>> derivatives are included in/applied to a model.
> ok I'll try to answer - hopefully if all ok Rik won't have to answer
> this .. :-P
>> 1. Are there multiple HRFs tested at each voxel (e.g.., the canonical
>> HRF, time-modulated HRFs and/or dispersion-modulated HRFs)? If so, is
>> it possible that different HRFs would be retained for different
>> voxels (e.g., the canonical HRF for voxel A and a time-modulated HRF
>> for voxel B)?
> yes it creates 3 regressors per conditions ie 3 different models of
> response; for each voxel the 3 regressors are fitted to the data (so
> data are explained by a linear mixture of the 3) but yes it possible
> that data in one voxel data are better explained by the hrf, in
> another voxel better explained by a derivative
>> 2. Or are the derivatives regressors in the model for the HRF, i.e.,
>> variables that can account for and thus reduce error/variance, much
>> like a covariate? This would imply that only one HRF is modeled at
>> each voxel, but time- and dispersion-related variance between voxels
>> is taken into account in the model, correct?
> well yes and no ; yes having 3 regressors now will reduce your error
> and yes/no as you can look at the effect of each regressor (everything
> that you through in the model accounts for some variance) - also note
> that because these are basis functions they are orthogonal to each
> other and therefore derivatives only explain some variance above what
> is explained by the hrf only (unless you use this in a block design
> which mixes things up ... search for an old e-mail from J Andersson)
>> 3. If derivatives are error-reducing regressors, why are they
>> represented as independent columns (1 for time, 1 for dispersion, for
>> each condition) in the design matrix? Relatedly, when F-contrasting 2
>> conditions (say, A and B), why is it necessary to explicitly include
>> the derivatives in the contrast specification (e.g.: 1 1 1 -1 -1 -1
>> for the A minus B contrast)?
> as explained above they form 3 regressors so they make 3 columns in X
> - the F contrast has to oppose basis functions one by one ie [1 0 0 -1
> 0 0;0 1 0 0 -1 0;0 0 1 0 0 -1] otherwise you are looking for a
> combination of vectors that explain different things (amplitude,
> latency, dispersion) using different rows means find voxels where A
> and B differ for the hrf and/or the latency and/or the dispersion -
> the contrast you entered mixes all together (like averaging
> amplitude+latency+dispersion)
It is basically a Taylor series expansion
(http://en.wikipedia.org/wiki/Taylor_series) of order 1. For a temporal
Taylor expansion it is the same as predicting a value of a signal at t +
dt when you now the rate of change at time t. Compare it with being able
to predict where your car will be when you are at a location X km from
somewhere and know you drive at V km/hr. In BOLD terms, when adding this
additional regressor to your model as an additional basis function, you
allow for slight deviations in actual BOLD response timing from the one
modeled by your HRF. To fully grasp the effect of temporal or dispersion
derivatives, a deeper understanding of both GLM modeling (eg, estimating
a sum of weighted regressors to explain a signal) combined with a Taylor
series is helpful. Look at figure 1 in Rik's paper mentioned above, it
nicely illustrates this.
>> 4. Lastly, is there any reason derivatives should NOT be included in
>> a 1st-level analysis (testing for fixed effects in a small group of
>> subjects, n=5)?
> I cannot think of any - seems a good idea to me ...
Watch out for correlations between conditions in an improperly
randomized rapid event related fMRI design (eg, with overlapping HRFs).
Adding derivatives of any kind can increase especially multiple
colinearity problems.
>
> Cyril
>
>
--
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Dr. S.F.W. Neggers
Division of Brain Research
Rudolf Magnus Institute for Neuroscience
Utrecht University Medical Center
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