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Subject:

Re: HRF derivatives & design matrix

From:

Jason Steffener <[log in to unmask]>

Reply-To:

Jason Steffener <[log in to unmask]>

Date:

Tue, 4 May 2010 10:45:46 -0400

Content-Type:

text/plain

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text/plain (169 lines)

Hello.
Just another point, please see below.

On Tue, May 4, 2010 at 9:07 AM, S.F.W. Neggers <[log in to unmask]> wrote:
> 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

As Rik and others (Vince Calhoun and myself ) have discussed the
physiological nature of the combination is important. The higher order
derivatives should only be interpretted in relation to the principle
HRF weight. So a voxel with no weight on the HRF term and high weight
on a derivative does not make much sense under normal physiological
conditions. So bottom line is that the combination of terms is what is
important, unless the derivative terms are kept as regressors of no
interest (as discussed by Kiehl et al.)

Kiehl:
http://www.ncbi.nlm.nih.gov/pubmed/11295369
Calhoun:
http://www.ncbi.nlm.nih.gov/pubmed/15110015
Steffener:
http://www.ncbi.nlm.nih.gov/pubmed/19913625

I hope this helps,
Jason

>>>
>>> 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
>>
>>
>
>
> --
> --------------------------------------------------
> Dr. S.F.W. Neggers
> Division of Brain Research
> Rudolf Magnus Institute for Neuroscience
> Utrecht University Medical Center
>
> Visiting : Heidelberglaan 100, 3584 CX Utrecht
>           Room B.01.1.03
> Mail     : Huispost B01.206, P.O. Box
>           3508 GA Utrecht, the Netherlands
> Tel      : +31 (0)88 7559609
> Fax      : +31 (0)88 7555443
> E-mail   :[log in to unmask]
> Web      :http://www.neuromri.nl/people/bas-neggers
> --------------------------------------------------
>
>
> ------------------------------------------------------------------------------
>
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> (Wet Hoger Onderwijs en Wetenschappelijk Onderzoek) en staat geregistreerd
> bij
> de Kamer van Koophandel voor Midden-Nederland onder nr. 30244197.
>
> Denk s.v.p aan het milieu voor u deze e-mail afdrukt.
>
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>
> This message may contain confidential information and is intended
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>



--
Jason Steffener, Ph.D.
Department of Neurology
Columbia University
http://www.cumc.columbia.edu/dept/sergievsky/cnd/steffener.html

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