Dear Brian,

Thanks for your email. To share our thoughts with the community I took the
liberty to forward your mail to the SPM list.

> 1) If I set my parameters to model exponential decay during
> a certain block, when I set up a contrast for this individual
> subject, should I compare this parametric column to another
> (ie fixation) or should I simply weight my parametric column
> as 1 and leave everything else blank? If I do this, are my
> t-values representing the extent to which they "fit" the
> exponential decay function that I have specified?

If ypou specify a contrast with a single 1 on the exp. decay regressor. This
gives you a statistic about how much of your variance is explained by this
regressor, on top of all mother regressors.

> 2) What does the time option under parametric modulation do?
> Is this linear?

Yes, but if you use order > 1 you get a polynomial expansion and can also
account for non-linear effects

> Is there a way to use the time option in
> order to create a SPM of the "rate of habituation" ? This
> would be great because I would then be able to enter these
> maps into a regression and make conclusions with regard to
> individual differences in rates of Habituation. I have
> thought of entering my "exponential decay" maps into a
> regression, but I do not think that this is really valid. In
> this case I would be regressing the extent to

Very interesting point. Given that SPM uses the GLM such an analysis is not
possible because your are trying to estimate parameter k in an equation like
f(x) = exp(1-k*x) where exp is the exponential function. This is non-linear.
There are however two options:
1) Take voxel timeseries that you are interested in and and use a nonlinear
estinmation technique to estimate k
2) Linearize the problem around a point of interest by using the idea of a
Taylor expansion: Practically you create two exponential decay curves using
two different values of k that are in the range of k that you are interested
in. The difference between the two curves can then be seen as the partial
derivative with respect to k i.e. shape. This is exactly the same idea as
used within SPM when trying to estimate latency differences of the hrf by
using the hrf with its time derivative.

> which each subject fits the decay model and not the rate of
> habituation. So
>
> theoretically, it would be great to create a "slope map".

Using this idea you will be able to generate slope maps similar to latency
maps as have been suggested by Rik Henson in his paper in Neuroimage:

http://www.ncbi.nlm.nih.gov/entrez/query.fcgi?cmd=Retrieve&db=PubMed&dopt=Ci
tation&list_uids=11771976


> Thank you very much for any advice, your time is greatly appreciated.
> Brian


-Christian

--
Prof. Dr. Christian Büchel
Institut für Systemische Neurowissenschaften
Haus S10, Universitätsklinikum Hamburg-Eppendorf, Martinistr. 52, D-20246
Hamburg, Germany
Tel.: +49-40-42803-4726
Fax.: +49-40-42803-9955
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http://www.uke.uni-hamburg.de/institute/systemische-neurowissenschaften/