Dear Marco,

> As a preliminar temptative approach we are trying to evaluate a very
> simplified model of learning on a set of fmri time series. The model we
> are considering is composed by 3 anatomical regions, on the basis of an
> a-priori hypothesis: the learning process we are investigating is supposed
> to modulate the connections strenghts between the 2 of the 3 areas
> considered in the model, due to causal input from the third region. To
> test this hypothesis we have been trying to do the following:
>
> 1. With SPM99, we first evaluated the t-test contrast comparing condition
> A (learning condition) with the baseline B (control). In this way we
> indeed, as a-priori postulated, find strong activations in the 3 regions
> of interest.
>
> 2. From the maximal activated voxel within these 3 regions, we extracted
> the first eigenvariate with the V.O.I. function of SPM99.
>
> 3. Since our original time series included additional tasks, which we
> didn't want to include in the EC analysis, we have edited the first
> eigenvariate to consider only those values corresponding to the fmri scans
> associated with task A.
> We have a first question here: do we have to take into account the delay
> of the hemodynamic response when editing the first eigenvariate? In other
> words, our TR being 3 sec, if stimulation of task A started at scan n, do
> we have to include the values of the first eigenvariate starting from the
> value associated with say scan n+2?

This is a conceptual issue. If you edit your time-series, ie cut out
only scans that were acquired during a certain condition the variance
and covariance between these areas is governed by fluctuations in the
BOLD response during this condition. In other words in a way you are
residualising your data with respect (removing variance due) to the task
of interest. This can be interesting, it tells you something about the
covariance of two regions while they are activated and in a way
"neglects" the common input by the stimulus.
In your case I would adopt a different approach and use the whole
time-series and introduce an additional influence/regressor which would
have ones when the condition you are interested in was presented and
zero elsewhere. You then create an interaction model. Let's assume you
want to test the the influence of A on B:

A--> B, you would then create the interaction variable i. The new model
is

A --> B
i-->B
A*i -->B

The latter connection (regression!) is the one you are interested in,
asking the question whether the influence of A on B is modulated by i,
i.e. stronger/weaker during your condition of interest.
By the way in this simple model the regression coefficients will be
identical to the patrh coefficients in a structural equation modelling
analysis!

> 4. We then tried with a statistical software package to compute the
> covariance matrix between the first eigenvariates of the 3 anatomical
> regions considered in the model. However, we are not much confident about
> the values found in such a way: our covariance values range from 10E-9 to
> 10E-8 and this looks a bit suspicious to us (very small covariance?).
> A covariance analysis performed in parallel on the values produces values
> which are significative. We have found in a few papers, that it might be
> possible to include correlation matrices instead of covariance matrices as
> an input for EC.
> We are confused about the correct approach to follow here.

This seems odd, but might be related to the scaling of your data. Check,
how big the correlations between whole fMRI time-series are. They should
be much bigger.

> 5. Finally, and what's causing us the most troubles: we have tried to
> design our connectivity model with LISREL 8.30 (Student Edition), but we
> have repeatedly failed.
> We are not sure whether we are doing something wrong and if LISREL is a
> suitable software for this type of analysis. Does anyone have any
> experience with the Student edition of LISREL or could anybody suggest a
> better software?

LISREL is a standard package for structural equation modelling and it
should do what you want. I have never used it, but have seen imaging
papers using LISREL for SEM. I am not sure but this was one of Randy
McIntosh's or Barry Horwitz's papers.

--

-Christian Buechel

--
Dr. Christian Buechel
Neurologische Universitaetsklinik, Haus B
Universitaets-Krankenhaus Eppendorf
Martinistr. 52
D-20246 Hamburg
Germany
Tel.: +49-40-42803-4726
Fax.: +49-40-42803-5086
email:[log in to unmask]
www.uke.uni-hamburg.de/kliniken/neurologie/pages/mitarbeiter/buechel_c.htm
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