Dear Serge,
> I have a difficulty in finding the right way to perform with SPM the
> following analysis.
> 1. In a PET study of the brain correlates of emotion, we use 5
> experimental conditions, which we consider, on the basis of behavioral
> studies, as stimuli of variable intensity (1, 2, 3, 4, 5) purported to
>
> induce variable levels of the emotional state (stimuli of graded
> intensity).
> 2. The second feature of this study is that we want to compare the rCBF
> responses to stimuli of graded intensity of two groups of subjects: (i)
>
> healthy subjects and (ii) patients who experience the emotional state
> with decreased intensity (at each given level of stimulus intensity).
> 3. The level of emotional response is assessed via a subjective measure,
>
> which may vary from 1 to 9.
> 4. In each of the two groups, we have studied the correlation between
> the level of stimuli (1, 2, 3, 4, 5) and the rCBF.
> 5. We have then studied the regions where the correlation between level
> of stimulus intensity and rCBF was different in the 2 groups, ie, we
> have studied the Group * Level of Stimuli interaction, and found a set
> of regions where rCBF grows (or decreases) more steeply in one group
> than in the other.
> 6. The subjective measure of emotion has also been found to be
> significantly related to the Group * Level of Stimuli interaction, ie,
> the level of emotion grows more steeply in one group than in the other.
>
> 7. However, for each particular region found in (5), we do not know
> whether its rCBF is, or is not, related to the differential variation of
>
> the subjective measure of emotion in the 2 groups. Clearly, both the
> differential variation of the subjective measure and the differential
> variation of rCBF in each region found in (5) are correlated with
> stimulus intensity. But this does not mean that, for all of these brain
>
> regions, the differential variation of rCBF is correlated with the
> differential variation of the subjective measure (finding a correlation
> between A and C and between B and C does not mean that A and B are
> correlated).
> 8. Our question, then, is: Which is the way to identify with SPM those
> regions found in (5) whose differential variation in the 2 groups in
> response to stimuli of graded intensity is correlated with the
> differential variation of level of emotional response in the 2 groups?
> Thanks for your help!
> Serge Stoleru
> PS. Is this question equivalent to identifying regions where rCBF is
> related with a second-order Group * Level of stimulus intensity * Level
>
> of emotion interaction? If yes, how is it possible to conduct this
> analysis with SPM?
You wrote further:
> What I mean by 'differential variation' is that, in
> response to the stimuli of graded
> intensity, the 2 groups, ie, patients and controls, do not respond in the
> same way. For instance, in some brain regions, rCBF is positively
> correlated with stimulus intensity in the patients' group, whereas rCBF is
> negatively correlated with stimulus intensity in the control group. In other
> regions, rCBF is positively correlated with stimulus intensity in the
> patients' group but not significantly correlated with stimulus intensity in
> the control group. In still other regions, rCBF is positively correlated
> with stimulus intensity in the both groups, but the correlation is higher in
> the controls.
> On the other hand, we also know that the two groups do not respond in the
> same way on the subjective measure of emotion: the correlation between
> stimulus intensity and the subjective measure is higher in controls. I also
> call the latter finding a 'differential variation' .
> Now, we would like to know if there is some relationship between the rCBF
> findings, ie, what I called 'differential variation' of rCBF, and the
> subjective measure finding, ie, the 'differential variation' on the
> subjective measure. Quite possibly, for some brain regions the 'differential
> variation' of rCBF is unrelated to the 'differential variation' on the
> subjective measure. However, for other brain regions, there may be a
> relation. My question is : Which are the brain regions where there is such a
> relation between the 'differential variation' of rCBF and the 'differential
> variation' on the subjective measure.
I think there are two issues here. One is a rather mathematical and the
other a conceptual one.
The mathematical one:
It can be assumed that your two regressors are correlated. Let's call
the compound of intensity vectors the I-regressor and the compound of
ratings the R-regressor.
To use both regressors in one model to fit rCBF, you have to
orthogonalize one regressor with respect to the other. (It makes maybe
most sense to orthogonalize R with respect to I.) If you do this, the
I-regressor will explain anything in the rCBF that is linearly related
to stimulus intensity. The R-regressor will therefore capture the
effects that deviate from the I-regressor, but conform to the ratings.
Potential problem: If the form of R is not really different from I, then
there won't be much left of R after orthogonalization...
The conceptual one:
You have one independent (causing) variable, the stimulus intensity. The
rCBF and the ratings are dependent variables. Therefore, if you fit rCBF
to a model containing only the intensity regressor(s), the fitted rCBF
will in some way be related to your ratings, just because rCBF and
ratings are dependent variables of the same causing thing. In other
words, a brain region showing evidence of different slopes of your
I-regressor(s) between patients and controls cannot be 'unrelated' to
the subjects' ratings. The relationship between ratings and stimulus
intensities is rather fixed for each subject. To see the nature of this
relationship for each subject, you could e.g. fit a 2nd or higher order
polynomial expansion of the intensities to the ratings (or the other way
around).
Stefan
--
Stefan Kiebel
Functional Imaging Laboratory
Wellcome Dept. of Cognitive Neurology
12 Queen Square
WC1N 3BG London, UK
Tel.: +44-(0)20-7833-7478
FAX : -7813-1420
email: [log in to unmask]
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