Dear Group

I am really stuck on how to do a nonlinear spm analysis problem in
my dataset which has 4 dissimilar conditon with 4 different anxiety
levels. I have read
(1) Buchel C Holmes AP, Rees G, and Friston KJ  (1997)
Characterizing stimulus-response functions using nonlinear
regressors in parameteric fMRI experiments. Neuroimage 8:140-148.

(2) Buchel C Wise RJS Mummery CJ Poline J-B and Friston KJ. (1996)
Nonlinear regression in parametric activation studies. NeuroImage 4:60-66


I have two groups of 7 subjects each (7 social phobic patients and 7
controls).

I have reason to believe from looking at between-group imaging data of
anticipation compared with rest, speech minus rest, and postpseeech minus
rest  that there is a non-linear (inverted U) relationship between anxiety
and  blood flow.

Each subject experiences four conditions

rest, anticipation, speech, and postspeech (thinking about the talk)

The 4 scans are 10 scans each and each conditon is repeated 4 times,
except rest is repeated 5 times as there is an extra rest at the end of
the time series.

For both groups, speech is the most anxiety provoking state and rest is
the least anxiety provoking state.

Patients show more self-reported anxiety than controls with rest,
anticipation, speech, post-speech, anticpation minus rest, speech minus
rest, and postspeech minus rest. The degree of difference between groups
is most prominent with speech and postspeech.

Between-group brain activity
can be summarizxed as follows:

        Anticpation minus rest  Speech minus rest    Postspeech minus rest

Cortex  Controls > Patients     Controls > Patients  Controls > Patients

Subcortex Patients > Controls   Controls > Patients  Controls > Patients


My hypothesis is that in our region of interests , both patients and
controls have a non-linear inverted U-shaped function that best describes
their relationshiop between anxiety and blood flow.  Also, I think that
patients have more anxiety so that when they make their speech, their
blood flow starts to decrease (is on the downslope of the inverrted U)
whereas controls are still on the upslope of the inverted U.


Here are my vectors of potential interest in my design of
 (rest, anticipation, speech, postspeech) conditions.
I am using spm2 as well as the medx image calculator.

                        (1,0,0,0)
                        (0,1,0,0)
                        (0,0,1,0)
                        (0,0,0,1)
                        (x1,x2,x3,x4)
                        (x1*x1, x2*x2, x3*x3, x4*x4)
                        (1,1,1,1)

where x1= anxiety during rest,
 x2= anxiety during anticipation
x3= anxiety during speech
x4= anxiety during postspeech

There is only one anxiety number for each condition (the average over all
speeches say) asked retrospectively after the scans are done.
Thus, I only have one number for speech and not 4 separate ones for each
speech, one number for rest and not 5 separate ones for each rest, etc.

Please let me know how to proceed. I am just stuck at whether to look at
individual subjects and their nonlinear regressions separately or look at
the group as a whole or try to figure out if I could tease some of the
difference due to condition (non-anxiety related) versus anxiety per se.

Almost every single subject reports that their highest anxiety occurred
during speech and their lowest was during rest. I likely will not be able
to sort out what differences are due to the widely disparant conditons of
rest, anticpation, speech, and postspeech versus what is purely due to
anxiety. This all assumes thast the same type of anxiety is occuring
during all 4 conditons.

Thanks for any help
Sincerely,
Jeff Lorberbaum