ok. my bad. I was thinking about it as if the deconvolution hadn't taken
place at the time the vectors were formed. so then you are correct it should
work out as you say. Which brings us back to your original question of which
is "best." since as you point out below conv((A-B)*xn,hrf) =
conv(A*xn,hrf)-conv(B*xn,hrf) I would say it doesn't matter except that by
separating the two conditions you could also examine the effective
connectivity in relation to each condition separately. This would be the
same as in the standard analysis if one included 2 event vectors separately
or combined them ahead of time.
darren
> -----Original Message-----
> From: SPM (Statistical Parametric Mapping)
> [mailto:[log in to unmask]] On Behalf Of Robert Welsh
> Sent: Friday, October 12, 2007 10:53 AM
> To: [log in to unmask]
> Subject: Re: [SPM] PPI Questions, a new approach
>
> Darren,
>
> Actually, if we have functions f, and g, and h, the
> distributivity property is:
>
> quantity (f-g) convolved with h is equal to quantity ( f
> convolved with h ) - (g convolved with h)
>
> That is,
>
> f*(g+h) = (f*g) + (f*h)
>
> Simple test to verify in matlab
>
> f = randn(400,1)
> g = randn(400,1)
> h = spm_hrf(2);
> sum( conv(f-g,h)) - (conv(f,h) - conv(g,h) )
>
> ans
>
> -1.6809e-15
>
> So you statement of
>
> conv((A-B)*xn,hrf) does not = conv(A*xn,hrf)-conv(B*xn,hrf)
>
> doesnt' seem to hold.
>
> Robert Welsh
>
>
> -+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+
> Robert C. Welsh, PhD
> Research Assistant Professor
> Departments of Radiology and Psychiatry
> University of Michigan
> (734) - 764 - 8541 (fax)
> (734) - 647 - 6781 (Ofc)
> rcwelsh @ med.umich.edu
>
> >>> d gitelman <[log in to unmask]> 10/11/2007 1:03 AM >>>
> Donald
>
> please see the paper
> Gitelman DR, Penny WD, Ashburner J, Friston KJ. (2003):
> Modeling regional and psychophysiologic interactions in fMRI:
> The importance of hemodynamic deconvolution. NeuroImage 19(1):200-207.
>
> PPI.ppiA-PPI.ppiB does not = PPI.ppi
>
> conv((A-B)*xn,hrf) does not = conv(A*xn,hrf)-conv(B*xn,hrf)
>
> I understand what you are saying but to examine A-B one has
> to form the interaction term with the deconvolved data, not
> with the convolved data as you are suggesting.
>
> darren
> ----------
> Darren Gitelman, MD
> Department of Neurology
> Northwestern University
> voice: (312) 908-8614
> fax: (312) 908-5073
> page: (312) 695-1849
> email: [log in to unmask]
> ----------
>
> > -----Original Message-----
> > From: SPM (Statistical Parametric Mapping)
> [mailto:[log in to unmask]]
> > On Behalf Of MCLAREN, Donald
> > Sent: Wednesday, October 10, 2007 3:09 PM
> > To: [log in to unmask]
> > Subject: [SPM] PPI Questions, a new approach
> >
> > An Alternative to the traditional PPI method proposed by Friston,
> > Penny, and Gitelman:
> >
> > The traditional approach is to enter the following into a GLM:
> > A is a vector of 1s when task A is present, 0 otherwise.
> > B is a vector of 1s when task B is present, 0 otherwise.
> > Xn=deconvolved neural signal
> >
> > Begin GLM:
> > PPI.Y=first eigenvariate adjusted for the effects of no interest
> > PPI.P=conv(A-B,hrf)
> > PPI.ppi=conv((A-B)*xn,hrf)
> >
> > The context-dependent connectivity is then tested with a
> T-contrast of
> > 1 above the PPI.ppi column.
> >
> > The proposed approach is to enter the following into a GLM:
> > N is a vector of 1s when task N is present, 0 otherwise
> >
> > Begin GLM:
> > PPI.Y= first eigenvariate adjusted for the effects of no interest
> > PPI.PA=conv(A,hrf)
> > PPI.ppiA=conv(A*xn,hrf)
> > PPI.PB=conv(B,hrf)
> > PPI.ppiB=conv(B*xn,hrf)
> >
> > If more than 2 tasks, add them below
> > PPI.PN=conv(N,hrf)
> > PPI.ppiN=conv(N*xn,hrf)
> >
> > The context-dependent connectivity is then tested with a
> T-contrast of
> > 1 above PPI.ppiA and *1 above PPI.ppiB and thus looks at where the
> > connectivity varies by task. Additionally, you can look for regions
> > that both tasks show similar connectivity patterns. Typically, this
> > might be illustrated by PPI.Y; however, PPI.Y is confounded
> by gaps in
> > stimulus presentation where the neural activity is not
> constrained and
> > might not be connected the same as during the task.
> >
> >
> >
> >
> > NOTE:
> > PPI.ppiA-PPI.ppiB=PPI.ppi=conv((A-B)*xn,hrf)=conv(A*xn,hrf)-co
> > nv(B*xn,hrf)
> >
> > The question arises is to which method best tests the
> > question, is their context-dependent connectivity differences
> > between tasks? Method 2 seems to be easily expanded to more
> > than 2 conditions. Method 2 also does make any assumptions
> > about the relative impact of the tasks on connectivity.
> >
> > Are both methods valid approaches? What are the
> > interpretations of each method? Any thoughts on this would be
> > appreciated.
> >
> > Thanks.
> >
> >
> > --
> > Best Regards, Donald McLaren
> > =====================
> > D.G. McLaren
> > University of Wisconsin - Madison
> > Neuroscience Training Program
> > Tel: (773) 406 2464
> > =====================
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