Dear experts,
would that mean that any attempt to determine %signal change relative to
the local mean is essentially nonsense when analyzing smoothed data
parametrically, or does GM-scaling as applied by SPM99 allow for some
related inference? Can the area-under-the-curve be of use in some way?
TIA- andreas
Karl Friston wrote:
>
> Dear Tom,
>
> > > Given two volumes V_1 and V_2 sampled at discrete points, in both V_1
> > > and V_2 homologous locations (A_1 and A_2) show the same mean and the
> > > same activation effect, where A_1 and A_2 are the only locations showing
> > > an activation effect. Let the voxel intensities in V_1 and V_2 around
> > > A_1 and A_2 be different. Now apply a spatial convolution L to both V_1
> > > and V_2.
> > >
> > > Note that the estimated mean intensities in the convolved V_1 and V_2 at
> > > voxel A_1 and A_2 will be different, whereas the measured activation
> > > effect will not be a function of the intensities around A_1 and A_2.
> >
> > But the assuption that "A_1 and A_2 are the only locations showing an
> > activation effect" seems a bit dodgy... we never have exactly zero
> > activation anywhere.
> >
> > What we get after convolution is a mix of everything from the
> > local neighborhood... the estimated baseline at A_1 after convolution is
> > a mixture of baseline around A_1... the estimated activation a mix
> > activation around A_1.
> >
> > > This example can be generalized to a range of other spatial
> > > configurations. In other words, relating the signal change to the voxel
> > > mean intensity can be misleading, if some low-pass filter L has been
> > > applied to the image prior to the statistical analysis.
> >
> > Smoothing the data means you're smoothing both the signal and the
> > baseline. Maybe there is a more compelling example where one would
> > get misleading answers?
>
> I think Stefan's point is simpler and more fundamental than it may
> appear. Any discrepancy between the effects of spatial convolution
> (e.g. partial volume effects of voxels in fMRI, PSF in PET or applied
> smoothing) on the background signal and the change induced by neuronal
> responses will render the ratio between change and background signal
> uninterpretable (strictly speaking). This discrepancy is unavoidable
> in fMRI because the signal has at least three components (vascular
> deoxyhemogloblin, intra-voxel magnetic feild inhomogenieties and
> conventional relaxation) which themselves change from voxel to voxel.
> This means any smoothing operator will have a different effect on the
> signal and the change in signal (because that change comes from only
> one signal component). A simple example of this would be a false
> reduction in proportional signal change caused by having two much CSF
> under the smoothing kernel relative to another equally activated
> region. In PET the same happens when the smoothing kernel is large
> relative to the activation. A focal activation of 2% in the center of
> the head of the caudate will be, apparently, reduced to 1% at the
> edge, if one uses a local ratio approach. This problem is eschewed if
> one uses a reference that is much greater than the size of the kernel
> (e.g. global reference).
>
> Thats my take anyway!
>
> With very best wishes - Karl
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