Dear Joe,
> Can anyone tell me how resel sizes are calculated? As I understand it,
> the size of the resel depends on three things: the smoothness of the
> original data, the voxel size of the image, and the smoothing applied
> to the images. Is this correct?
Nearly. Resel stands for 'resolution element'. The number of resels
is a measure of volume that can be thought of as normalized for
intrinsic smoothness. It is independent of voxel size. The size of a
resel, expressed in voxels, is the FHWH of a Gaussian smoothing kernel
that would produce the same smoothness in voxel-space. When making
corrections for multiple comparisons one only needs to know the number
of resels that comprise the search volume. The size of one resel (i.e.
FWHM) is calculated using the variance-covariance matrix of the first
partial spatial derivatives.
> I've been comparing some PET and fMRI data that we've collected and we
> found that to achieve similar resel sizes (and therefore similar
> numbers of statistical comparisons), we had to smooth the PET data much
> more than our fMRI data (16 vs 8mm FWHM) even though both data sets
> used isotropic 2mm^3 voxels. I assume this indicates that the
> intrinsic smoothness of the PET data is less than that of the fMRI
> data? Presumably this is why fMRI images are typically smoothed with
> small kernels (5-8mm) while PET data images are smoothed with larger
> kernels (12-16mm)?
I think that you may be miscontruing resel number with a smoothness
metric. It is not - it is a metric of volume. PET data is generally
'smoother' than fMRI data. I suspect that your PET data covers a
greater brain volume than your fMRI data and therefore the PET data,
despite being smoother (see FWHM in the SPM table footnotes) comprises
more resels. If you are doing a cross comparison I would only analyse
those voxels sampled in both modalities. Applied smoothing tends to
'swamp' intrinsic spatial autocorrelations so in theory a 16 mm FWHM
applied to both PET and fMRI data should render the number of resels
similar. A more precise estimate of the smoothing required to balance
the two data sets can be estimated using the FWHM estimates from an
analysis prior to smoothing.
> Also, I'd like to use matlab to visualize these differences in the
> intrinsic smoothness of the data and wondered how to best do this.
> Would the surface of a mesh plot for a slice from a particular scan
> illustrate the smoothness (or lack thereof) of the data? If so, can
> anyone tell me what matrix contains a slice of raw data (before
> smoothing, after normalization)?
It would but clearly the spatial correlations would include those due
to the mean profile and any functional activation. Smoothness is
generally estimated on the residuals of a fitted statistical model.
The final release of SPM99 will automatically write images of local
smoothness esimates (expressed in terms of resels per voxel) but at the
moment you could just subtract two consecutive fMRI (and PET) scans to
illustrate the differential smoothness.
With best wishes - Karl
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