Dear Michael,
The code inside FSL, in smoothest, does indeed implement
RESELS = (4*log(2))^(3/2) / DLH
however, the reported DLH is corrected for a function of the
degrees of freedom, whereas the DLH used in this calculation
does not have this correction. In fact, the internal code does not
implement this equation as it is written here, but instead does:
dLh = 1/sqrt(8*ssx*ssy*ssz)
FWHMx = sqrt(8*log(2)*ssx)
resels = FWHMx * FWHMy * FWHMz
where ssx are sum of squares.
The FWHM here is in voxels.
To convert to average FWHM in mm you would do
FWHMav = (resels * pixdim1*pixdim2*pixdim3)^(1/3)
So I suspect that it is the degrees of freedom function
(that gives 1.1 for low degrees of freedom) that is
responsible for the mismatch with Tom's equations
which is for Z-based inputs. See the technical report at:
http://www.fmrib.ox.ac.uk/analysis/techrep/tr00df1/tr00df1/node7.html
for more details of the correction required for
converting t-derived info to the Z-based equations
required for the dLh that GRF needs (and has to
be fed into cluster).
All the best,
Mark
On 18 Feb 2011, at 19:06, Michael Harms wrote:
> Hello,
> I was wondering if someone could help us with a couple questions
> regarding the stats/smoothness file.
>
> According to this Mar 31, 2008 post in the archives from Tom (Re:
> minimal smoothness and GRF Theory)
>
> https://www.jiscmail.ac.uk/cgi-bin/webadmin?
> A2=ind0803&L=FSL&P=R74667&1=FSL&9=A&I=-3&J=on&d=No+Match%3BMatch%
> 3BMatches&z=4
>
> the relationship between RESELS and DHL is:
>
> RESELS = (4*log(2))^(3/2) / DHL
>
> But when I use that formula with the DLH in the smoothness file from a
> Level 2 combination of runs, the calculated RESEL value doesn't match.
> i.e.,
> stats/smoothness file:
> DLH 0.0609609
> VOLUME 289699
> RESELS 83.3048
>
> whereas (4*log(2))^(1.5) / .0609609 = 75.7315
>
> Is that formula no longer strictly true for higher level analyses?
>
> Also, what would be the best way to convert a RESELS value to an AvgFWHM
> in mm? Tom indicated that AvgFWHM = RESELS^(1/3), but that is in
> voxels, and voxels at the first level are frequently not isotropic. So,
> is the correct way to convert to AvgFWHM(mm) just:
>
> AvgFWHM(mm) = (RESELS*pixdim1*pixdim2*pixdim3)^(1/3) ??
>
> thanks,
> -MH
>
>
> --
> Michael Harms, Ph.D.
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> Washington University School of Medicine
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