[MINC-users] determinant of non-linear local deformation fields (fwd)

[David Seminowicz]

Hi Marc and others, did you ever find a good way to do modulated VBM with
minc tools?  dave



-----Original Message-----
From: minc-users-bounces at bic.mni.mcgill.ca
[mailto:minc-users-bounces at bic.mni.mcgill.ca] On Behalf Of Marc BOUFFARD
Sent: Thursday, August 07, 2008 11:43 AM
To: minc-users at bic.mni.mcgill.ca
Subject: Re: [MINC-users] determinant of non-linear local deformation fields
(fwd)



On Fri, 1 Aug 2008, Andrew Janke wrote:

> Hi Marc,
>
> On Wed, Jul 30, 2008 at 01:38, Marc BOUFFARD <bouffard at bic.mni.mcgill.ca>
wrote:
> > I have a question about deformation grids obtained from non-linear
> > registration using nlpfit.  These grids contain the 3D displacements at
> > each voxel applied to the source to match the template or to the
template
> > to match the source?
>
> (note that this all presumes you did something like this: where
> fred.mnc is our input subject)
>
>    bestlinreg fred.mnc template.mnc linear_part.xfm
>    nlpfit -init_xfm linear_part.xfm fred.mnc template.mnc
nonlinear_part.xfm
>
> If this is so then the nlxfm is from the source to the target. (after
> the linear transformation if there is one). This incidentally is why
> we calculate a model to individual transformation when we want to
> average a number of transformations during building a model.
>
> > Now if the determinant is calculated from those grids with mincblob and
it
> > is found that voxel x has a value greater than 1.  Does this mean the
> > region in the neighborhood of x has expanded relative to the source  or
> > relative to the target?
>
> Perhaps best by example:
>
> 0.5 == the area in question is 50% smaller in the template than the source
> 1 == no change
> 1.5 == the area in question is 50% larger in the template than the source.
>
> > In a further step, to obtain modulated VBM data should the standard VBM
> > data be multiplied by the determinant of the Jacobian matrix or its
> > inverse?
>
> You lost me, what do you define as "modulated" VBM data?  I would take
> a punt there are a few different takes on it.
>
I am trying to apply the method used in SPM VBM but with the minc tools.
Assuming we have the gray matter classified images linearly transformed
then in "standard VBM" we would just apply the linear model to that and
solve for a contrast of interest with glim_image, e.g., group 1 - group 2.
Now, if the data is additionally non-linearly transformed another step
called modulation can be applied:

"in order to preserve the actual amounts of gray matter within each
structure, a further processing step that multiplies (modulates) the
images by the relative voxel volumes can be incorporated.  These relative
volumes are simply the Jacobian determinants of the deformation field."
(Ashburner and Friston, Neuroimage 11 805-821)

So according to that we just need to multiply by the Jacobian determinants
but apparently the deformation fields calculated in SPM are relative to
the target and not the source like with nlpfit (does that make sense?).
So, logically if the deformation fields are relative to the source to the
target(as you mention above) we should multiply by the voxel-wise inverse
of the Jacobian determinant to get the same effect as with SPM?

Marc
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