Working with the deformation fields is a nice idea, although it can be tricky.  
A single point in a displacement field is not especially informative.  A more 
useful measure would involve seeing how the points vary with respect to 
neighbouring points (for example, by examining the Laplacians), as this gives 
a better indication of the degree of deformation involved.  Alternatively, 
you could look at a map of Jacobian determinants, which shows the degree of 
expansion or contraction at each point (this can be done with the DARTEL 
toolbox).

DARTEL has been formulated so that it assumes a multinomial distribution for 
the intensities, rather than a simple mean-squares difference.  The idea here 
is that regions in the template that are closer to one or zero will be more 
heavily weighted.  It is these regions in which there is good overlap, 
indicating closer registration, which gives the algorithm more confidence in 
the alignment.  In regions where the template has values further from the 
extremes, then the cost function is weighted relatively lower (with respect 
to the regularisation).  In these regions, there is less overlap and the 
algorithm is less confident about how structures should be matched.  The 
result is (hopefully) that there is more detailed deformations where good 
alignment is possible, and less detail in the deformations where it is not 
quite as easy to obtain a good match (eg in parietal regions).  This is a bit 
like weighting the registration by the inverse of the variance at each point.  
For example, if a voxel in the template has a WM probability of 0.999 (almost 
all ones at this point), then the variance has to be low and the matching 
term of the registration is therefore heavily weighted.  If there is a WM 
probability of 0.5, then the variance is higher (the same number of ones and 
zeros) and the weighting is lower.

If you are interested, there is a template generated from 471 subjects in 
http://www.fil.ion.ucl.ac.uk/misc/ in the Template.nii file.  The first 
volume in the file is GM, the second is GM and the third is WM.  If the 
imported images (tissue class segments) were binary, then such maps provide a 
useful indication of the overlap of GM with GM etc.  Note that this overlap 
by itself does not necessarily indicate accurate registration, as the wrong 
sulci may be matched together.  I have tried to avoid this as far as possible 
by setting up the execution so that the early iterations are more heavily 
regularised, and the templates smoother (a coarse-to-fine strategy).  This 
seems to help, but there may still be some incorrectly aligned sulci - 
especially for those regions where folding patterns are more variable (eg 
parietal).

I don't know if you have access to these papers, but the one by Baloch, Verma 
and Davatzikos (Poster Session II) from IPMI this year  ( 
http://www.informatik.uni-trier.de/~ley/db/conf/ipmi/ipmi2007.html ), treated 
tissue probability maps and Jacobian determinants as seperate channels of 
data.  Maybe there is something there that could be helpful.

Best regards,
-John


On Tuesday 11 December 2007 22:53, Alex Fornito wrote:
> Hi John,
>
> Thanks for your detailed response and recommendations re: using DARTEL.
>
>  From your response, I see that, because spatial normalization may
> not account for more fine-grain anatomical variations, differences in
> grey matter concentration may arise either due to misalignment or a
> real difference in the amount of regional grey matter.
>
> Using Jacobian modulation corrects for this to some extent, but it
> depends on registration accuracy - the better the registration, the
> more accurately the modulated measure will represent the true volume.
> If you are investigating a patient group with a greater degree of
> variability in brain morphology than is seen in the normal
> population, the deformations will be more variable and potentially be
> less accurate. Thus, applying Jacobian modulation might reduce
> sensitivity for detecting group differences because the variance in
> the resulting modulate grey matter volume measures is increased.
>
> In contrast, using unmodulated measures of grey matter concentration
> attempts to minimize this anatomical variability, and will therefore
> increase the likelihood of significant differences emerging, but it
> may be unclear whether this difference is due to misalignment or a
> true difference in the relative amount of grey matter.
>
> If this is so, would it make sense to examine the deformation fields
> of each group to see if one group has greater variability in the same
> areas where differences are detected?
>
> Thanks again,
> Alex
>
>
>
> At this stage, I am trying to get my head around why it might be
> harder to detect differences in modulated volume measures than
> traditional concentration measures.
>
> To clarify your response:
> > This is the nature of statistical testing.  There are definately
> > cases where
> > the Jacobian correction may decrease sensitivity to differences.
> > Consider a
> > situation where (for example) the hippocampal volume may be
> > correlated with
> > the size of the temporal lobe in the general population, and the
> > registration
> > is only using about 1000 parameters to roughly model the global
> > brain shape.
> > By not correcting, you could be partially factoring out the effects of
> > variations in temporal lobe volume.  The deformations can capture
> > larger
> > temporal lobe volume differences, but not the finer differences in the
> > hippocampi - so not modulating is a bit like a localised
> > proportional scaling
> > correction.  This may increase your t-stats, but it makes a clear
> > interpretation of the findings very difficult.
>
> In VBM of grey matter concentration, the normalization may act in a
> manner that effectively partials out variance in local, yet
> reasonably large regional volumes. Following your example, within the
> temporal lobes, it might scale the hippocampus in a manner that
> reduced individual differences in temporal lobe volume; in the
> frontal lobes it may do the same with respect to a specific frontal
> sub-region (e.g., Broca's area). In this way, it might be akin to
> having a regionally specific covariates; e.g., when testing for
> differences in the hippocampus, variance due to temporal lobe volume
> is partialled out; when testing for differences in Broca's area,
> variance due to frontal lobes volume is partialled out; with the
> relationship between local and more diffuse variations being
> determined by the degrees of freedom and smoothing of the
> normalization algorithm. This is a somewhat simplified example, but I
> use it to try and get it clear in my head.
>
> One limitation of this is that the normalization may not account for
> smaller anatomical variations, and resulting differences in grey
> matter concentration may be real, or due to misalignment.
>
> With Jacobian modulated grey matter volume, this localized
> proportional scaling is absent
>
> On 12/12/2007, at 2:38 AM, John Ashburner wrote:
> >> I'm fairly new to VBM and am trying to get my head around differences
> >> in testing for grey matter concentration or volume; specifically with
> >> respect to why one would find a difference in concentration but not
> >> volume in the same sample (as I have read in several papers).
> >
> > If you are just starting out, then it may be a good time to try out
> > the new
> > DARTEL toolbox in SPM5.
> >
> > Segment: all the images to generate *_seg_sn.mat files.
> > Dartel->Import: uses the *_seg_sn.mat files to generate rigidly
> > aligned GM and
> > WM images.
> > Dartel->Warp (create template): Uses the imported GM and WM images
> > to generate
> > flow fields U_*.nii that can be used for mapping between images.
> > Dartel_>Warp: Use the flow fields and imported GM/WM images to
> > generate more
> > closely inter-subject aligned (spatially normalised - but to the
> > subjects
> > average shape, rather than the MNI templates) modulated GM/WM.
> > Smooth: by less than would be needed for the normal VBM preprocessing.
> > Stats: for visualising the most significant differences.
> >
> > Note that the results are not in MNI space (although the tools are
> > all there
> > that would allow you to warp them to MNI space via registering the
> > group
> > averages with the MNI data - the Deformations Utility is useful
> > here for
> > composing warps).
> >
> > From our experience in the FIL, we find that preprocessing with
> > DARTEL gives
> > higher t-stats than the SPM5 segmentation.  We also didn't see as
> > much of the
> > significant differences due to systematic misregistration (eg insula
> > differences because one population has bigger ventricles than the
> > other).
> > From the fact that we generally find a smaller number of more
> > significant
> > focal differences, I would generally conclude that a greater
> > proportion of
> > these are actually due to real volumetric differences.
> >
> >>  From what I understand, the modulation step corrects signal
> >> intensities for the volumetric contractions/expansions that occur
> >> during spatial normalization, allowing absolute volume to be
> >> calculated.
> >
> > If the spatial normalisation and segmentation was extremely accurate
> > (impossible in practice) then all the spatially normalised GM would be
> > identical.  Sometimes it is interesting to examine the limitations
> > of the
> > registration model, but normally it is more interesting to actually
> > examine
> > volumetric differences by including a Jacobian transformation of
> > variables
> > (modulation).  By analogy, it wouldn't make so much sense to model
> > data with
> > a GLM or DCM, and report only t-test results applied to the
> > residual errors.
> > This would only show where (in time)  the model didn't fit the data
> > so well.
> >
> >> I had an initial thought that, because the modulated volume measure
> >> is adjusted for the deformations that occur during normalization, a
> >> failure to detect a grey matter volume difference between two groups
> >> might arise if one group had more heterogeneous brain morphology than
> >> the other. This heterogeneity would lead to higher variability in the
> >> deformation fields required for normalization, and therefore, the
> >> corrections applied during modulation. This would then increase the
> >> variance of the resulting grey matter volume measures, affecting the
> >> statistics.
> >
> > This is the nature of statistical testing.  There are definately
> > cases where
> > the Jacobian correction may decrease sensitivity to differences.
> > Consider a
> > situation where (for example) the hippocampal volume may be
> > correlated with
> > the size of the temporal lobe in the general population, and the
> > registration
> > is only using about 1000 parameters to roughly model the global
> > brain shape.
> > By not correcting, you could be partially factoring out the effects of
> > variations in temporal lobe volume.  The deformations can capture
> > larger
> > temporal lobe volume differences, but not the finer differences in the
> > hippocampi - so not modulating is a bit like a localised
> > proportional scaling
> > correction.  This may increase your t-stats, but it makes a clear
> > interpretation of the findings very difficult.
> >
> >> I later thought that grey matter concentration should  still be
> >> affected by this heterogeneity, given that it is  calculated after
> >> spatial normalization and should therefore be affeted by variability
> >> in deformation fields. However, I  noticed on a previous posting made
> >> by John that he states "With different levels of registration
> >> accuracy, there is a continuum between testing for GM volume
> >> differences from the Jacobian determinants through to testing GM
> >> volume differences purely from the conventional VBM point of view".
> >
> > The continuum is about ensuring that the volumes of tissue computed
> > from each
> > structure remain the same.  For example, if you integrate the
> > intensities in
> > a native-space GM image, then you obtain the same estimate as you
> > would if
> > you integrate over a spatially normalised and modulated (Jacobian
> > corrected)
> > GM image.  If spatial normalisation is less precise, then you need
> > more
> > smoothing to replicate similar values in the smoothed, modulated,
> > GM images,
> > but the data essentially all try to represent the volume of
> > tissue.  In my
> > view, the more accurate the preprocessing model, then the more easy it
> > becomes to interpret the results, and the less smoothing is needed to
> > blur-out the effects of misalignment.
> >
> > Best regards,
> > -John
>
> Alex Fornito
> JN Peters Research Fellow
> Melbourne Neuropsychiatry Centre
> Department of Psychiatry
> The University of Melbourne
>
> Postal address:
> Melbourne Neuropsychiatry Centre
> National Neuroscience Facility
> Levels 2 & 3, 161 Barry St
> Carlton South Vic 3053 Australia
>
> Ph:	  +61 3 8344 1861
> Fax:  +61 3 9348 0469
>
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