> 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