1. VBM Susie Henley and Stefan Klöppel Based on slides by John Ashburner

2. Overview Voxel-based Morphometry Problems with VBM
Alternative Approaches

3. VBM (voxel-based morphometry)
VBM: whole-brain analysis, does not require a priori assumptions about ROIs; unbiased way of localising structural changes
Does a voxel by voxel comparison of local tissue volume.

4. Pre-processing for VBM
-should discuss why each of the steps is done, e.g. “align brains up, divide tissue types, correct for changes in volume introduced in warping, and smooth to further correct for registration error”

5. VBM Preprocessing in SPM5
It uses a generative model, which involves:
Segmentation into tissue types
GM, WM and CSF
Bias Correction
Corrects intensity inhomogeneities in images
Normalisation
Aligns images, puts them into the same (standard) space
These steps are cycled through until normalisation and segmentation criteria are met

6. Segmentation
Uses information from tissue probability maps (TPMs) and the intensities of voxels in the image to work out the probability of a voxel being GM, WM or CSF
Mention that maps are deformed during segmentation
ICBM Tissue Probabilistic Atlases. These tissue probability maps are kindly provided by the International Consortium for Brain Mapping, John C. Mazziotta and Arthur W. Toga.

7. Bias correction Warping
Estimates a function to correct for bias in the image and applies it
Warping
The tissue probability maps (which are in standard space) are warped to match the image
this gives parameters for registering the image into standard space later

8. The generative model
Keeps doing these steps iteratively until the objective function is minimised
Results in images that are segmented, bias-corrected, and registered into standard space
Does the objective function model error? Does it keep going until it thinks it can’t reduce error any more/isn’t changing parameters any more and therefore it has found the best parameters for the data?

9. Modulation Vox[i, v] normalisation modulation Vox[i, v*δV]
Vox[i/δV, v*δV]
modulation
Vox[i, v]
During modulation voxel intensities are multiplied by the local value in the deformation field from normalisation, so that total GM/WM signal remains the same
Change of intensity now represents volume relative to template
During normalisation some volumes will change, e.g. TL of AD “stretches” and doubles in size
During modulation the voxel intensities are multiplied by the Jacobians from the normalisation process, so in this case the intensities are halved
Intensity at each point now represents the relative volume at that point

10. How optional is modulation ?
Unmodulated data: compares “the proportion of grey or white matter to all tissue types within a region”
Hard to interpret
Therefore not very useful for looking at e.g. the effects of degenerative disease
Modulated data: compares volumes
Unmodulated data may be useful for highlighting areas of poor registration (perfectly registered unmodulated data should show no differences between groups)

11. Smoothing
Reasons:
Each voxel becomes weighted average of surrounding ones
Data are more normally distributed
Smooth out incorrect normalisation
Most studies use a kernel between 8 and 14 mm. depending on the size of the expected effect.

12. VBM: analysis
Control AD
Take a single voxel, and ask e.g. “are the intensities in the AD images significantly lower than those in the control images for this particular voxel?”
i.e. do a simple t-test on the voxel intensities

13. VBM: group comparison
At each voxel intensity is actually modelled as a function of explanatory or confounding variables
V=β1(AD) + β2(control)
+ β3(age) +β4(gender) + β5(TIV) + μ + ε
In practice most models are set up with similar covariates as above, with the “contrast” of interest being the t-test between β1 and β2

14. SPM
Highlight all voxels where intensities (volume) in patient images are significantly lower than controls: this is a statistical parametric map
The colour bar shows the t-value

15. Correcting confounds
Bigger brains will have bigger GM or WM volumes which could confound comparisons
Include TIV as covariate to correct for differences due to head size
With TIV as a covariate we can compare GM assuming no differences in head size
Here one brain is bigger than the other (and possibly has more GM because of that)

16. Global or local change? A B
Brains are of similar size but GM differs globally and locally
As it stands we would find greater volume in B relative to A except in the thin area on the right-hand side A B
Including total GM or WM volume as a covariate adjusts for global atrophy and looks for regionally-specific changes
With global GM as a covariate we will find greater volume in A relative to B only in the thin area on the right-hand side

17. Which to use?
Comparisons should usually be adjusted for head size (TIV)
Inferences may then be based on global differences
e.g. what’s the global effect of disease X?
Alternatively you may wish to look at regionally specific changes
e.g. having adjusted for overall atrophy, are there any regions which still show relative sparing or loss of tissue? di

18. Some Explanations of the Differences
Folding
Mis-classify
Mis-register
Thickening
Thinning
Mis-classify
Mis-register

19. Validity of the statistical tests in SPM
Errors (residuals) need to be normally distributed throughout brain for stats to be valid
After smoothing this is usually true BUT
Invalidates experiments that compare one subject with a group
Correction for multiple comparisons
Valid for corrections based on peak heights (voxel-wise)
Not valid for corrections based on cluster extents
This requires smoothness of residuals to be uniformly distributed but it’s not in VBM because of the non-stationary nature of underlying neuroanatomy
Bigger blobs expected in smoother regions, purely by chance

20. Alternatives Improve normalisation use multivariate approaches
Lao: ‘Morphological classification of brains via high-dimensional shape transformations and machine learning methods‘ (2004) NeuroImage.

21. Multivariate Approaches
An alternative to mass-univariate testing (SPMs)
Shape is multivariate
Generate a description of how to separate groups of subjects
Use training data to develop a classifier
Use the classifier to diagnose test data

22. Points to think about What do results mean? VBM generally
Limitations of spatial normalisation for aligning small-volume structures (e.g. hippo, caudate)
VBM in degenerative brain diseases:
Spatial normalisation of atrophied scans
Optimal segmentation of atrophied scans
Optimal smoothing width for expected volume loss

23. Useful refs
Ashburner & Friston. VBM – the Methods. Neuroimage Jun;11(6 Pt 1):805-21
Good et al. A Voxel-based morphometric study of ageing in 465 normal adult human brains. Neuroimage Jul;14(1 Pt 1):21-36