1. VBM Voxel-based morphometry
Nicola Hobbs & Marianne Novak
Thanks to Susie Henley

2. Overview Background Pre-processing steps Analysis Multiple comparisons
Pros and cons of VBM
Optional extras

3. Background
VBM is a voxel-wise comparison of local tissue volumes within a group or across groups
Whole-brain analysis, does not require a priori assumptions about ROIs; unbiased way of localising structural changes
Can be automated, requires little user intervention  compare to manual ROI tracing

4. Basic Premise Spatial normalisation (alignment) into standard space
Segmentation of tissue classes
Modulation - adjust for volume changes during normalisation
Smoothing - each voxel is a weighted average of surrounding voxels
Statistics - localise & make inferences about differences

5. VBM Processing

7. Step 1: normalisation
Aligns images by warping to standard stereotactic space
Affine step – translation, rotation, scaling, shearing
Non-linear step
Adjust for differences in
head position/orientation in scanner
global brain shape
Any remaining differences (detectable by VBM) are due to smaller-scale differences in volume

8. SPATIALLY NORMALISED IMAGE
NORMALISATION
ORIGINAL IMAGE
SPATIALLY NORMALISED IMAGE
TEMPLATE IMAGE

10. SPATIALLY NORMALISED IMAGE
2. Tissue segmentation
Aims to classify image as GM, WM or CSF
Two sources of information
a) Spatial prior probability maps
b) Intensity information in the image itself
GREY MATTER
WHITE MATTER
CSF
SPATIALLY NORMALISED IMAGE
Assigns each voxel a (probable) tissue type based on a combination of spatial prior probability maps and the voxel intensity
Also includes image intensity non-uniformity correction;

11. a) Spatial prior probability maps
Smoothed average of GM from MNI
Intensity at each voxel represents probability of being GM
SPM compares the original image to this to help work out the probability of each voxel in the image being GM (or WM, CSF)

12. b) Image intensities
Intensities in the image fall into roughly 3 classes
SPM can also assign a voxel to a tissue class by seeing what its intensity is relative to the others in the image
Each voxel has a value between 0 and 1, representing the probability of it being in that particular tissue class
Includes correction for image intensity non-uniformity

13. Generative model Segmentation into tissue types Bias Correction
Normalisation
These steps cycled through until normalisation and segmentation criteria are met

15. Step 3: modulation
Corrects for changes in volume induced by normalisation
Voxel intensities are multiplied by the local value in the deformation field from normalisation, so that total GM/WM signal remains the same
Allows us to make inferences about volume, instead of concentration

16. Modulation i modulation i / δV normalisation X δV
E.g. During normalisation TL in AD subject expands to double the size
Modulation multiplies voxel intensities by Jacobian from normalisation process (halve intensities in this case).
Intensity now represents relative volume at that point

17. Is modulation optional?
Unmodulated data: compares “the proportion of grey or white matter to all tissue types within a region”
Hard to interpret
Not 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)

19. Step 4: Smoothing Convolve with an isotropic Gaussian kernel
Each voxel becomes weighted average of surrounding voxels
Smoothing renders the data more normally distributed (Central Limit theorem)
Required if using parametric statistics
Smoothing compensates for inaccuracies in normalisation
Makes mass univariate analysis more like multivariate analysis
Filter size should match the expected effect size
Usually between 8 – 14mm

20. Smoothing SMOOTH WITH 8MM KERNEL 8 mm
Images are smoothed using a Gaussian kernel (we usually use 8mm FWHM)
The intensity of each voxel is therefore a weighted average of the surrounding voxels
Makes data more normally distrubuted
8 mm

21. VBM: Analysis What does the SPM show in VBM? Cross-sectional VBM
Multiple comparison corrections
Pros and cons of VBM
Optional extras

22. VBM: Cross-sectional analysis overview
T1-weighted MRI from one or more groups at a single time point
Analysis compares (whole or part of) brain volume between groups, or correlates volume with another measurement at that time point
Generates map of voxel intensities: represent volume of, or probability of being in, a particular tissue class
Get map of voxel intensities
Eg memory test and hippo vol

23. What is the question in VBM analysis?
Control AD
Take a single voxel, and ask: “are the intensities in the AD images significantly different to those in the control images for this particular voxel?”
eg is the GM intensity (volume) lower in the AD group cf controls?
ie do a simple t-test on the voxel intensities

24. Statistical Parametric Maps (SPM)
Repeat this for all voxels
Highlights all voxels where intensities (volume) are significantly different between groups: the SPM
SPM showing regions where Huntington’s patients have lower GM intensity than controls
Colour bar shows the t-value

25. VBM: group comparison
Intensity for each voxel (V) is a function that models the different things that account for differences between scans:
V = β1(AD) + β2(control) + β3(covariates) + β4(global volume) + μ + ε
+ β3(age) + β4(gender) + β5(global volume) + μ + ε
V = β1(AD) + β2(control)
In practice, the contrast of interest is usually t-test between β1 and β2
Voxel intensity is a function that models all the different things that account for differences between scans. Use AD vs controls as example.
Beta value is slope of association of scans or values at that voxel
Covariates are explanatory or confounding variables
eg “is there significantly more GM in the control than in the AD scans?”

26. VBM: correlation
Correlate images and test scores (eg Alzheimer’s patients with memory score)
SPM shows regions of GM or WM where there are significant associations between intensity (volume) and test score
V = β1(test score) + β2(age) + β3(gender) + β4(global volume) + μ + ε
Contrast of interest is whether β1 (slope of association between intensity & test score) is significantly different to zero
Combine group comparison and correlation analyses.

27. Correcting for Multiple Comparisons
200,000 voxels per scan ie 200,000 t-tests
If you do 200,000 t-tests at p<0.05, by chance 10,000 will be false positives
Bad practice…
A strict Bonferroni correction would reduce the p value for each test to
However, voxel intensities are not independent, but correlated with their neighbours
Bonferroni is therefore too harsh a correction and will lose true results

28. Familywise Error SPM uses Gaussian Random Field theory (GRF)1
Using FWE, p<0.05: 5% of ALL our SPMs will contain a false positive voxel
This effectively controls the number of false positive regions rather than voxels
Can be thought of as a Bonferroni-type correction, allowing for multiple non-independent tests
Good: a “safe” way to correct
Bad: but we are probably missing a lot of true positives 1

29. False Discovery Rate FDR more recent
q value
FDR
q<0.05
False Discovery Rate
FDR more recent
It controls the expected proportion of false positives among suprathreshold voxels only
Using FDR, q<0.05: we expect 5% of the voxels for each SPM to be false positives (1,000 voxels)
Bad: less stringent than FWE so more false positives
Good: fewer false negatives (ie more true positives)
But: assumes independence of voxels: avoid….?
Voxel

30. VBM Pros VBM Cons 1. Objective analysis
2. Do not need priors – more exploratory
3. Automated
VBM Cons
1. False positives: misregistration, FDR
False negatives: FWE
More difficult to pick up differences in areas with high inter-subject variance: low signal to noise ratio
Comparing VBM to less automated or more manual tools measuring regional tissue volumes

31. Other VBM Issues
Optimised VBM: GM to GM warping, then applied to whole brain image (better GM alignment); Good et al, Neuroimage (SPM 2)
Diffeomorphic warping: DARTEL
Multivariate techniques: including classification/SVM
Longitudinal scan analysis: two time points especially

32. 18 iterations to form template
Ashburner Neuroimage 2007

33. Standard preprocessing: areas of decreased volume in depressed subjects
DARTEL preprocessing: areas of decreased volume in depressed subjects

34. Longitudinal VBM
Baseline and follow-up image are registered together non-linearly (fluid registration), NOT using spm software
Voxels at follow-up are warped to voxels at baseline
Represented visually as a voxel compression map showing regions of contraction and expansion

35. Fluid Registered Image
FTD
(semantic dementia)
Voxel compression map
1 year
expanding
contracting

36. Optimised VBM Native space images Standard space images
1. Affine registration to SPM2 T1 template
4. Normalisation using parameters from step 3; GM is well-aligned
Standard space images
Standard space images
2. Segmentation
5. Segmentation
GM segments
GM segments
3. Estimate normalisation parameters for GM segments to SPM2 GM template
6. Modulation: correcting for spatial changes introduced in normalisation
Normalisation parameters
GM to GM
Mod GM
7. Masking: segments are multiplied by binary region to exclude any non-brain
Masked GM
8. Smoothed at 8mm FWHM
Smoothed, Masked, mod GM

37. Resources and references
(the SPM homepage)
(neurimaging wiki homepage)
(for multiple comparisons info)
Ashburner J, Friston KJ. Voxel-based morphometry--the methods. Neuroimage 2000; 11: (the original VBM paper)
Good CD, Johnsrude IS, Ashburner J, Henson RN, Friston KJ, Frackowiak RS. A voxel-based morphometric study of ageing in 465 normal adult human brains. Neuroimage 2001; 14: (the optimised VBM paper)
Ridgway GR, Henley SM, Rohrer JD, Scahill RI, Warren JD, Fox NC. Ten simple rules for reporting voxel-based morphometry studies. Neuroimage 2008.