Transcript Slide 1

Voxel-based morphometry
Floris de Lange
Most slides taken/adapted from:
Nicola Hobbs & Marianne Novak
• Background (What is VBM?)
• Pre-processing steps
Multiple comparisons
Pros and cons of VBM
Optional extras
What is VBM?
• 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
Basic Steps
1. Spatial normalisation (alignment) into standard
2. Segmentation of tissue classes
3. Modulation - adjust for volume changes during
4. Smoothing - each voxel is a weighted average of
surrounding voxels
5. Statistics - localise & make inferences about
VBM Processing
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
Normalization – linear transformations
• parameter affine transform
• 3 translations
• 3 rotations
• 3 zooms
• 3 shears
• Fits overall shape and size
Normalization – nonlinear transformations
Deformations consist of a linear combination of
smooth basis functions
These are the lowest frequencies of a 3D discrete
cosine transform (DCT)
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
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)
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
Bias correction
• The contrast of a scan may not be the same
• This makes it more difficult to partition the scan in
different tissue types
• Bias correction estimates and removes this bias
with bias
Generative model
• Segmentation into tissue types
• Bias Correction
• Normalisation
• These steps cycled through until normalisation
and segmentation criteria are met
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
i / δV
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
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)
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
• 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
8 mm
VBM: Analysis
What does the SPM show in VBM?
Cross-sectional VBM
Multiple comparison corrections
Pros and cons of VBM
Optional extras
VBM: Cross-sectional analysis overview
• T1-weighted MRI from one or more groups at a single time
• 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
What is the question in VBM analysis?
• 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
• ie do a simple t-test on the voxel intensities
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
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 +
• Contrast of interest is whether β1 (slope of association
between intensity & test score) is significantly different to
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 0.00000025
• However, voxel intensities are not independent, but correlated
with their neighbours
• Bonferroni is therefore too harsh a correction and will lose true
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
q value
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….?
VBM Pros
1. Objective analysis
2. Do not need priors – more exploratory
3. Automated
VBM Cons
1. SPM normalization procedure is rather crude
2. Not ideal for subcortical (well-delineated) structures
3. More difficult to pick up differences in areas with high
inter-subject variance: low signal to noise ratio
Standard preprocessing: areas of decreased volume in depressed subjects
DARTEL preprocessing: areas of decreased volume in depressed subjects
Resources and references
• (the SPM homepage)
• (neurimaging wiki
• (for multiple
comparisons info)
• Ashburner J, Friston KJ. Voxel-based morphometry--the methods. Neuroimage
2000; 11: 805-821 (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: 21-36 (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.