vbm voxel-based morphometry
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VBMVoxel-based morphometry
Floris de Lange
Most slides taken/adapted from:
Nicola Hobbs & Marianne Novak
http://www.fil.ion.ucl.ac.uk/mfd/
Overview
• Background (What is VBM?)• Pre-processing steps
• Analysis• 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 space
2. Segmentation of tissue classes
3. Modulation - adjust for volume changes during normalisation
4. Smoothing - each voxel is a weighted average of surrounding voxels
5. Statistics - localise & make inferences about differences
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
SPATIALSPATIAL
NORMALISATIONNORMALISATION
ORIGINAL ORIGINAL IMAGEIMAGE
SPATIALLY SPATIALLY NORMALISED NORMALISED
IMAGEIMAGETEMPLATE TEMPLATE
IMAGEIMAGE
• parameter affine transform• 3 translations• 3 rotations• 3 zooms• 3 shears
• Fits overall shape and size
Normalization – linear transformations
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)
GREY MATTERGREY MATTER WHITE MATTERWHITE MATTER CSF CSF
SPATIALLY SPATIALLY NORMALISED NORMALISED
IMAGE 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
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 everywhere
• This makes it more difficult to partition the scan in different tissue types
• Bias correction estimates and removes this bias
Image with bias
artefact
Corrected image
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 concentration
Modulation
• 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
i
modulation
i / δV
normalisation
iX δV
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 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
SMOOTH SMOOTH WITH 8MM WITH 8MM
KERNELKERNEL
Smoothing
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 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
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 controls?
• ie do a simple t-test on the voxel intensities
AD Control
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 + ε
• Contrast of interest is whether β1 (slope of association between intensity & test score) is significantly different to zero
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 results
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 http://www.mrc-cbu.cam.ac.uk/Imaging/Common/randomfields.shtml
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….?
q<0.05
Voxel
FDRq value
VBM Pros
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
1. Objective analysis2. Do not need priors – more exploratory3. Automated
VBM Cons
Standard preprocessing: areas of decreased volume in depressed subjects
DARTEL preprocessing: areas of decreased volume in depressed subjects
Resources and references
• http://www.fil.ion.ucl.ac.uk/spm (the SPM homepage)• http://imaging.mrc-cbu.cam.ac.uk/imaging/CbuImaging (neurimaging wiki homepage)• http://www.mrc-cbu.cam.ac.uk/Imaging/Common/randomfields.shtml (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.
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