Voxel Based Morphometry
Methods for Dummies 2012
Merina Su and Elin van Duin
Rebel with a cause
“… a linear relationship between grey
matter volume (GM) in a region of
lateral orbitofrontal cortex
(lOFCGM) and the tendency to shift
reported desire for objects toward
values expressed by other people.”
Daniel K. Campbell-Meiklejohn, Ryota Kanai, Bahador Bahrami, Dominik R. Bach, Raymond J. Dolan, Andreas
Roepstorff, Chris D. Frith. Structure of orbitofrontal cortex predicts social influence. Current Biology, 2012; 22
(4): R123 DOI: 10.1016/j.cub.2012.01.012
VBM
• General Idea
• Preprocessing
• Analysis
VBM overview
• Based on comparing regional volumes of tissue among
populations of subjects
Whole brain instead of comparing volumes of particular
structures such as the hippocampus
• Produce a map of statistically significant differences
among populations of subjects
– compare a patient group with a control group
– identify correlations with age, test-score etc.
Computational neuranatomy
Deformation-based morphometry
Looks at macroscopic differences in brain shape. Uses
the deformation fields needed to warp an individual
brain to a standard reference.
Tensor-based morphometry
Differences in the local shape of brain structures
Voxel based morphometry
Differences in regional volumes of tissue
Procedure overview
Spatial normalisation
• Transforming all the subject’s data to the
same stereotactic space
• Corrects for global brain shape differences
• Choice of the template image shouldn’t bias
final result
Segmentation
• Images are partitioned into:
- Grey matter
- White matter
- CSF
Extra tissue maps can be
generated
• SPM uses a generative model,
which involves:
- Mixture of Gaussians
- Bias Correction Component
- Warping Component
Segmentation
2 sources of information:
1.
Spatial prior probability maps:
• Intensity at each voxel = probability of being
GM/WM/CSF
• Comparison: original image to priors
• Obtained: probability of each voxel in the image
being a certain tissue type
2) Intensity information in the image itself
• Intensities in the image fall into roughly 3
classes
• SPM assigns a voxel to a tissue class based on its
intensity 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
frequency
Segmentation
image intensity
Smoothing
Modulation
Non-modulated:
Modulated:
– Relative concentration/
- Absolute volumes
density: the proportion of GM
(or WM) relative to other
tissue types within a region
– Hard to interpret
Modulation: multiplying the spatially normalised gray matter (or other
tissue class) by its relative volume before and after spatial transformation
Preprocessing in SPM: Diffeomorphic Anatomical
Registration using Exponentiated Lie algebra (DARTEL)
registration
• Use New Segment for
characterising intensity
distributions of tissue classes, and
writing out “imported” images that
DARTEL can use
• Run DARTEL to estimate all the
deformations
• DARTEL warping to generate
smoothed, “modulated”, warped
grey matter.
Limitations of the current model
• Assumes that the brain consists of only the tissues
modelled by the TPMs
– No spatial knowledge of lesions (stroke, tumours, etc)
• Prior probability model is based on relatively young
and healthy brains
– Less accurate for subjects outside this population
• Needs reasonable quality images to work with
– No severe artefacts
– Good separation of intensities
– Reasonable initial alignment with TPMs.
Assumptions
• You must be measuring the right thing, i.e. your
segmentation must correctly identify gray and white
matter
• Avoid confounding effects: use the same scanner and
same MR sequences for all subjects
• For using parametric tests the data needs to be
normally distributed
SPM for group fMRI
Group-wise
statistics
fMRI time-series
Preprocessing
Spatially Normalised
spm T
“Contrast” Image
Image
Preprocessing
Spatially Normalised
“Contrast” Image
Preprocessing
Spatially Normalised
“Contrast” Image
fMRI time-series
fMRI time-series
SPM for Anatomical MRI
Group-wise
statistics
Anatomical MRI
Preprocessing
Spatially Normalised
spm T
Grey MatterImage
Image
Preprocessing
Spatially Normalised
Grey Matter Image
Preprocessing
Spatially Normalised
Grey Matter Image
Anatomical MRI
Anatomical MRI
Statistical analysis VBM
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Types of analysis
What does SPM show?
Multiple corrections problem
Things to consider…
Interpreting results
Types of analysis
• Group comparison
• Correlation
a known
score or
value
• Where in the brain do the
Simpsons and the Griffins have
differences in brain volume?
• Where in the brain are there
associations between brain
volume and test score?
General Linear Model
e.g, compare the GM/ WM differences between 2
groups
Y = Xβ + ε
H0: there is no difference between
these groups
β: other covariates, not just the mean
VBM: group comparison
GLM: Y = Xβ + ε
•
Intensity for each voxel (V) is a function that models the different things that account
for differences between scans:
•
V = β1(Simpsons) + β2(Griffin) + β3(covariates) + β4(global volume) + μ + ε
• V = β1(Simpsons) + β2(Griffin) + β3(age) + β4(gender) + β5(global volume) + μ + ε
• In practice, the contrast of interest is usually t-test between β1
and β2
“Is there significantly more GM (higher v) in the controls than in the AD scans
and does this explains the value in v much better than any other covariate?”
Statistical Parametric Mapping…
–
parameter estimate
group 1
standard error
group 2
=
voxel by voxel
modelling

statistic image
or
SPM
VBM: correlation
• Correlate images and test scores (eg Simpson’s family with IQ)
• 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
What does SPM show?
• Voxel-wise (mass-univariate:
independent statistical tests for
every single voxel)
• Group comparison:
– Regions of difference between
groups
• Correlation:
– Region of association with test
score
Multiple Comparison Problem
• Introducing false positives when you deal with more
than one statistical comparison
– detecting a difference/ an effect when in fact it does not
exist
Read: Brett, Penny & Kiebel (2003): An Introduction to Random Field Theory
http://imaging.mrc-cbu.cam.ac.uk/imaging/PrinciplesRandomFields
Multiple Comparisons: an example
• One t-test with p < .05
– a 5% chance of (at least) one false positive
• 3 t-tests, all at p < .05
– All have 5% chance of a false positive
– So actually you have 3*5% chance of a false positive
= 15% chance of introducing a false positive
p value = probability of the null-hypothesis being true
Here’s a happy thought
• In VBM, depending on your resolution
– 1000000 voxels
– 1000000 statistical tests
• do the maths at p < .05!
– 50000 false positives
• So what to do?
– Bonferroni Correction
– Random Field Theory/ Family-wise error (used in SPM)
Bonferroni
• Bonferroni-Correction (controls false positives at individual
voxel level):
– divide desired p value by number of comparisons
– .05/1000000 = p < 0.00000005 at every single voxel
• Not a brilliant solution (false negatives)!
• Added problem of spatial correlation
– data from one voxel will tend to be similar to data from nearby voxels
Family-wise Error
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SPM uses Gaussian Random Field theory (GRF)1
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Using FWE, p<0.05: 5% of ALL our SPMs will contain a false positive voxel
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This effectively controls the number of false positive regions rather than voxels
Can be thought of as a Bonferroni-type correction, allowing for multiple nonindependent tests
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Good: a “safe” way to correct
Bad: but we are probably missing a lot of true positives
http://www.mrc-cbu.cam.ac.uk/Imaging/Common/randomfields.shtml
Validity of 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
Things to consider
• Uniformly bigger brains may have uniformly more GM/
WM
brain A
brain B
differences without
accounting for TIV
(TIV = total intracranial
volume)
brain A
brain B
differences after TIV
has been “covaried
out” (differences caused
by bigger size are
uniformally distributed with
hardly any impact at local
level)
Global or local change?
• Without TIV: greater volume in B
relative to A except in the thin
area on the right-hand side
Brains of similar size with GM
differences globally and locally
• With TIV: greater volume in A
relative to B only in the thin area
on the right-hand side
Including total GM or WM volume as a covariate adjusts for
global atrophy and looks for regionally-specific changes
Interpreting results
Mis-classify
Mis-register
Folding
Thinning
Mis-register
Thickening
Mis-classify
More things 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
Extras/alternatives
• Multivariate techniques
– 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
• Longitudinal analysis
– 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
Fluid Registered Image
FTD
(semantic
dementia)
Voxel
compression
map
1 year
contracting
expanding
In summary
• Pro
• Con
– Fully automated: quick and not
susceptible to human error and
inconsistencies
– Unbiased and objective
– Not based on regions of interests;
more exploratory
– Picks up on differences/ changes
at a global and local scale
– Has highlighted structural
differences and changes between
groups of people as well as over
time
• AD, schizophrenia, taxi drivers,
quicker learners etc
– Data collection constraints
(exactly the same way)
– Statistical challenges:
– Results may be flawed by
preprocessing steps (poor
registration, smoothing) or by
motion artefacts
– Underlying cause of difference
unknown
– Question about GM density/
interpretation of data- what are
these changes when they are not
volumetric?
Key Papers
• Ashburner & Friston (2000). Voxel-based morphometry- the methods.
NeuroImage, 11: 805-821
• Mechelli, Price, Friston & Ashburner (2005). Voxel-based morphometry of
the human brain: methods and applications. Current Medical Imaging
Reviews, 1: 105-113
– Very accessible paper
• Ashburner (2009). Computational anatomy with the SPM software.
Magnetic Resonance Imaging, 27: 1163 – 1174
– SPM without the maths or jargon
References and Reading
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Literature
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Ashburner & Friston, 2000
Mechelli, Price, Friston & Ashburner, 2005
Sejem, Gunter, Shiung, Petersen & Jack Jr [2005]
Ashburner & Friston, 2005
Seghier, Ramlackhansingh, Crinion, Leff & Price, 2008
Brett et al (2003) or at http://imaging.mrc-cbu.cam.ac.uk/imaging/PrinciplesRandomFields
Crinion, Ashburner, Leff, Brett, Price & Friston (2007)
Freeborough & Fox (1998): Modeling Brain Deformations in Alzheimer Disease by Fluid Registration of Serial 3D MR Images.
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Thomas E. Nichols: http://www.sph.umich.edu/~nichols/FDR/
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stats papers related to statitiscal power in VLSM studies:
Kimberg et al, 2007; Rorden et al, 2007; Rorden et al, 2009
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PPTs/ Slides
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Hobbs & Novak, MfD (2008)
Ged Ridgway: www.socialbehavior.uzh.ch/symposiaandworkshops/spm2009/VBM_Ridgway.ppt
John Ashburner: www.fil.ion.ucl.ac.uk/~john/misc/AINR.ppt
Bogdan Draganski: What (and how) can we achieve with Voxel-Based Morphometry; courtesey of Ferath Kherif
Thomas Doke and Chi-Hua Chen, MfD 2009: What else can you do with MRI? VBM
Will Penny: Random Field Theory; somewhere on the FIL website
Jody Culham: fMRI Analysiswith emphasis on the general linear model; http://www.fmri4newbies.com