voxel based morphometry methods for dummies 2012 merina su and elin van duin
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Voxel Based Morphometry
Methods for Dummies 2012Merina Su and Elin van Duin
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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
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VBM
• General Idea• Preprocessing• Analysis
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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.
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Computational neuranatomy
Deformation-based morphometryLooks at macroscopic differences in brain shape. Uses the deformation fields needed to warp an individual brain to a standard reference.
Tensor-based morphometryDifferences in the local shape of brain structures
Voxel based morphometryDifferences in regional volumes of tissue
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Procedure overview
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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
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Segmentation
• Images are partitioned into:- Grey matter- White matter- CSFExtra tissue maps can be generated
• SPM uses a generative model, which involves:- Mixture of Gaussians- Bias Correction Component- Warping Component
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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
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Segmentation
freq
uenc
y
image intensity
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Smoothing
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Modulation
Non-modulated:– Relative concentration/ density: the proportion of GM (or WM) relative to other tissue types within a region– Hard to interpret
Modulated:- Absolute volumes
Modulation: multiplying the spatially normalised gray matter (or other tissue class) by its relative volume before and after spatial transformation
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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.
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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.
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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
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SPM for group fMRIfMRI time-series
Preprocessing spm T
Image
Group-wisestatistics
Spatially Normalised “Contrast” Image
Spatially Normalised “Contrast” Image
Spatially Normalised “Contrast” Image
Preprocessing
Preprocessing
fMRI time-series
fMRI time-series
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SPM for Anatomical MRI Anatomical MRI
Preprocessing spm T
Image
Group-wisestatistics
Spatially Normalised Grey Matter Image
Spatially Normalised Grey Matter Image
Spatially Normalised Grey Matter Image
Preprocessing
Preprocessing
Anatomical MRI
Anatomical MRI
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Statistical analysis VBM
• Types of analysis• What does SPM show?• Multiple corrections problem• Things to consider…• Interpreting results
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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?
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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
General Linear Model
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VBM: group comparison
• 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
GLM: Y = Xβ + ε
“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?”
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Statistical Parametric Mapping…
gCBF
rCBF
x
o
o
o
o
o
o
x
x
x
x
x
g..
k1
k2
k
group 1 group 2
voxel by voxelmodelling
–
parameter estimate standard error
=
statistic imageor
SPM
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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
• Contrast of interest is whether β1 (slope of association between intensity & test score) is significantly different to zero
V = β1(test score) + β2(age) + β3(gender) + β4(global volume) + μ + ε
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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
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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
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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
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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)
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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
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• 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
Family-wise Error
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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
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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)
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Global or local change?
• Without TIV: greater volume in B relative to A except in the thin area on the right-hand side
• With TIV: greater volume in A relative to B only in the thin area on the right-hand sideBrains of similar size with GM
differences globally and locally
Including total GM or WM volume as a covariate adjusts for global atrophy and looks for regionally-specific changes
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Interpreting results
ThickeningThinning
Folding
Mis-classify
Mis-classify
Mis-register
Mis-register
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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
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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
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Fluid Registered ImageFTD
(semantic dementia)
Voxel compression map
1 year
expandingcontracting
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In summary
• Pro– 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
• Con– 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?
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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
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References and Reading• Literature
• 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.
• Thomas E. Nichols: http://www.sph.umich.edu/~nichols/FDR/
• stats papers related to statitiscal power in VLSM studies:• Kimberg et al, 2007; Rorden et al, 2007; Rorden et al, 2009
• PPTs/ Slides
• 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