Voxel based morphometry
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Voxel Based Morphometry. Methods for Dummies 2012 Merina Su and Elin van Duin. Rebel with a cause.

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Voxel Based Morphometry

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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


  • 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 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

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


  • 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


2 sources of information:

  • 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



image intensity


Non-modulated:– Relative concentration/ density: the proportion of GM (or WM) relative to other tissue types within a region– Hard to interpret


- Absolute volumes


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.


  • 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


fMRI time-series


Spatially Normalised

“Contrast” Image

spm TImage

fMRI time-series


Spatially Normalised

“Contrast” Image

fMRI time-series


Spatially Normalised

“Contrast” Image

SPM for Anatomical MRI


Anatomical MRI


Spatially Normalised

Grey Matter Image

spm TImage

Anatomical MRI


Spatially Normalised

Grey Matter Image

Anatomical MRI


Spatially Normalised

Grey Matter Image

Statistical analysis VBM

Types of analysis

What does SPM show?

Multiple corrections problem

Things to consider…

Interpreting results

Types of analysis

Group comparison


a known score or value

  • Where in the brain are there associations between brain volume and test score?

  • Where in the brain do the Simpsons and the Griffins have differences in brain volume?

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

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

GLM: Y=Xβ + 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…

group 1

group 2

parameter estimate

standard error

statistic image



voxel by voxelmodelling

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


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-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

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

Family-wise Error

1 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

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)

Uniformly bigger brains may have uniformly more GM/ WM

Global or local change?

Brains 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

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 side

Interpreting results








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


  • 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




(semantic dementia)

Voxel compression map

1 year

In summary


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


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

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