Voxel Based Morphometry

Methods for Dummies 2012Merina 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 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

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

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

Segmentation

freq

uenc

y

image intensity

Smoothing

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

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 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

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

Statistical analysis VBM

• 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?

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

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?”

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

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

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

• 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

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

• 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

Interpreting results

ThickeningThinning

Folding

Mis-classify

Mis-classify

Mis-register

Mis-register

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 ImageFTD

(semantic dementia)

Voxel compression map

1 year

expandingcontracting

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?

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• 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