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 Voxel-based morphometry of MRI data involves spatially normalizing all the images to the same stereotactic space, extracting the gray matter from the normalized images, smoothing, and finally performing a statistical analysis to localize, and make inferences about, group differences. So you preprocess the data in a way that makes it sensitive to differences in certain tissue volumes. The output from the method is a statistical parametric map showing regions where tissue matter, like gray matter, concentration differs significantly between groups.

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: 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 frequency 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

Group-wise statistics SPM for group fMRI Group-wise statistics fMRI time-series Preprocessing Spatially Normalised “Contrast” Image spm T Image fMRI time-series Preprocessing Spatially Normalised “Contrast” Image fMRI time-series Preprocessing Spatially Normalised “Contrast” Image

Group-wise statistics SPM for Anatomical MRI Group-wise statistics Anatomical MRI Preprocessing Spatially Normalised Grey Matter Image spm T Image Anatomical MRI Preprocessing Spatially Normalised Grey Matter Image Anatomical MRI Preprocessing 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 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 Y = Xβ + ε H0: there is no difference between e.g, compare the GM/ WM differences between 2 groups Y = Xβ + ε From: Thomas Doke and Chi-Hua Chen, MfD 2009 H0: there is no difference between these groups β: other covariates, not just the mean 20

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?” 21

Statistical Parametric Mapping… group 1 group 2 – parameter estimate standard error statistic image or SPM = voxel by voxel modelling

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 23

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 25

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 26

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) 27

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 28

Family-wise 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

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 mean scaling? TIV as covariate? 31

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 side 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 32

Interpreting results Mis-register Mis-classify Folding Thinning Thickening Thinning Mis-classify Mis-register 33

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 Longitudinal analysis 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 expanding contracting

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