VBM Voxel-Based Morphometry Suz Prejawa Greatly inspired by MfD talk from 2008: Nicola Hobbs & Marianne Novak Overview Intro Pre-processing- a whistle stop tour What does the SPM show in VBM? VBM & CVBM The GLM in VBM Covariates Things to consider
Multiple comparison corrections Other developments Pros and cons of VBM References and literature hints Literature and references Intro VBM = vovel based morphometry morpho = form/ gestalt metry = to measure/ measurement Studying the variability of the form (shape and size) of things detects differences in the regional concentration of grey matter (or other) at a local scale whilst discounting global brain shape differences
Whole-brain analysis - does not require a priori assumptions about ROIs Fully automated VBM- simple! 1. Spatial normalisation 2. Tissue segmentation The data are pre-processed 3. Modulation to sensitise the statistical tests to *regional* tissue 4. Smoothing volumes 5. Statistical analysis output: statistical (parametric) maps showing regions where certain tissue type differs significantly between groups/ correlate with a specific parameter, eg age, test-score
VBM Processing Normalisation All subjects T1 MRI* entered into the same stereotactic space (using the same template) to correct for global brain shape differences does NOT aim to match all cortical features exactly- if it did, all brains would look identical (defies statistical analysis) * needs to be high resolution MRI (1 or 1.5mm) ORIGINAL IMAGE SPATIAL NORMALISATION
TEMPLATE IMAGE SPATIALLY NORMALISED IMAGE Normalisation- detailed 1) Affine transformation Translation, rotation, scaling, shearing Matches overall position and size FIT 2) Non-linear step Process of warping an image MI to fit onto a template
Aligns sulci and other structures to a common space Template The amount of warping (deforming) the MRI has to undergo to fit the template = nonlinear registration Subject MRI Segmentation normalised images are partioned into
grey matter white matter CSF Segmentation is achieved by combining probability maps/ Bayesion Priors (based on general knowledge about normal tissue distribution) with mixture model cluster analysis (which identifies voxel intensity distributions of particular tissue types in the original image) GM WM CSF Spatial prior probability maps
Smoothed average of tissue volume, eg GM, from MNI Priors for all tissue types Intensity at each voxel in the prior represents probability of being tissue of interest, eg GM SPM compares the original image to priors to help work out the probability of each voxel in the image being GM (or WM, CSF) Mixture Model Cluster Analysis Intensities in T1 fall into roughly 3 classes SPM can assign a voxel to a tissue class by seeing what its intensity is relative to the others in the image Each voxel has a value between 0 and 1,
representing the probability of it being in a particular tissue class Includes bias correction for image intensity nonuniformity due to the MRI process Generative Model looks for the best fit of an individual brain to a template Cycle through the steps of: Tissue classification using image intensities Bias correction Image warping to standard space using spatial prior probability
maps Continues until algorithm can non longer model data more accurately Results in images that are segmented, bias-corrected and registered into standard space. Beware of optimised VBM reduces the misinterpretation of significant differences, eg misregistering enlarged ventricles as GM Standard and optimised VBM are both old-school these days. Bigger, Better, Faster and more
Beautiful: Unified segmentation Ashburner & Friston (2005): This paper illustrates a framework whereby tissue classification, bias correction, and image registration are integrated within the same generative model. Crinion, Ashburner, Leff, Brett, Price & Friston (2007): There have been significant advances in the automated normalization schemes in SPM5, which rest on a unified model for segmenting and normalizing brains. This unified model embodies the different factors that combine to generate an anatomical image, including the tissue class generating a signal, its displacement due to anatomical variations and an intensity modulation due to field inhomogeneities during acquisition of the image. For lesioned brains: Seghier, Ramlackhansingh, Crinion, Leff & Price, 2008: Lesion identification using unified segmentation-normalisation models and fuzzy clustering Modulation Is optional processing step but tends to be
applied Corrects for changes in brain VOLUME caused by non-linear spatial normalization multiplication of the spatially normalised GM (or other tissue class) by its relative volume before and after warping*, ie: iB = iA x [VA / VB] * Jacobian determinants of the deformation field An Example Template Smaller Brain iA = 1 iB = iA x [VA / VB] Normalisation vB = 2
Modulation iB = ? vA = 1 iB = 1 x [1 / 2] = 0.5 Larger Brain Template iA = 1 Normalisation vB = 2 Modulation iB = ?
vA = 4 iB = 1 x [4 / 2] = 2 Signal intensity ensures that total amount of GM in a subjects temporal lobe is the same before and after spatial normalisation and can be distinguished between subjects Modulated vs Unmodulated Unmodulated Concentration/ density proportion of GM (or WM) relative to other tissue types within a region Modulated
Volume Comparison between absolute volumes of GM or WM structures Hard to interpret may be useful for highlighting areas of poor registration (perfectly registered unmodulated data should show no differences between groups) useful for looking at the effects
of degenerative diseases or atrophy What is GM density? The exact interpretation of GM concentration or density is complicated, and depends on the preprocessing steps used It is not interpretable as neuronal packing density or other cytoarchitectonic tissue properties, though changes in these microscopic properties may lead to macro- or mesoscopic VBM-detectable differences Modulated data is more concrete Smoothing Primary reason: increase signal to noise ratio With isotropic* Gaussian kernel usually between 7 & 14 mm
Choice of kernel changes stats Effect: data becomes more normally distributed Each voxel contains average GM and WM concentration from an area around the voxel (as defined by the kernel) Brilliant for statistical tests (central limit theorem) Compensates for inexact nature of spatial normalisation, smoothes out incorrect registration * isotropic: uniform in all directions Smoothing Before convolution Convolved with a circle Convolved with a Gaussia Weighted effect
3 3 Units are mm of original grey matter per mm of Pre-processed data for four subjects Warped, Modulated Grey Matter 12mm FWHM Smoothed Version Interim Summary 1. Spatial normalisation 2. Tissue segmentation 1. First and second step may be combined 3. Modulation (not necessarily but likely) 4. Smoothing
5. The fun begins! Analysis and how to deal with the results What does the SPM show in VBM? Voxelwise (mass-univariate: independent statistical tests for every single voxel) Employs GLM, providing the residuals are normally distributed, GLM: Y = X + + Outcome: statistical parametric maps, showing areas of significant difference/ correlations Look like blobs Uses same software as fMRI SPM showing regions where Huntingtons patients have lower GM intensity than controls One way of looking at data
VBM Continuous VBM ANOVA/ t-test Comparing groups/ populations ie, identify if and where there are significant differences in GM/ WM volume/ density between groups Multiple regression Correlations with behaviour ie, how do tissue distribution/ density correlate with a score on a test or some other
covariate of interest a known score or value Both use a continuous measure of GM/ WM (there are other techniques that use binary measures, eg VLSM) Using the GLM for VBM e.g, compare the GM/ WM differences between 2 groups Y = X + + H0: there is no difference between these groups : other covariates, not just the mean VBM: group comparison
GLM: Y = X + + Intensity for each voxel (V) is a function that models the different things that account for differences between scans: V = 1(AD) + 2(control) + 3(covariates) + 4(global volume) + + V = 1(AD) + 2(control) + 3(age) + 4(gender) + 5(global volume) + + which covariate () best explains the values in GM/ WM In practice, the contrast of interest is usually t-test between 1 and 2, *** *** Eg, 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? CVBM: correlation Correlate images and test scores (eg Alzheimers patients with memory score) SPM shows regions of GM or WM where there are significant associations between intensity (volume) and test score
V = 1(test score) + 2(age) + 3(gender) + 4(global volume) + + Contrast of interest is whether 1 (slope of association between intensity & test score) is significantly different to zero all VBM statistical analyses use an ANCOVA model so Essentially, distinguishing CVBM and VBM may be a bit artificial (no returns for CVBM in literature- as tested by G Flandin). Things to consider Global or local differences Uniformly bigger brains may have uniformly more GM/ WM considering the effects of overall size (total intracranial volume) may make a difference at a local level
brain A brain B differences without accounting for TIV (TIV = global measure) 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) Brains of similar size with GM differences globally and locally Mechelli et al 2005 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 Or see http://imaging.mrc-cbu.cam.ac.uk/imaging/PrinciplesRandomFields Theyre the same guys 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 Heres 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 FWE
FWE: When a series of significance tests is conducted, the familywise error rate (FWE) is the probability that one or more of the significance tests results in a a false positive within the volume of interest (which is the brain) SPM uses Gaussian Random Field Theroy to deal with FER A body of mathematics defining theoretical results for smooth statistical maps Not the same as Bonferroni Correction! (because GRF allows for multiple non-independent tests) Finds the right threshold for a smooth statistical map which gives the required FWE; it controls the number of false positive regions rather than voxels * You may read up on this at your leisure here: Brett et al (2003) or at http://imaging.mrc-cbu.cam.ac.uk/imaging/PrinciplesRandomFields
Gaussian Random Field Theory Finds the right threshold for a smooth statistical map which gives the required FWE; it controls the number of false positive regions rather than voxels Calculates the threshold at which we would expect 5% of equivalent statistical maps arising under the null hypothesis to contain at least one area above threshold Slide modified from Duke course So which regions (of statistically significant regions) do I have left after I have thresholded the data and how likely is it that the same regions would occur under the null hypothesis? Euler Characteristic (EC) threshold threshold an an image
image at at different different points points -- EC EC == number number of of remaining remaining blobs blobs after after an an image image has has been been thresholded
thresholded -- RFT RFT can can calculate calculate the the expected expected EC EC which which corresponds corresponds to to our our required required FEW FEW -- Which Which expected
expected EC EC ifif FEW FEW set set at at .05? .05? Good: a safe way to correct Bad: but we are probably missing a lot of true positives Other developments Standard vs optimised VBM Tries to improve the somewhat inexact nature of normalisation Unified segmentation has overtaken these approaches but be aware of them (used in literature) DARTEL toolbox / improved image registration Diffeomorphic Anatomical Registration Through Exponentiated
Lie algebra (SPM5, SPM8) more precise inter-subject alignment (multiple iterations) more sensitive to identify differences more accurate localization Other developments II not directly related to VBM Multivariate techniques VBM = mass-univariate approach identifying structural changes/ differences focally but these may be influenced by inter-regional dependences (which VBM does not pick up on) Multivariate techniques can assess these inter-regional dependences to characterise anatomical differences between groups Longitudinal scan analysis- captures structural changes over time within subjects May be indicative of disease progression and highlight how & when the disease progresses (eg, in Alzheimers Disease)
Fluid body registration Fluid-Registered Images 1. match successive scans to baseline scan from the same person and identify where exactly changes occur over time 2. by warping one to the other and analysing the warping parameters View through the baseline scan of an Alzheimer disease patient
The color overlay shows the level of expansion or contraction occuring between repeat scan & baseline scan Whats cool about VBM? Cool 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 local scale In vivo, not invasive Has highlighted structural
differences and changes between groups of people as well as over time AD, schizophrenia, taxi drivers, quicker learners etc Not quite so cool Data collection constraints (exactly the same way) Statistical challenges: Multiple comparisons, false positives and negatives extreme values violate normality assumption Results may be flawed by preprocessing steps (poor registration, smoothing) or by motion artefacts (Huntingtons vs
controls)- differences not directly caused by brain itself Esp obvious in edge effects Question about GM density/ interpretation of data- what are these changes when they are not volumetric? Key Papers Ashburner & Friston (2000). Voxel-based morphometrythe 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: 105113 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 
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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