VBM Voxelbased morphometry Nicola Hobbs Marianne Novak Thanks

VBM Voxel-based morphometry Nicola Hobbs & Marianne Novak Thanks to Susie Henley

Overview • Background • Pre-processing steps • • Analysis Multiple comparisons Pros and cons of VBM Optional extras

Background • VBM is a voxel-wise comparison of local tissue volumes within a group or across groups • Whole-brain analysis, does not require a priori assumptions about ROIs; unbiased way of localising structural changes • Can be automated, requires little user intervention compare to manual ROI tracing

Basic Premise 1. Spatial normalisation (alignment) into standard space 2. Segmentation of tissue classes 3. Modulation - adjust for volume changes during normalisation 4. Smoothing - each voxel is a weighted average of surrounding voxels 5. Statistics - localise & make inferences about differences

VBM Processing

Step 1: normalisation • Aligns images by warping to standard stereotactic space • Affine step – translation, rotation, scaling, shearing • Non-linear step • Adjust for differences in • head position/orientation in scanner • global brain shape • Any remaining differences (detectable by VBM) are due to smaller-scale differences in volume

ORIGINAL IMAGE SPATIAL NORMALISATION TEMPLATE IMAGE SPATIALLY NORMALISED IMAGE

2. Tissue segmentation • Aims to classify image as GM, WM or CSF • Two sources of information SPATIALLY a) Spatial prior probability maps NORMALISED b) Intensity information in the image itself IMAGE GREY MATTER WHITE MATTER CSF

a) Spatial prior probability maps • Smoothed average of GM from MNI • Intensity at each voxel represents probability of being GM • SPM compares the original image to this to help work out the probability of each voxel in the image being GM (or WM, CSF)

b) Image intensities • Intensities in the image fall into roughly 3 classes • SPM can also 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 that particular tissue class • Includes correction for image intensity non-uniformity

Generative model • Segmentation into tissue types • Bias Correction • Normalisation • These steps cycled through until normalisation and segmentation criteria are met

Step 3: modulation • Corrects for changes in volume induced by normalisation • Voxel intensities are multiplied by the local value in the deformation field from normalisation, so that total GM/WM signal remains the same • Allows us to make inferences about volume, instead of concentration

Modulation i i i / δV X δV normalisation modulation • E. g. During normalisation TL in AD subject expands to double the size • Modulation multiplies voxel intensities by Jacobian from normalisation process (halve intensities in this case). • Intensity now represents relative volume at that point

Is modulation optional? • Unmodulated data: compares “the proportion of grey or white matter to all tissue types within a region” • Hard to interpret • Not useful for looking at e. g. the effects of degenerative disease • Modulated data: compares volumes • Unmodulated data may be useful for highlighting areas of poor registration (perfectly registered unmodulated data should show no differences between groups)

Step 4: Smoothing • Convolve with an isotropic Gaussian kernel • Each voxel becomes weighted average of surrounding voxels • Smoothing renders the data more normally distributed (Central Limit theorem) • Required if using parametric statistics • Smoothing compensates for inaccuracies in normalisation • Makes mass univariate analysis more like multivariate analysis • Filter size should match the expected effect size • Usually between 8 – 14 mm

Smoothing SMOOTH WITH 8 MM KERNEL 8 mm

VBM: Analysis • • • What does the SPM show in VBM? Cross-sectional VBM Multiple comparison corrections Pros and cons of VBM Optional extras

VBM: Cross-sectional analysis overview • T 1 -weighted MRI from one or more groups at a single time point • Analysis compares (whole or part of) brain volume between groups, or correlates volume with another measurement at that time point • Generates map of voxel intensities: represent volume of, or probability of being in, a particular tissue class

What is the question in VBM analysis? AD Control • Take a single voxel, and ask: “are the intensities in the AD images significantly different to those in the control images for this particular voxel? ” • eg is the GM intensity (volume) lower in the AD group cf controls? • ie do a simple t-test on the voxel intensities

Statistical Parametric Maps (SPM) • Repeat this for all voxels • Highlights all voxels where intensities (volume) are significantly different between groups: the SPM • SPM showing regions where Huntington’s patients have lower GM intensity than controls • Colour bar shows the t-value

VBM: group comparison • Intensity for each voxel (V) is a function that models the different things that account for differences between scans: • V = β 1(AD) + β 2(control) + β 3(covariates) + β 4(global volume) + μ + ε • V = β 1(AD) + β 2(control) + β 3(age) + β 4(gender) + β 5(global volume) + μ + ε • In practice, the contrast of interest is usually t-test between β 1 and β 2 • eg “is there significantly more GM in the control than in the AD scans? ”

VBM: correlation • Correlate images and test scores (eg Alzheimer’s patients with memory score) • SPM shows regions of GM or WM where there are significant associations between intensity (volume) and test score • V = β 1(test score) + β 2(age) + β 3(gender) + β 4(global volume) + μ + ε • Contrast of interest is whether β 1 (slope of association between intensity & test score) is significantly different to zero

Correcting for Multiple Comparisons • 200, 000 voxels per scan ie 200, 000 t-tests • If you do 200, 000 t-tests at p<0. 05, by chance 10, 000 will be false positives • Bad practice… • A strict Bonferroni correction would reduce the p value for each test to 0. 00000025 • However, voxel intensities are not independent, but correlated with their neighbours • Bonferroni is therefore too harsh a correction and will lose true results

Familywise 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

q value FDR False Discovery Rate • FDR more recent q<0. 05 Voxel • It controls the expected proportion of false positives among suprathreshold voxels only • Using FDR, q<0. 05: we expect 5% of the voxels for each SPM to be false positives (1, 000 voxels) • Bad: less stringent than FWE so more false positives • Good: fewer false negatives (ie more true positives) • But: assumes independence of voxels: avoid…. ?

VBM Pros 1. Objective analysis 2. Do not need priors – more exploratory 3. Automated VBM Cons 1. False positives: misregistration, FDR 2. False negatives: FWE 3. More difficult to pick up differences in areas with high inter -subject variance: low signal to noise ratio

Other VBM Issues • Optimised VBM: GM to GM warping, then applied to whole brain image (better GM alignment); Good et al, Neuroimage 2001 (SPM 2) • Diffeomorphic warping: DARTEL • Multivariate techniques: including classification/SVM • Longitudinal scan analysis: two time points especially

18 iterations to form template Ashburner Neuroimage 2007

Standard preprocessing: areas of decreased volume in depressed subjects DARTEL preprocessing: areas of decreased volume in depressed subjects

Longitudinal VBM • Baseline and follow-up image are registered together nonlinearly (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 contracting expanding

Optimised VBM 1. Affine registration to SPM 2 T 1 template Native space images Standard space images 2. Segmentation GM segments 3. Estimate normalisation parameters for GM segments to SPM 2 GM template Normalisation parameters GM to GM 4. Normalisation using parameters from step 3; GM is well-aligned Standard space images 5. Segmentation GM segments 6. Modulation: correcting for spatial changes introduced in normalisation Mod GM 7. Masking: segments are multiplied by binary region to exclude any non-brain Masked GM 8. Smoothed at 8 mm FWHM Smoothed, Masked, mod GM

Resources and references • http: //www. fil. ion. ucl. ac. uk/spm (the SPM homepage) • http: //imaging. mrc-cbu. cam. ac. uk/imaging/Cbu. Imaging (neurimaging wiki homepage) • http: //www. mrc-cbu. cam. ac. uk/Imaging/Common/randomfields. shtml (for multiple comparisons info) • Ashburner J, Friston KJ. Voxel-based morphometry--the methods. Neuroimage 2000; 11: 805 -821 (the original VBM paper) • Good CD, Johnsrude IS, Ashburner J, Henson RN, Friston KJ, Frackowiak RS. A voxel-based morphometric study of ageing in 465 normal adult human brains. Neuroimage 2001; 14: 21 -36 (the optimised VBM paper) • Ridgway GR, Henley SM, Rohrer JD, Scahill RI, Warren JD, Fox NC. Ten simple rules for reporting voxel-based morphometry studies. Neuroimage 2008.