VBMVoxel-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

SPATIALSPATIAL

NORMALISATIONNORMALISATION

ORIGINAL ORIGINAL IMAGEIMAGE

SPATIALLY SPATIALLY NORMALISED NORMALISED

IMAGEIMAGETEMPLATE TEMPLATE

IMAGEIMAGE

GREY MATTERGREY MATTER WHITE MATTERWHITE MATTER CSF CSF

SPATIALLY SPATIALLY NORMALISED NORMALISED

IMAGE IMAGE

2. Tissue segmentation

• Aims to classify image as GM, WM or CSF• Two sources of information

a) Spatial prior probability maps

b) Intensity information in the image itself

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

• 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

i

modulation

i / δV

normalisation

iX δV

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 – 14mm

SMOOTH SMOOTH WITH 8MM WITH 8MM

KERNELKERNEL

Smoothing

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

• T1-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?

• 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

AD Control

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 = β1(AD) + β2(control) + β3(covariates) + β4(global volume) + μ + ε

• V = β1(AD) + β2(control)

• In practice, the contrast of interest is usually t-test between β1 and β2

+ β3(age) + β4(gender) + β5(global volume) + μ + ε

• 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 = 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

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

False Discovery Rate

• FDR more recent

• 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….?

q<0.05

Voxel

FDRq value

VBM Pros

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

1. Objective analysis2. Do not need priors – more exploratory3. Automated

VBM Cons

Other VBM Issues

• Longitudinal scan analysis: two time points especially

• 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

Ashburner Neuroimage 2007

18 iterations to form template

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 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

Native space images

Standard space images

GM segments

Normalisation parametersGM to GM

1. Affine registration to SPM2 T1 template

2. Segmentation

3. Estimate normalisation parameters for GM

segments to SPM2 GM template

Standard space images

4. Normalisation using parameters from step 3; GM is well-aligned

GM segments

5. Segmentation

Mod GM

6. Modulation: correcting for spatial changes

introduced in normalisation

Masked GM

7. Masking: segments are multiplied by binary

region to exclude any non-brain

Smoothed, Masked, mod GM

8. Smoothed at 8mm FWHM

Optimised VBMOptimised VBM

Resources and references

• http://www.fil.ion.ucl.ac.uk/spm (the SPM homepage)• http://imaging.mrc-cbu.cam.ac.uk/imaging/CbuImaging (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.