VBMVoxel-based morphometry

Floris de Lange

Most slides taken/adapted from:

Nicola Hobbs & Marianne Novak

http://www.fil.ion.ucl.ac.uk/mfd/

Overview

• Background (What is VBM?)• Pre-processing steps

• Analysis• Multiple comparisons• Pros and cons of VBM• Optional extras

What is VBM?

• 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 Steps

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

• parameter affine transform• 3 translations• 3 rotations• 3 zooms• 3 shears

• Fits overall shape and size

Normalization – linear transformations

Normalization – nonlinear transformations

Deformations consist of a linear combination of smooth basis functions

These are the lowest frequencies of a 3D discrete cosine transform (DCT)

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

Bias correction

• The contrast of a scan may not be the same everywhere

• This makes it more difficult to partition the scan in different tissue types

• Bias correction estimates and removes this bias

Image with bias

artefact

Corrected image

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: 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. SPM normalization procedure is rather crude

2. Not ideal for subcortical (well-delineated) structures

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

Standard preprocessing: areas of decreased volume in depressed subjects

DARTEL preprocessing: areas of decreased volume in depressed subjects

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.