1. Methods for Dummies 2015-2016 Voxel-Based Morphometry (VBM)
Jason Carpenter
Samuel Tribich
Expert: Claudia Blaiotta
April, 2016

2. OVERVIEW VBM General Idea VBM Preprocessing Segmentation
Spatial normalization w/ DARTEL
Modulation
Smoothing
Limitations
Statistical analysis
Interpretation of results
Applications of VBM
Brief demonstration
Ten rules for reporting VBM studies

3. General Idea Voxel-wise comparison of regional volumes of tissue
(e.g. grey matter or white matter)
Between two groups of subjects
Patients v. controls
For neuroanatomical correlates of subject characteristics
Scores
Traits e.g. age
Genetic influences

4. Voxel-wise statistical analysis Estimate deformations
VBM Overview
Preprocessing
Segment
Run DARTEL
Modulation
Smoothing
Voxel-wise statistical analysis
Estimate deformations
Normalize to MNI Space
Segmentation – partitioning into different tissue types
Estimate deformations – warping the voxels to fit into a common space
Modulation – convert from density to volume
Smoothing – Low-pass filtering of the segmented, normalized, warped, modulated image

5. Preprocessing: Segmentation
T1-weighted images are partitioned into:
grey matter (GM)
white matter (WM)
CSF
Extra tissue maps can be generated (bone, soft tissue)
Segmentation is achieved by combining:
Tissue Probability maps/Bayesion Priors (TPMs) based on general knowledge about normal tissue distribution
Mixture of Gaussians (MOG) cluster analysis identifies voxel intensity distributions of particular tissue types in the original image.
Non-linear registration (warping) of TPM to register with individual subjects
Bias correction spatially smoothes the intensity variability, which is worse at higher field strengths
Optimization of algorithm to find best parameters which maximize log-probability
Standard & simplest approach to have T1-weighted images, but if multiple modalities are available, its worth adopting multi-spectral approach because it might improve accuracy of segmentations. T1- & T2-/(proton density)PD-weighted images (multi-spectral analysis). Multi-spectral involves the same steps but MOG is multivariate (multivariate Gaussians)
Can also adopt multi-spectral approach
Combination of T1-/T2-/PD-weighted images
Same steps, but multivariate Gaussians (MOG)

6. Segmentation: Tissue Probability Maps (TPM)
Each TPM indicates the prior probability for a particular tissue at each point in MNI space
TPMs are warped to match the subject. GM WM
CSF
Bone
Soft
Tissue
Air/
Background

7. Segmentation: Mixture of Gaussians (MOG)
Classification is based on a Mixture of Gaussians model (MOG), which represents the intensity probability density by a number of Gaussian distributions.

8. Segmentation: Mixture of Gaussians (MOG)
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.

9. Segmentation: Bias correction
Bias field: Exponential of linear combination of basis functions
Optimization: Compute the coefficients of the linear combination
These are maximum aposteriori estimates of model
Diff regularization settings you can choose in SPM to force bias field to be more/less smooth
Corrupted Image
Bias Field
Corrected Image

10. Preprocessing: Spatial normalization w/ DARTEL
= Diffeomorphic Anatomical Registration using Exponentiated Lie Algebra
Registration of GM/WM segmentations to a standard space
Involves prior knowledge e.g. stretches, scales, shifts and warps
Applies millions of parameters which provide non-linear warp to study specific space
Results in average tissue-specific image
Study-specific grey and white matter templates
Allows for more precise inter-subject alignment
Avoid transformations which do not preserve topology of anatomy
Done through regularization term within the algorithm

11. Jacobians determinants Encode relative volumes.
Preprocessing: Modulation
Deformation Field
Jacobians determinants Encode relative volumes.

12. Preprocessing: Modulation
Voxel intensities can be further modulated by Jacobian determinant of warps:
Whether want to compare grey matter density (unmodulated) or volume (modulated).
During modulation voxel intensities are multiplied by the local value in the deformation field from normalisation, so that total GM/WM signal remains the same
Change of intensity now represents volume relative to template
Multiplication of the warped (normalized) tissue intensities so that their regional or global volume is preserved
Unmodulated
Concentration/density
Proportion of GM or WM relative to other tissue types within a region
Hard to interpret
It may be useful for highlighting areas of poor registration (perfectly registered unmodulated data should show no differences between groups)
Unmodulated: differences you see are mainly representative of registration error. Even when you align images, they will never be exactly the same.
Modulated
Volume
Comparison between absolute volumes of GM or WM structures
Useful for looking at the effects of degenerative diseases or atrophy

13. Preprocessing: Smoothing
Each voxel after smoothing effectively becomes the result of applying a weighted region of interest (ROI).
The degree of blurring should relate to the accuracy with which the data can be registered, more blurring if the intersubject registration is less accurate.
Before convolution
Convolved with a circle
Convolved with a Gaussian
Intensity at each voxel is a weighted combination of intensities in the region of interest of the surrounding voxels.

14. Preprocessing: Smoothing
The Jacobian-corrected warped tissue class images would then be blurred by low-pass filtering the images
With isotropic Gaussian kernel
usually between 7 & 14 mm
Choice of kernel changes statistics
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
Removing high-spatial frequencies from the images
Compensates for misregistration

15. Preprocessing: Limitations
Assumes that the brain consists of only the tissues modelled by the TPMs
No spatial knowledge of lesions (stroke, tumours, etc)
Prior probability model (TPMs) based on healthy brains (IXI dataset from London).
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.
Evaluations show DARTEL performs at state-of-the art
Klein et al., (2009) NeuroImage 46(3):

16. Statistical analysis 1: testing group differences
Analyses performed to localise significant differences between two or more experimental groups, using the pre-processed data.
For consideration:
Which covariates to include? e.g. age, gender
Which search volume?
What threshold?
Correct for multiple comparisons?
To do this…

17. Statistical analysis 2: General Linear Model
General Linear Model (GLM) is applied voxel-wise (independent statistical tests for every voxel).
GLM provides a flexible framework that allows a variety of different statistical tests to be performed:
Group comparisons
Correlations with covariates of interest
To do this..

18. Statistical analysis 2: General Linear Model
GLM: Y = Xβ + ε
General principle: design matrix is specified, which models the source of variance among the data.
Linear model is ____ where Y is the imaging data, X is a design matrix and epsilon is a matrix to account for errors or noise. The errors are not dependent on X as they are assumed not to be correlated across measurements. For optimisation we want to find B that best fits the data.

19. Statistical analysis 3: parametric tests
Standard parametric tests can be used to perform mass univariate statistical analysis, provided there is normal distribution of residuals
t tests
F tests
Data is rendered more normally distributed by smoothing during pre-processing, increasing the validity of parametric statistical tests.
Output of these parametric procedures is a statistical parametric map showing regions of GM or WM with significant difference / correlation.
These look like blobs
Source:

20. Statistical analysis 4: multiple comparisons
The statistical parametric map comprises results of many voxel-wise statistical tests.
When dealing with more than one statistical comparison, start to introduce false positives
Depending on MRI resolution, may be performing millions of statistical tests.
Therefore, must correct for multiple comparisons when assessing the significance of an effect in any given voxel.

21. Statistical analysis 4: multiple comparisons
Options for correcting for multiple comparisons include Bonferroni, Family Wise Error, False Discovery Rate and Random Fields Theory.
Random Field theory finds right threshold for a smooth statistical map which gives the required FWE – controls the number of false positive regions rather than voxels & allows multiple non-independent tests.
Changing the p value and using different corrections will change the number of voxels that exceed the significance threshold.
… to correct for the multiple dependent comparisons

22. Statistical analysis: summary
GLM is applied voxel-wise.
Parametric statistical tests performed, assuming normal distribution of residuals (validity can be increased by smoothing).
Random Field Theory used to correct for multiple comparisons.

23. Interpretation: potential confounds
Sample issues:
Sample size – small effect sizes may be missed in smaller cohorts
Age, gender ratios, education, disease severity across groups
Reliability of MRI images
Ideally should be acquired from same scanner with same MR sequences
Processing:
Results should reflect systematic volumetric differences, such as folding or thickness, rather than artifacts arising from misclassification or mis-registration.

24. Interpretation: brain size
Regional volumes are likely to vary as a function of the whole brain volume.
Need to control for “global brain volume”: grey matter + white matter + CSF.
Uniformly bigger brains may have uniformly more GM/WM.
Brains of similar size may have GM differences globally and locally.
Including global brain volume as a covariate adjusts for global atrophy and looks for regionally-specific changes.
Depending on whether or not you consider global difference in TIV, your VBM analysis will interpret the effect of the chink dramatically different:
TIV not accounted for at a global level in GLM: VBM would identify greater volume in right brain apart from the area of the chink, whereas at the chink both brains would be identified as have equal volumes
If TIV is globally discounted for, then both brains will have equal distribution of volume throughout the brain except for the chink area- the LEFT brain will register with more volume (because all tissue is equally distributed in left brain, whereas there is dramatic drop in volume in the chink in right brain and this drop will be picked up in VBM in terms of volume differences between left and right brain)

25. Interpretation: correlations
Correlations do not imply causal relationships.
Can undertake VBM-independent ROI analyses to investigate possible anatomical convergence between functional and morphological methods.
Brain stimulation techniques can provide independent support for a causal link between structure and function (TMS / tDCS disrupting the function of a region, confirming functional involvement of the area in a task – but poor localisation)

26. Applications of VBM: healthy subjects
A Voxel-Based Morphometric Study of Ageing in 465 Normal Adult Human Brains (Good et al., 2001): introduction of an optimised version of VBM
Investigating the regional effect of age.
Findings: heterogeneic response of various compartments of the brain to ageing, with accelerated loss of grey matter volume symmetrically in both parietal lobes (angula gyri), pre- and post-central gyri, insula and anterior cingulate cortex.

27. Applications of VBM: healthy subjects
Voxel-based morphometry in opera singers: Increased gray-matter volume in right somatosensory and auditory cortices (Boris Kleber et al, Neuroimage 2016)
Findings: right hemispheric volume increases in professional singers in ventral primary somatosensory cortex and adjacent rostral supramarginal gyrus, as well as secondary somatosensory and primary auditory cortices – the “singing network”.

28. Applications of VBM: patients
Useful for characterising subtle changes in brain structure in a variety of diseases associated with neurological & psychiatric dysfunction.
Examples:
Developmental and congenital disorders
Autism
Bipolar disorder
Temporal lobe epilepsy
Down syndrome
Parkinson disease
Huntington disease
Alzheimer disease

29. Applications of VBM: patients
Biological heterogeneity of obsessive-compulsive disorder: A voxel-based morphometric study based on dimensional assessment (K Okada et al. 2015, Psychiatry Clin Neurosci)
Findings: specific negative correlations between symptomatic dimension scores and regional GM volumes, mainly as decreased right cerebellum in ‘aggression/checking’ (left below) and decreased right insula in ‘contamination/washing’ (right below).
Also differences between responders & non-responders to CBT – imaging biomarker to help stratify to correct treatment, by predicting who will respond.

30. VBM brief demonstration (pre-processing)

31. VBM brief demonstration (pre-processing)

32. VBM brief demonstration (pre-processing)

33. VBM brief demonstration (pre-processing)

34. VBM brief demonstration (pre-processing)
Normalising to MNI space also smoothes the images.

35. Ten rules for reporting VBM studies
Set out rationale of study and describe data fully.
Explain how brain segmentations are produced.
Describe method of inter-subject spatial normalisation.
Make your statistical design transparent.
Be clear about the significance of your findings.
Present results unambiguously.
Clarify and justify any non-standard statistical analysis.
Guard against common pitfalls.
Recognise the limitations of the technique.
Interpret your results cautiously and in context.
(Ridgway et al. 2008)

36. References Klein et al., (2009) NeuroImage 46(3):786-802
SPM Course (2010/2011/2015) Ashburner VBM Slides
MfD Course (2013/2014) VBM Slides
Ashburner & Friston (2000, NeuroImage, Voxel-Based Morphometry – The Methods)
Mechelli, Price, Friston & Ashburner (2005). Voxel-based morphometry of the human brain: methods and applications. Current Medical Imaging Reviews, 1:
Ashburner (2009). Computational anatomy with the SPM software. Magnetic Resonance Imaging, 27: 1163 – 1174
Henley et al. 2009: Pitfalls in the Use of Voxel-Based Morphometry as a Biomarker: Examples from Huntington Disease
Good et al. (2001) A Voxel-Based Morphometric Study of Ageing in 465 Normal Adult Human Brains: introduction of an optimised version of VBM
Kleber et al. (2016) Voxel-based morphometry in opera singers: Increased gray-matter volume in right somatosensory and auditory cortices. Neuroimage
Okada et al. (2015) Biological heterogeneity of obsessive-compulsive disorder: A voxel-based morphometric study based on dimensional assessment. Psychiatry Clin Neurosci
Ridgway et al. (2008) Ten simple rules for reporting voxel-based morphometry studies. Neuroimage