1. MfD 2013-2014 Voxel-Based Morphometry (VBM)
Andrea Gajardo-Vidal
Clarisse Aichelburg

2. OVERVIEW VBM: Basic Approach, Basic Idea & Application, Advantage
The original VBM: Spatial normalisation, segmentation, smoothing and statistical analysis.
VBM: new approach
What does SPM show in VBM?: DARTEL toolbox
Some important applications (literature hints)
Further Considerations: Potential Confounds, Statistical Analysis
Take home messages
References

3. 1.VBM: Basic Approach
Voxel-wise comparison of the local volume of GM between two groups of subjects
involves spatially normalizing high-resolution images from all participants into the same stereotactic space, segmenting and smoothing GM segments
Voxel-wise parametric statistical tests comparing the smoothed GM images from the two groups is performed

4. 1.VBM: Basic Idea & Application
Not biased to one particular structure, instead assesses anatomical differences throughout the brain
Investigates patterns of brain change
in development
in disease
due to learning/ brain plasticity
As well as neuroanatomical correlates of subject characteristics
Scores
Traits
Genetic influences

5. 1.VBM: Advantage
link between an individual’s performance or trait as measured in an ecologically valid environment (outside the scanner) to brain structures measurements obtained in the scanner
can administer multiple tasks to the same set of participants, and correlations between tasks can be analyzed
one-to-one mapping between a cognitive function and the structure of a brain region
when a single region is identified it needs to be interpreted in the context of known functions of the region

6. 2. VBM: The original proposal (Ashburner & Friston, 2000)
Spatial normalisation: involves transforming all the subjects’ data to the same stereotactic space.
Tissue segmentation:the spatially normalized images are next partitioned into gray matter (GM), white matter (WM), cerebrospinal fluid (CSF) and three other background classes, using a modified mixture model cluster analysis technique which identifies voxel intensity distributions of particular tissue types.
Smoothing: the gray matter images are now smoothed by convolving with an isotropic Gaussian kernel. This makes the subsequent voxel-by-voxel analysis comparable to a region of interest approach.
Logit transform: Often, prior to performing statistical tests on measures of concentration, the data are transformed using the logit transformation in order to render them more normally distributed.
Statistical analysis: the final step of a VBM analysis involves a voxel-wise statistical analysis. This employs the general linear model (GLM), a flexible framework that allows a variety of different statistical tests such as group comparisons and correlations with covariates of interest.

8. Group-wise Normalisation Voxel-wise statistical analysis
3. VBM: New approach
Segmentation
Group-wise Normalisation
(DARTEL)
Modulation
Smoothing
Voxel-wise statistical analysis

9. VBM: New approach
More recently, there was a change to the VBM framework, such that the pre-processed data were scaled such that the total volume of tissue in each structure is preserved after warping the data to a standard reference space . This correction is by scaling by the Jacobian determinant of the deformation and is colloquially known as MODULATION.” The result is that the pre-processed data represent a quantitative measure (tissue volume per unit volume of spatially normalized image).
Unified segmentation and spatial normalisation
More flexible group-wise normalisation using DARTEL
Volume-preserving transformation/warping
Gaussian smoothing
Optional computation of tissue totals/globals
Voxel-wise statistical analysis

10. Segmentation T1 images are partioned into:
grey matter
white matter
CSF
Extra tissue maps can be generated (2 additional ones)
Segmentation is achieved by combining :
Tissue Probability maps/ Bayesion Priors (TPMs) 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).
***In order to separate grey matter from other tissues, there must be a high contrast between grey matter and other surrounding tissues. If grey matter is not clearly visible, then it cannot be precisely segmented

11. Segmentation: TPMs – Tissue prior probability maps
Each TPM indicates the prior probability for a particular tissue at each point in MNI space
TPMs are warped to match the subject.
ICBM Tissue Probabilistic Atlases. These tissue probability maps are kindly provided by the International Consortium for Brain Mapping, John C. Mazziotta and Arthur W. Toga.

12. Segmentation Intensities in the image fall into roughly 3 classes.
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.
Each voxel has a value between 0 and 1, representing the probability of it being in that particular tissue class.

13. 4. DARTEL toolbox
DARTEL=Diffeomorphic Anatomical Registration using Exponentiated Lie algebra (DARTEL).
More sophisticated registration model which improves image registration
More precise inter-subject alignment (multiple iterations: more than registrations rather than registration parameters from the previous model).
More sensitive to identify more accurate localization

14. Spatial normalisation with DARTEL
Limited flexibility registration has been criticised
MNI/ICBM templates/priors are not universally representative
VBM is crucially dependent on registration performance
Inverse transformations are useful, but not always well-defined
More flexible registration requires careful modelling and regularisation (prior belief about reasonable warping)
The DARTEL toolbox combines several methodological advances to address these limitations
Evaluations show DARTEL performs at state-of-the art (see Klein et al., (2009) NeuroImage 46(3): )

15. Modulation (preserved amount)
Voxel intensities can be further modulated by determinant of Jacobean of warps: i.e, whether want to compare gray 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 (normalised) tissue intensities so that their regional or global volume is preserve

16. Modulated vs. Unmodulated
Volume
Comparison between absolute volumes of GM or WM structures
Useful for looking at the effects of degenerative diseases or atrophy
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)

17. 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 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

18. Smoothing
The data are typically convolved with a Gaussian, so the result is a weighted count of voxels containing the tissue (see figure).
***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.

19. Smoothing

20. Statistical analysis :GLM
Statistical analysis of the preprocessed data are performed by fitting a GLM at each voxel.
Y = Xβ + ε
Voxel wise (independent statistical tests for every single voxel).
The general principle: a design matrix is specified, which model the source of variance among the data. For example, if were N subjects in the study , then the design matrix would contain N arrows.
Outcome: statistical parametric maps, showing areas of significant difference/ correlations
Look like blobs
Uses same software as fMRI

21. Using the GLM for VBM
Typically the matrix may contain blocks that represent the group from which each subject belongs (Ashburner, 2008).
e.g., compare the GM/ WM differences between 2 groups (healthy controls vs. some population of patients)
H0: there is no difference between
these groups
β: other covariates, not just the mean

22. Validity of the statistical tests in SPM
Errors (residuals) need to be normally distributed throughout brain for stats to be valid
Invalidates experiments that compare one subject with a group
Correction for multiple comparisons
Valid for corrections based on peak heights (voxel-wise)
This requires smoothness of residuals to be uniformly distributed but it’s not in VBM because of the non-stationary nature of underlying neuroanatomy
Bigger blobs expected in smoother regions, purely by chance
Alternatives
Improve normalisation

23. VBM: simple demonstration

27. When we normalise to MNI space we also are smoothing your images.
With this final step, the pre-processing is done!
Now we can perform statistical analysis of the preprocessed data.

28. VBM: most important applications to 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
Regional effect of age: Our data support the theory of a heterogeneic response of various compartments of the brain to ageing. We observed accelerated loss of grey matter volume symmetrically in both parietal lobes (angula gyri), preand postcentral gyri, insula, and anterior cingulate cortex.

29. VBM: most important application to diseased subjects
Voxel-Based Morphometry of the Human Brain: Methods and Applications (Mechelli et al., 2005)
For example in: developmental and congenital disorders , autism , bipolar disorders, temporal lobe epilepsy, Down’s syndrome Parkinson’s disease , Huntington's disease , Alzheimer’s disease and primary progressive aphasia . The use of VBM with highly distorted brains presents special challenges however, due to the difficulties that arise during spatial normalisation. Of particular interest, from a methodological point of view, is a investigation of temporal lobe epilepsy by Keller et al. (2004). The authors used both standard and optimised VBM and furthermore compared “modulated” and “non-modulated” procedures.

30. 5.Further Considerations: Potential Confounds
Behavioural and MRI measurements must be reliable
e.g. images must be acquired from the same scanner and same MR sequences
Participants
sample size
the larger the sample size, the greater the power to detect differences
though if the effect size is large, differences can be observed with smaller cohorts
e.g. age, gender ratios, education, disease severity across groups

31. 5.Further Considerations: Potential Confounds
Processing
VBM analyses results should reflect systematic volumetric differences, such as folding or thickness, rather than artifacts, such as misclassification or misregistration
steps often vary across studies (Whitwell and Jack, 2005)

32. 5.Further considerations
Different brains have different sizes
Regional volumes are likely to vary as a function of the whole brain volume
Need to correct for “global brain volume”
Total GM volume
Whole brain volume
Total intra-cranial volume
Brains of similar size with GM differences globally and locally (Mechelli et al., 2005)

33. 5.Further considerations: Statistical Analysis
The multiple-comparison problem
In VBM, depending on your resolution
voxels
statistical tests
So at p < .05
50000 false positives
different options for correcting for multiple comparisons
e.g. Bonferroni, FEW, FDR
changing the p value and using different corrections will change the number of voxels that exceed the significance threshold

34. 5. Further Considerations: Correlations
Correlations do not imply causal relationships
VBM Independent ROI Analyses
investigating possible anatomical convergence between functional and morphological methods
Brain stimulation techniques can provide independent support for a causal link between structure and function
disrupting the function of a region via brain stimulation (TMS, tDCS) can confirm the functional involvement of the area in a task

35. 5. Further Considerations: Correlations
Positive & Negative Correlations
Evidence for the notion of “the more brain the better”
versus evidence associating better performance with less brain volume
depends on specific brain region as well as particular process assessed
What is the physiological link between the interindividual variability in a given structure and a cognitive ability?
significance of “macroscopic” variations, whatever their direction, is not yet understood in terms of “microscopic” variations (Eriksson et al., 2009)

36. 6. Take home messages
VBM performs voxel-wise statistical analysis on smoothed (modulated) normalised tissue segments
SPM8 performs segmentation and spatial normalisation in a unified generative model
Based on Gaussian mixture modelling, with DCT-warped spatial priors, and multiplicative bias field
The new segment toolbox includes non-brain priors and more flexible/precise warping of them
Subsequent (currently non-unified) use of DARTEL improves normalisation for VBM.

37. 6. Take home messages
VBM uses the machinery of SPM to localise patterns in regional volumetric variation
Use of “globals” as covariates is a step towards multivariate modelling of volume and shape
More advanced approaches typically benefit from the same preprocessing methods
New segmentation and DARTEL close to state of the art
Though possibly little or no smoothing

38. 6. Take home messages Consider potential confounds and correlations
10 Rules for reporting VBM studies (Ridgway et al., 2008)
set out rationale of study and describe data fully
explain how brain segmentations are produced
describe method of inter-subject spatial normalization
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
recognize the limitations of the technique
interpret your results cautiously and in context

39. 7. Key papers & References
Ashburner & Friston (2000, NeuroImage, Voxel-Based Morphometry – The Methods)
Ridgway et al. (2008, NeuroImage, Ten simple rules for reporting voxel-based morphometry studies)
Kanai & Rees (2011, Nature Reviews Neuroscience, The structural basis of inter-individual differences in human behaviour and cognition)
Logothetis (2008, Nature, What we can do and what we cannot do with fMRI)
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
Good, C., Johnsrude, I. S., Ashburner, J., Henson, R. N. A., Friston, K. J., Frackowiak, R. S. J. (2001). A voxel-based morphometric study of ageing in 465 normal adult human brains. NeuroImage 14(1), 21-36

40. Thank you for listening…
and special thanks to our expert John Ashburner