1. Computational Anatomy: VBM and Alternatives

2. Overview Volumetric differences Voxel-based Morphometry
Serial Scans
Jacobian Determinants
Voxel-based Morphometry
Multivariate Approaches
Difference Measures
Another approach

3. Deformation Field
Original
Warped
Template
Deformation field

4. Jacobians Jacobian Matrix (or just “Jacobian”)
Jacobian Determinant (or just “Jacobian”) - relative volumes

5. Serial Scans Early Late Difference
Data from the Dementia Research Group, Queen Square.

6. Regions of expansion and contraction
Relative volumes encoded in Jacobian determinants.

7. Late
Early
Late CSF
Early CSF
CSF “modulated” by relative volumes
Warped early
Difference
Relative volumes

8. Late CSF - modulated CSF
Late CSF - Early CSF
Late CSF - modulated CSF
Smoothed

9. Smoothing Smoothing is done by convolution.
Each voxel after smoothing effectively becomes the result of applying a weighted region of interest (ROI).
Before convolution
Convolved with a circle
Convolved with a Gaussian

10. Overview Volumetric differences Voxel-based Morphometry
Method
Interpretation Issues
Multivariate Approaches
Difference Measures
Another approach

11. Voxel-Based Morphometry
Produce a map of statistically significant differences among populations of subjects.
e.g. compare a patient group with a control group.
or identify correlations with age, test-score etc.
The data are pre-processed to sensitise the tests to regional tissue volumes.
Usually grey or white matter.
Can be done with SPM package, or e.g.
HAMMER and FSL

12. Pre-processing for Voxel-Based Morphometry (VBM)

13. SPM5 Segmentation includes Warping
Tissue probability maps are deformed to match the image to segment y1 c1 g a y2 y3 c2 c3 m s2 b a0 Ca b0 Cb yI cI

14. SPM5b Pre-processed data for four subjects
Warped, Modulated Grey Matter
12mm FWHM Smoothed Version

15. Validity of the statistical tests in SPM
Residuals are not normally distributed.
Little impact on uncorrected statistics for experiments comparing groups.
Invalidates experiments that compare one subject with a group.
Corrections for multiple comparisons.
Mostly valid for corrections based on peak heights.
Not valid for corrections based on cluster extents.
SPM makes the inappropriate assumption that the smoothness of the residuals is stationary.
Bigger blobs expected in smoother regions.

16. Interpretation Problem
What do the blobs really mean?
Unfortunate interaction between the algorithm's spatial normalization and voxelwise comparison steps.
Bookstein FL. "Voxel-Based Morphometry" Should Not Be Used with Imperfectly Registered Images. NeuroImage 14: (2001).
W.R. Crum, L.D. Griffin, D.L.G. Hill & D.J. Hawkes. Zen and the art of medical image registration: correspondence, homology, and quality. NeuroImage 20: (2003).
N.A. Thacker. Tutorial: A Critical Analysis of Voxel-Based Morphometry.

17. Some Explanations of the Differences
Folding
Mis-classify
Mis-register
Thickening
Thinning
Mis-classify
Mis-register

18. Overview Volumetric differences Voxel-based Morphometry
Multivariate Approaches
Scan Classification
Difference Measures
Another approach

19. “Globals” for VBM Shape is multivariate SPM is mass univariate
Dependencies among volumes in different regions
SPM is mass univariate
“globals” used as a compromise
Can be either ANCOVA or proportional scaling
Where should any difference between the two “brains” on the left and that on the right appear?

20. Training and Classifying?
Control
Training Data ? ? ?
Patient
Training Data

21. Classifying ?
Controls ? ? ?
Patients
y=f(wTx+w0)

22. Support Vector Classifier (SVC)

23. Support Vector Classifier (SVC)
w is a weighted linear combination of the support vectors
Support
Vector
Support
Vector

24. Nonlinear SVC

25. Regression (e.g. against age)

26. Overview Volumetric differences Voxel-based Morphometry
Multivariate Approaches
Difference Measures
Derived from Deformations
Derived from Deformations + Residuals
Another approach

27. Distance Measures
Classifiers such as SVC use measures of distance between data points (scans).
I.e. measure of how different each scan is from each other scan.
Distance measures can be derived from deformations.

28. Deformation Distance Summary
Deformations can be considered within a small or large deformation setting.
Small deformation setting is a linear approximation.
Large deformation setting accounts for the nonlinear nature of deformations.
Miller, Trouvé, Younes “On the Metrics and Euler-Lagrange Equations of Computational Anatomy”. Annual Review of Biomedical Engineering, 4: (2003) plus supplement
Beg, Miller, Trouvé, L. Younes. “Computing Large Deformation Metric Mappings via Geodesic Flows of Diffeomorphisms”. Int. J. Comp. Vision, 61: (2005)

29. Computing the geodesic: problem statement
I0: Template
I1:Target
By shifting focus from the diffeomorphism phi to the velocity field that generates it places the problem in the class of an Optimization problem where the estimate of the velocity field desired to generate the diffeomorphism phi that we are after is found at the minimum of this cost function.
The first the measure the smoothness properties of the velocity field, this is necessary to ensure that the solutions to the
ODE and PDE governing the dynamics of the map are diffeomorphisms.
The second term measure the amount of mis-match in the given images under the transformation that this velocity field generates.
Slide from Tilak Ratnanather

30. One-to-One Mappings
One-to-one mappings between individuals break down beyond a certain scale
The concept of a single “best” mapping may become meaningless at higher resolution
Pictures taken from

31. Overview Volumetric differences Voxel-based Morphometry
Multivariate Approaches
Difference Measures
Another approach

32. Anatomist/BrainVISA Framework
Free software available from:
Automated identification and labelling of sulci etc.
These could be used to help spatial normalisation etc.
Can do morphometry on sulcal areas, etc
J.-F. Mangin, D. Rivière, A. Cachia, E. Duchesnay, Y. Cointepas, D. Papadopoulos-Orfanos, D. L. Collins, A. C. Evans, and J. Régis. Object-Based Morphometry of the Cerebral Cortex. IEEE Trans. Medical Imaging 23(8): (2004)

33. Design of an artificial neuroanatomist
Elementary
folds
Fields of
view of
neural nets 3D
retina
Bottom-up
flow
Sulci

34. Correlates of handedness
14 subjects
128 subjects
Central sulcus
surface is larger
in dominant hemisphere

35. Some of the potentially interesting posters
(#728 T-PM ) A Matlab-based toolbox to facilitate multi-voxel pattern classification of fMRI data.
(#699 T-AM ) Pattern classification of hippocampal shape analysis in a study of Alzheimer's Disease
(#697 M-AM ) Metric distances between hippocampal shapes predict different rates of shape changes in dementia of Alzheimer type and nondemented subjects: a validation study
(#721 M-PM ) Unbiased Diffeomorphic Shape and Intensity Template Creation: Application to Canine Brain
(#171 T-AM ) A Population-Average, Landmark- and Surface-based (PALS) Atlas of Human Cerebral Cortex
(#70 M-PM ) Cortical Folding Hypotheses: What can be inferred from shape?
(#714 T-AM ) Shape Analysis of Neuroanatomical Structures Based on Spherical Wavelets