Computational Anatomy: VBM and Alternatives

1. Computational Anatomy: VBM and Alternatives

2. Overview • Volumetric differences • 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 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 http://oasis.rad.upenn.edu/sbia/ http://www.fmrib.ox.ac.uk/fsl/

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

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

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 14:1454-1462 (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 20:1425-1437 (2003). • N.A. Thacker.Tutorial:A Critical Analysis of Voxel-Based Morphometry.http://www.tina-vision.net/docs/memos/2003-011.pdf

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

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

19. “Globals” for VBM • Shape is multivariate • 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 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, 4:375-405 (2003) plus supplement • Beg, Miller, Trouvé, L. Younes. “Computing Large Deformation Metric Mappings via Geodesic Flows of Diffeomorphisms”.Int. J. Comp. Vision, 61:1573-1405 (2005)

29. Computing the geodesic: problem statement I0: Template I1:Target 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 http://www.messybeast.com/freak-face.htm

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

32. Anatomist/BrainVISA Framework • Free software available from: http://brainvisa.info/ • 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):968-982 (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