Computational Anatomy VBM and Alternatives Overview Volumetric differences

Computational Anatomy: VBM and Alternatives

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

Deformation Field Original Warped Deformation field Template

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

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

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

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

Late CSF - modulated CSF Late CSF - Early CSF Smoothed

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

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

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/

Pre-processing for Voxel-Based Morphometry (VBM)

SPM 5 Segmentation includes Warping Tissue probability maps are deformed to match the image to segment g a 0 a Ca c 1 y 1 m c 2 y 2 s 2 c 3 y 3 b c. I y. I Cb b 0

SPM 5 b Pre-processed data for four subjects Warped, Modulated Grey Matter 12 mm FWHM Smoothed Version

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.

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. Neuro. Image 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. Neuro. Image 20: 1425 -1437 (2003). * N. A. Thacker. Tutorial: A Critical Analysis of Voxel-Based Morphometry. http: //www. tina-vision. net/docs/memos/2003011. pdf

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

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

“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?

Training and Classifying ? ? Patient Training Data Control Training Data ? ?

Classifying ? ? Patients Controls ? ? y=f(w. Tx+w 0)

Support Vector Classifier (SVC)

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

Nonlinear SVC

Regression (e. g. against age)

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

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.

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)

Computing the geodesic: problem statement I 0: Template I 1: Target Slide from Tilak Ratnanather

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

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

Anatomist/Brain. VISA 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)

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

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

Some of the potentially interesting posters * (#728 T-PM ) A Matlab-based toolbox to facilitate multi-voxel pattern classification of f. MRI 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