Computational Anatomy: VBM and Alternatives

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

Deformation Field Original Warped Template Deformation field

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

Late CSF - modulated CSF Late CSF - Early CSF Late CSF - modulated CSF Smoothed

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

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)

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

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

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

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

“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?

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

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

Support Vector Classifier (SVC)

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

Nonlinear SVC

Regression (e.g. against age)

Overview Volumetric differences Voxel-based Morphometry Multivariate Approaches Difference Measures Derived from Deformations 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 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

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/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)

Design of an artificial neuroanatomist Elementary folds Fields of view of neural nets 3D retina 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 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