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Computational Anatomy: VBM and Alternatives

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

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TemplateWarpedOriginal Deformation Field Deformation field

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

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

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

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Late Early Warped earlyDifference Early CSFLate CSF Relative volumes CSF modulated by relative volumes

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Late CSF - Early CSF Late CSF - modulated CSF Smoothed

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

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

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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

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Pre-processing for Voxel-Based Morphometry (VBM)

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SPM5 Segmentation includes Warping Tissue probability maps are deformed to match the image to segment y1y1 c1c1 y2y2 y3y3 c2c2 c3c3 C C yIyI cIcI

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

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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.

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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 pdf

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

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

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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?

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

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Classifying Controls Patients ? ? ? ? y=f(w T x+w 0 )

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Support Vector Classifier (SVC)

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Support Vector Support Vector Support Vector w is a weighted linear combination of the support vectors

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Nonlinear SVC

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Regression (e.g. against age)

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

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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.

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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)

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

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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

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

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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)

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

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Correlates of handedness 14 subjects128 subjects Central sulcus surface is larger in dominant hemisphere

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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

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