3 Deformation FieldOriginalWarpedTemplateDeformation 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 LateEarlyLate CSFEarly CSFCSF “modulated” by relative volumesWarped earlyDifferenceRelative volumes
8 Late CSF - modulated CSF Late CSF - Early CSFLate CSF - modulated CSFSmoothed
9 Smoothing Smoothing is done by convolution. Each voxel after smoothing effectively becomes the result of applying a weighted region of interest (ROI).Before convolutionConvolved with a circleConvolved with a Gaussian
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 segmenty1c1gay2y3c2c3ms2ba0Cab0CbyIcI
14 SPM5b Pre-processed data for four subjects Warped, Modulated Grey Matter12mm 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 FoldingMis-classifyMis-registerThickeningThinningMis-classifyMis-register
19 “Globals” for VBM Shape is multivariate SPM is mass univariate Dependencies among volumes in different regionsSPM is mass univariate“globals” used as a compromiseCan be either ANCOVA or proportional scalingWhere should any difference between the two “brains” on the left and that on the right appear?
20 Training and Classifying ?ControlTraining Data???PatientTraining Data
26 Overview Volumetric differences Voxel-based Morphometry Multivariate ApproachesDifference MeasuresDerived from DeformationsDerived from Deformations + ResidualsAnother approach
27 Distance MeasuresClassifiers 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 supplementBeg, 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: TemplateI1:TargetBy 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 theODE 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 MappingsOne-to-one mappings between individuals break down beyond a certain scaleThe concept of a single “best” mapping may become meaningless at higher resolutionPictures taken from
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, etcJ.-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 ElementaryfoldsFields ofview ofneural nets3DretinaBottom-upflowSulci
34 Correlates of handedness 14 subjects128 subjectsCentral sulcussurface is largerin 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