TemplateWarpedOriginal Deformation Field Deformation field
Jacobians Jacobian Matrix (or just Jacobian) Jacobian Determinant (or just Jacobian) - relative volumes
Early Late Difference Data from the Dementia Research Group, Queen Square. Serial Scans
Regions of expansion and contraction *Relative volumes encoded in Jacobian determinants.
Late Early Warped earlyDifference Early CSFLate CSF Relative volumes CSF modulated by relative volumes
Late CSF - Early CSF Late CSF - modulated CSF Smoothed
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).
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
Pre-processing for Voxel-Based Morphometry (VBM)
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
Warped, Modulated Grey Matter 12mm FWHM Smoothed Version SPM5b Pre-processed data for four subjects
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: (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
Some Explanations of the Differences Thickening Thinning Folding Mis-classify Mis-register
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 Control Training Data Patient Training Data ? ? ? ?
Support Vector Support Vector Support Vector w is a weighted linear combination of the support vectors
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: (2003) plus supplement Beg, Miller, Trouvé, L. Younes. Computing Large Deformation Metric Mappings via Geodesic Flows of Diffeomorphisms. Int. J. Comp. Vision, 61: (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
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)
Design of an artificial neuroanatomist 3D retina Bottom-up flow Fields of view of neural nets Elementary folds Sulci
Correlates of handedness 14 subjects128 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