2 Motivation for Computational Anatomy See Wednesday’s symposium 13:30-15:00Cortical Fingerprinting: What Anatomy Can Tell Us About Functional ArchitectureThere are many ways of examining brain structure. Depends on:The question you want to askThe data you haveThe available software
4 Deformation FieldOriginalWarpedTemplateDeformation field
5 Jacobians Jacobian Matrix (or just “Jacobian”) Jacobian Determinant (or just “Jacobian”) - relative volumes
6 Serial Scans Early Late Difference Data from the Dementia Research Group, Queen Square.
7 Regions of expansion and contraction Relative volumes encoded in Jacobian determinants.
8 Rigid Registration Software Packages AIR: Automated Image RegistrationFLIRT: FMRIB’s Linear Image Registration ToolMNI_AutoRegSPMVTK CISG Registration Toolkit...and many others...
9 Nonlinear Registration Software Only listing public software that can (probably) estimate detailed warps suitable for longitudinal analysis.HAMMERMNI_ANIMAL Software PackageSPM2VTK CISG Registration Toolkit…there is much more software that is less readily available...
10 LateEarlyLate CSFEarly CSFCSF “modulated” by relative volumesWarped earlyDifferenceRelative volumes
11 Late CSF - modulated CSF Late CSF - Early CSFLate CSF - modulated CSFSmoothed
12 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
14 Voxel-Based Morphometry I. C. Wright et al. A Voxel-Based Method for the Statistical Analysis of Gray and White Matter Density Applied to Schizophrenia. NeuroImage 2: (1995).I. C. Wright et al. Mapping of Grey Matter Changes in Schizophrenia. Schizophrenia Research 35:1-14 (1999).J. Ashburner & K. J. Friston. Voxel-Based Morphometry - The Methods. NeuroImage 11: (2000).J. Ashburner & K. J. Friston. Why Voxel-Based Morphometry Should Be Used. NeuroImage 14: (2001).C. D. Good et al. Automatic Differentiation of Anatomical Patterns in the Human Brain: Validation with Studies of Degenerative Dementias. NeuroImage 17:29-46 (2002).
15 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
16 Pre-processing for Voxel-Based Morphometry (VBM)
17 VBM Preprocessing in SPM5b Segmentation in SPM5b also estimates a spatial transformation that can be used for spatially normalising images.It uses a generative model, which involves:Mixture of Gaussians (MOG)Bias Correction ComponentWarping (Non-linear Registration) Component
18 Mixture of Gaussiansc1y1mgc2y2s2a0ac3y3bb0CacIyICb
19 Bias Field y r(b) y r(b) y1 c1 g a y2 y3 c2 c3 m s2 b a0 Ca b0 Cb yI cIyr(b)y r(b)
20 Tissue Probability Maps Tissue probability maps (TPMs) are used instead of the proportion of voxels in each Gaussian as the prior.ICBM Tissue Probabilistic Atlases. These tissue probability maps are kindly provided by the International Consortium for Brain Mapping, John C. Mazziotta and Arthur W. Toga.
22 Deforming the Tissue Probability Maps Tissue probability maps are deformed according to parameters a.y1c1gay2y3c2c3ms2ba0Cab0CbyIcI
23 SPM5b Pre-processed data for four subjects Warped, Modulated Grey Matter12mm FWHM Smoothed Version
24 Statistical Parametric Mapping… group 1group 2–parameter estimatestandard errorstatistic imageor SPM=voxel by voxel modelling
25 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.
26 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.
27 Some Explanations of the Differences FoldingMis-classifyMis-registerThickeningThinningMis-classifyMis-register
28 Cortical Thickness Mapping Direct measurement of cortical thickness may be better for studying neuro-degenerative diseasesSome example referencesB. Fischl & A.M. Dale. Measuring Thickness of the Human Cerebral Cortex from Magnetic Resonance Images. PNAS 97(20): (2000).S.E. Jones, B.R. Buchbinder & I. Aharon. Three-dimensional mapping of cortical thickness using Laplace's equation. Human Brain Mapping 11 (1): (2000).J.P. Lerch et al. Focal Decline of Cortical Thickness in Alzheimer’s Disease Identified by Computational Neuroanatomy. Cereb Cortex (2004).Narr et al. Mapping Cortical Thickness and Gray Matter Concentration in First Episode Schizophrenia. Cerebral Cortex (2005).Thompson et al. Abnormal Cortical Complexity and Thickness Profiles Mapped in Williams Syndrome. Journal of Neuroscience 25(16): (2005).
30 Multivariate Approaches Z. Lao, D. Shen, Z. Xue, B. Karacali, S. M. Resnick and C. Davatzikos. Morphological classification of brains via high-dimensional shape transformations and machine learning methods. NeuroImage 21(1):46-57, 2004.C. Davatzikos. Why voxel-based morphometric analysis should be used with great caution when characterizing group differences. NeuroImage 23(1):17-20, 2004.K. J. Friston and J. Ashburner. Generative and recognition models for neuroanatomy. NeuroImage 23(1):21-24, 2004.
31 “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?
32 Multivariate Approaches An alternative to mass-univariate testing (SPMs)Generate a description of how to separate groups of subjectsUse training data to develop a classifierUse the classifier to diagnose test dataData should be pre-processed so that clinically relevant features are emphasiseduse existing knowledge
33 Training and Classifying ?ControlTraining Data???PatientTraining Data
38 Support Vector Classifier (SVC) w is a weighted linear combination of the support vectorsSupportVectorSupportVector
39 Going Nonlinear y = f(Si ai (xi,x) + w0) Linear classification is by y = f(wTx + w0)where w is a weighting vector, x is the test data, w0 is an offset, and f(.) is a thresholding operationw is a linear combination of SVs w = Si ai xiSo y = f(Si ai xiTx + w0)Nonlinear classification is byy = f(Si ai (xi,x) + w0)where (xi,x) is some function of xi and x.e.g. RBF classification (xi,x) = exp(-||xi-x||2/(2s2))
41 Over-fittingTest dataA simpler model can often do better...
42 Cross-validation Methods must be able to generalise to new data Various control parametersMore complexity -> better separation of training dataLess complexity -> better generalisationOptimal control parameters determined by cross-validationTest with data not used for trainingUse control parameters that work best for these data
43 Two-fold Cross-validation Use half the data for training.and the other half for testing.
44 Two-fold Cross-validation Then swap around the training and test data.
45 Leave One Out Cross-validation Use all data except one point for training.The one that was left out is used for testing.
46 Leave One Out Cross-validation Then leave another point out.And so on...
48 Other Considerations Should really take account of Bayes Rule: P(sick | data)= P(data | sick) x P(sick) P(data | sick) x P(sick) + P(data | healthy) x P(healthy)Requires prior probabilitiesSometimes decisions should be weighted using Decision TheoryUtility Functions/Riske.g. a false negative may be more serious than a false positive
49 Overview Volumetric differences Voxel-based Morphometry Multivariate ApproachesDifference MeasuresDerived from DeformationsDerived from Deformations + ResidualsAnother approach
50 Distance MeasuresKernel-based 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.The measure is likely to depend on the application.
51 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.Uses Lie Group Theory.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)Tilak Ratnanather gave me the following two slides…
52 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.
53 Metrics on 3D Hippocampus in Neuro-psychiatric Disorders. Data from the lab. of Dr. Csernansky, Washington University, St Louis.3D Hippocampus: Young to SchizophreniaYoung1.3862.5413.696Schizophrenia4.6203D Hippocampus: Young to Alzheimer’sYoungAlzheimer’s1.4302.6213.8134.766
54 Accuracy of Automated Volumetric Inter-subject Registration Hellier et al. Inter subject registration of functional and anatomical data using SPM. MICCAI'02 LNCS 2489 (2002)Hellier et al. Retrospective evaluation of inter-subject brain registration. MIUA (2001)
55 One-to-One MappingsOne-to-one mappings break down beyond a certain scaleThe concept of a single “best” mapping may become meaningless at higher resolutionPictures taken from
56 A Combined Distance Measure Exact registration may not be possible.Base distance measures on deformations plus residuals after registration.Could use a related framework to that used for registering/segmenting.Distance measures should be adjusted based on user expertise.E.g. Some brain regions may be more informative than others, so give them more weighting.Differences may be focal or more globalCould use some sort of high- or low-pass filtering.
58 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)
59 Design of an artificial neuroanatomist ElementaryfoldsFields ofview ofneural nets3DretinaBottom-upflowSulci
60 Correlates of handedness 14 subjects128 subjectsCentral sulcussurface is largerin dominant hemisphere
61 Handedness correlates : localization after affine normalization
62 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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