1. Framework for the Statistical Shape Analysis of Brain Structures using SPHARM-PDM M. Styner, I. Oguz, S. Xu, C. Brechbuehler, D. Pantazis, J. Levitt, M. Shenton, G. Gerig UNC, ETHZ, USC, Harvard, NA-MIC

2. 2 Brain Morphometry Brain Morphometry in Neurological Disorders –Morphometry  Pathology –Schizophrenia, Autism, Alzheimer’s, Depression, MPS, Krabbe, FragileX Group Difference SZCnt Difference Stats Difference

3. 3 Concept: Shape Analysis Group analysis of a brain region Traditional analysis: only regional volume Additional shape analysis via SPHARM PDM Binary Segmentation Volumetric analysis: Size, Growth Shape Representation Statistical analysis Local processes

4. 4 Table of Contents Motivation: –Brain morphometry Methodology: –SPHARM PDM –Statistical Testing Tool development Example –Caudate shape in Schizo-typal Personality Disorder (PSD) Discussion & Outlook

5. 5 Segmentation Spherical Parameterization SPHARM-PDM Hotelling T 2 Surface Distance Statistical Hypothesis Testing Representation Preprocessing - Correspondence - Alignment - Scaling Analysis Shape Analysis Workflow

6. 6 Representation: SPHARM-PDM 1 10 3 6 Hierarchical description Spherical harmonics basis 1.Surface & Parameterization 2.Fit coefficients of parameterized basis functions to surface 3.Reconstruct object  PDM

7. 7 Representation: SPHARM-PDM Correspondence by parameterization –First order ellipsoid Initialization for other methods –Prior talk Heimann, Oguz IPMI 2003 comparison Alignment –Rigid-Body Procrustes to template Normalization with uniform scaling: –Original size: as is –Cranial cavity size normalization –User choice

8. 8 Group Shape Difference Corresponding aligned surfaces Analyze shape differences –Features per surface point –Multivariate: Point locations –Hotelling T 2 two sample metric At each location: Hypothesis test –Difference between groups? –P-value of group mean difference –Significance map Non-parametric permutation tests –No distribution assumption

9. 9 P-value Correction Many tests computed independently –Biased, highly optimistic Corrected significance map –As if only one test performed Bonferroni correction –Global False-Positive rate, simple –Very pessimistic –p corr = p/n = 0.05/1000 = 0.00005 Non-parametric permutation tests –Minimum statistic of raw p-values –Global False-Positive rate –Still pessimistic False Discovery Rate –Allow an expected rate of falsely significant tests ISBI 2004 Pantazis, Leahy, Nichols, Styner Correction

10. 10 Tool Development Methodology  clinically useful tools Computer scientists create tools Our shape analysis tools: –Enable clinical investigators to create knowledge –In use: Harvard (BWH, VAB), NIMH, Duke (CIVM, NIRL), UIUC, GeorgiaTech, UUtah, U. Bern, U. Zaragoza, ANU Canberra, UNC –Open Source, UNC NeuroLib, Tested, Validated –CVS download and linux binaries with examples

11. 11 Shape Analysis Tools I Command line –Scripting simple SegPostProcess –Spherical Topology –Smoothing –Up-interpolation –Interior filling GenParaMesh –Surface Mesh –Spherical Parameterization Brechbuehler CVGIP Segmentation: e.g. using InsightSNAP Output: Binary 3D Image Parameterization: GenParaMesh Output: Surface Mesh + Parameterization SPHARM-PDM: ParaToSPHARMMesh Output: SPHARM + Aligned Surface Preprocessing: SegPostProcess Output: Binary 3D Image For Each Datasets Statistical Testing: StatNonParamPDM Output: Significance + Descriptive Maps For Each Comparison

12. 12 Shape Analysis Tools II ParaToSPHARMMesh –SPHARM-PDM –Alignment StatNonParamPDM –Descriptive Statistics Mean, Variance –Significance Map Raw, Corrected Examples, Scripts Many parameters –See manuscript Segmentation: e.g. using InsightSNAP Output: Binary 3D Image Parameterization: GenParaMesh Output: Surface Mesh + Parameterization SPHARM-PDM: ParaToSPHARMMesh Output: SPHARM + Aligned Surface Preprocessing: SegPostProcess Output: Binary 3D Image For Each Datasets Statistical Testing: StatNonParamPDM Output: Significance + Descriptive Maps For Each Comparison

13. 13 Example Caudate Shape Right Caudate –Basal Ganglia structure –Schizo-typal Personality Disorder (15 subjects) –Controls (14 subjects) –Male subjects only Segmentation with 3D Slicer v2 (BWH)

14. 14 Caudate Study Correspondence –KWMeshVisu Descriptive Statistics Covariance ellipsoidsMean Difference Medial Lateral

15. 15 Caudate Study Hypothesis testing –Levels of correction Global shape difference –Mean difference p = 0.009 Right caudate different between Cnt and SPD Interpretation by clinicians

16. 16 Discussion Comprehensive set of open source tools for shape analysis using SPHARM-PDM –Command line tools –Local group differences –Applied in UNC studies: Twin similarity, Schizophrenia, Autism, Fragile-X Visualization: –Quality Control is important –KWMeshVisu: prior talk Oguz

17. 17 Outlook MANCOVA for group variables –Age, gender, clinical scores Open hippocampus dataset for testing Testing environment for other data –Deformation field –Cortical thickness data Questions? Support: –National Alliance for Medical Image Computing, NIH Roadmap Grant U54 EB005149-01 –UNC Neurodevelopmental Disorders Research Center HD 03110 –NIH NIBIB grant P01 EB002779, EC-funded BIOMORPH project 95-0845, VA Merit Award, VA Research Enhancement Award Program, NIH R01 MH50747, K05 MH070047 NA-MIC

18. 18 Humans Large Variability Monkey Reduced complexity and variability Mouse Genetic control Small variability No folding Translational Research Brain Morphometry Studies of normal development Studies in animals

19. 19 CVS and Dashboard Doxygen CVS repository for source, nightly compilation and testing Code/Dashboard master Dashboard

20. 20 Statistical Hypothesis Testing At each location: Hypothesis test –Significant difference between groups? –P-value of group mean difference Schizophrenia group vs Control group –Significance map –Threshold α, e.g. 5% Non-parametric permutation tests –No distribution assumption –P-values directly from observed distribution

21. 21 Permutation Hypothesis Tests Estimate distribution –Permute group labels N a, N b in Group A and B Create M permutations Compute feature S j for each perm Histogram  Distribution p-value: #Perms larger / #Perms total S0S0 SjSj SjSj perm #

22. 22 SPHARM Parameterization Spherical topology of segmentation Mapping of surface to unit sphere –Difficult, no unique ordering of points in 3D –Initialize with heat equation mapping –Optimization for equal area ratio mapping with minimal angular distortion

23. 23 Example: Hippocampus in SZ Temporal lobe, Limbic system Storage of auditory and visual memories 56 Schizophrenics vs 26 Controls Surface difference Main differences at tail Styner, Lieberman, Pantazis, Gerig: Boundary and Medial Shape Analysis of the Hippocampus in Schizophrenia, Medical Image Analysis, 2004, pp 197-203 Styner, Lieberman, Gerig: Boundary and Medial Shape Analysis of the Hippocampus in Schizophrenia, MICCAI 2003, II, pp. 464-471 Diff between Means

24. 24 UNC Shape Analysis Group analysis of a brain region Regional volume and shape analysis Binary Segmentation Volumetric analysis: Size, Growth Shape Representation Statistical analysis Local processes Group Difference SZCnt

25. 25 UNC Shape Analysis UNC Open Source –Comprehensive set of analysis tools –Visualization tools Separate talk later