Framework for the Statistical Shape Analysis of Brain Structures using SPHARM-PDM

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. Brain Morphometry • Brain Morphometry in Neurological Disorders • Morphometry  Pathology • Schizophrenia, Autism, Alzheimer’s, Depression, MPS, Krabbe, FragileX Difference Difference SZ Cnt Group Difference Stats

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

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. Shape Analysis Workflow Segmentation Preprocessing Representation Spherical Parameterization • Correspondence • Alignment • Scaling SPHARM-PDM Analysis Hotelling T2 Surface Distance Statistical Hypothesis Testing

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

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. Group Shape Difference • Corresponding aligned surfaces • Analyze shape differences • Features per surface point • Multivariate: Point locations • Hotelling T2 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. 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 • pcorr = 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 Correction ISBI 2004 Pantazis, Leahy, Nichols, Styner

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

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

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. Caudate Study • Correspondence • KWMeshVisu • Descriptive Statistics Covariance ellipsoids Mean Difference Medial Lateral

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

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

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. S0 Permutation Hypothesis Tests • Estimate distribution • Permute group labels • Na , Nb in Group A and B • Create M permutations • Compute feature Sj for each perm • Histogram  Distribution • p-value: #Perms larger / #Perms total Sj # perm Sj

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. 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 Diff between Means 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

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

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