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

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Brain Morphometry

• Brain Morphometry in Neurological Disorders– Morphometry Pathology– Schizophrenia, Autism, Alzheimer’s, Depression, MPS,

Krabbe, FragileX

GroupDifference

SZ Cnt

Difference

Stats

Difference

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Concept: Shape Analysis• Group analysis of a brain region• Traditional analysis: only regional volume• Additional shape analysis via SPHARM PDM

QuickTime™ and aTIFF (LZW) decompressor

are needed to see this picture.

Binary Segmentation

Volumetric analysis: Size, Growth

Shape Representation Statistical analysis

Local processes

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Table of Contents

• Motivation: – Brain morphometry

• Methodology: – SPHARM PDM– Statistical Testing

• Tool development• Example

– Caudate shape in Schizo-typal Personality Disorder (PSD)

• Discussion & Outlook

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Segmentation

SphericalParameterization

SPHARM-PDM

Hotelling T2

Surface Distance

StatisticalHypothesis Testing

Representation

Preprocessing

- Correspondence- Alignment- Scaling

Analysis

Shape Analysis Workflow

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Representation: SPHARM-PDM

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• Hierarchical description• Spherical harmonics basis1. Surface & Parameterization2. Fit coefficients of parameterized

basis functions to surface3. Reconstruct object PDM

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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

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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

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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

ISBI 2004 Pantazis, Leahy, Nichols, Styner

Correction

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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

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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 InsightSNAPOutput: Binary 3D Image

Parameterization: GenParaMeshOutput: Surface Mesh + Parameterization

SPHARM-PDM: ParaToSPHARMMeshOutput: SPHARM + Aligned Surface

Preprocessing: SegPostProcessOutput: Binary 3D Image

For Each Datasets

Statistical Testing: StatNonParamPDMOutput: Significance + Descriptive Maps

For Each Comparison

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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 InsightSNAPOutput: Binary 3D Image

Parameterization: GenParaMeshOutput: Surface Mesh + Parameterization

SPHARM-PDM: ParaToSPHARMMeshOutput: SPHARM + Aligned Surface

Preprocessing: SegPostProcessOutput: Binary 3D Image

For Each Datasets

Statistical Testing: StatNonParamPDMOutput: Significance + Descriptive Maps

For Each Comparison

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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)

QuickTime™ and aMPEG-4 Video decompressor

are needed to see this picture.

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Caudate Study

• Correspondence– KWMeshVisu

• Descriptive Statistics

QuickTime™ and aMPEG-4 Video decompressor

are needed to see this picture.

Covariance ellipsoids Mean DifferenceMedial Lateral

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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

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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

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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

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Humans• Large Variability

Monkey• Reduced complexity

and variability

Mouse• Genetic control• Small variability• No folding

TranslationalResearch

Brain Morphometry

• Studies of normal development

• Studies in animals

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CVS and Dashboard

Doxygen

• CVS repository for source, nightly compilation and testing

• Code/Dashboard master

Dashboard

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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

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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

S0

Sj

Sj

perm

#

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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

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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 197-203Styner, Lieberman, Gerig: Boundary and Medial Shape Analysis of the Hippocampus in Schizophrenia, MICCAI 2003, II, pp. 464-471

Diff between Means

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UNC Shape Analysis

• Group analysis of a brain region

• Regional volume and shape analysis

QuickTime™ and aTIFF (LZW) decompressor

are needed to see this picture.

Binary Segmentation

Volumetric analysis: Size, Growth

Shape Representation Statistical analysis

Local processes

GroupDifference

SZ Cnt

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UNC Shape Analysis

• UNC Open Source– Comprehensive set of analysis tools– Visualization tools

• Separate talk later