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, Alzheimers, 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
Shape Representation
Statistical analysis
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
Shape Analysis Tools I

• Command line
• Scripting simple
• SegPostProcess
• Spherical Topology
• Smoothing
• Up-interpolation
• Interior filling
• GenParaMesh
• Surface Mesh
• Spherical Parameterization
• Brechbuehler CVGIP

12
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 a, e.g. 5
• Non-parametric permutation tests
• No distribution assumption
• P-values directly from observed distribution

21
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
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