Shape analysis to assess neurodevelopment and neurodegeneration

1
Shape analysis to assess neurodevelopment and
neurodegeneration

• Guido Gerig, UNC Chapel Hill
• IPAM June, 2004
• Acknowledgements
• Martin Styner, Sarang Joshi, Stephen Pizer, Tom
  Fletcher, Tim Terriberry

2
Outline

• Motivation
• (Neuroimaging)
• Driving Clinical Questions
• Shape/Manifolds
• Applications of Shape Analysis
• Hippocampal morphology in SZ
• Twin study
• Shape similarity vs. genetic similarity
• Identical twins discordant for SZ

3
Neuroimaging

• Multidisciplinary
• Radiology, Imaging Research
• Psychiatry, Psychology, Neurology
• Computer Science
• Mathematics, Applied Math
• (Bio)Statistics
• Biomedical Engineering
• Biology
• .

4
Courtesy of Bruce Rosen, A.A. Martinos Center,
Boston
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Neuromaging

• Sampling of anatomy Aperture / Scale
• Measurement of physical properties
• Multimodal Imaging
• Longitudinal follow-up
• Link from in-vivo imaging to ex-vivo tissue
  analysis

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Conventional Imaging
T1 Gradient Echo 1x1x1.5mm3
Dual-Echo Spin-Echo 1x1x3mm3
Tradeoff Tissue Contrast / Spatial Resolution
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3Tesla Siemens UNC W. Lin
2D FSE 1x1x1mm3 (T2w, PDw), T1 MPRage 1x1x1mm3
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3D T2w FSE 1x1x1mm3John Mugler, Radiology 2000
1.5T GE, T2w 1x1x1mm3, single 9.4minute 3D
acquisition
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Henri M. Duvernoy, The Human Hippocampus An
Atlas of Applied Anatomy, Springer-Verlag, New
York, 1988, Fig. 2., p. 15
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Hippocampus seen by different pulse sequences
3T, T1 PRage and T2w FSE, 1mm3
1.5T, T2w, 1.5mm3
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Visible Human 1.0 (180um)Peter Ratiu, BWH (NLM
Project)
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Neonatal scans 3T MRI
T1 3D MPRage 1x1x1 mm3
FSE T2w 1x1x2 mm3
FSE PDw 1x1x2 mm3
3T Siemens Allegra, UNC Weili Lin Scan Time
Structural MRI (T1, SpinEcho) 8min, DTI 4min -gt
12 Min tot
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Longitudinal Analysis in Schizophrenia Study
Baseline (registered to Talairach coord.)
6 months (registered to baseline)
18 months (registered to baseline)
Registration using MIRIT (mutual information
registration, developed by Frederic Maes, KUL,
Belgium). Registration type Rigid (translation,
rotation).
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Longitudinal Analysis in Schizophrenia Study
baseline
6 months
18 months
growth
shrinking
Difference 6mt - baseline
Difference 18mt - 6mt
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Fluid Deformation Baseline to 6mt
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Validation Duke Quality Control

• Dataset Same subject scanned 2-times (24 hour
  window) at 5 different sites (4 GE, 1 Philips)
  within 60 days
• Automatic brain tissue segmentation using
  three-channel (T1, T2w, PDw) MRI
• Results show excellent reliability and stability
  of multi-site scanning and brain tissue
  segmentation

• M. Styner, C. Charles, J. Park, G. Gerig,
  Multisite validation of image analysis methods -
  Assessing intra and inter site variability, Proc.
  SPIE MedIm 02, 09/2002

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Atlas-based EM Segmentation of multi-modal MRI
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Reliability of Segmentation
QC control series (Cecil Charles, Duke
University), EM-Segmentation UNC (Same subject,
four GE 1.5T scanners with 2 replications,
several months)
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Evaluation of MRI Acquisition protocols
Contrast to Noise Ratio as a function of field
strength, spatial resolution, and pulse sequence
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Summary Imaging

• Multimodal better tissue contrast
• Spatial resolution Scale at which we do the
  measurements
• Noninvasive, in-vivo imaging Longitudinal
  Follow-up
• Todo Validation, cross-comparison
• Open issues
• Technology change compatibility
• Different sequences Do we measure the same
  properties?
• Scale, resolution, level of details
• Inter-site calibration, standardization

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Clinical Neuroimaging Research Projects at UNC

• Schizophrenia Research
• Neonatal Study Infants at Risk
• Prodromal (subjects at risk)
• First Episode FE
• Schizo-affected adolescents(TAPS)
• Treatment Studies (CHOR, CATIE)
• Autism / Fragile-X (w. Stanford)
• Twin Study / Sibling Study
• Neurodevelopment Research Center NDRC
• Surgical Planning Tumor Vascularity
• Neonatal screening by 3D ultrasound/ 3D MRI
• Neonatal twin study (heritability)
• .

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Representative Clinical Study Neuropathology of
Schizophrenia

• When does it develop ?
• Fixed or Progressive ?
• Neurodevelopmental or Neurodegenerative ?
• Neurobiological Correlations ?
• Clinical Correlations ?
• Treatment Effects ?

Noninvasive neuroimaging studies using MRI/fMRI
to study morphology and function
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Natural History of Schizophrenia
Stages of Illness
Prodromal/Onset/Deterioration
Chronic/Residual
Premorbid
Healthy ? ? WorseningSeverity ofSigns
andSymptoms
Deterioration
Schizophrenia is a genetic neurodevelopmental
disorder with environmental interactions that
begins to manifest its symptoms predominantly in
the second and third decades and runs a
progressive course.
Gestation/Birth
10
20
30
40
50
Puberty
Years
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Shape Modeling

• Shape Representation
• High dimensional warping Miller,Christensen,Joshi
  / Thompson,Toga / Ayache, Thirion
• Boundary / Surface Bookstein / Cootes, Taylor /
  Duncan,Staib / Szekely, Gerig / Leventon, Grimson
  / Davatzikos
• Skeleton / Medial model Pizer / Goland /
  Bouix,Siddiqui / Kimia / Styner, Gerig
• Issues Correspondence, Invariance Properties,
  Scale

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Criteria for shape models

• generality
• stability
• specificity
• intuitiveness
• compactness
• shape and intensity
• time-efficient analysis
• conversion between different modeling schemes

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Shape in Mathematics

• Kendall, Dryden and Mardia, Bookstein, Small
• Efficient representation of data,transformations,
  shape distributions
• Shape is all the geometrical information that
  remains when location, scale and rotational
  effects are filtered out from an object.

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Data Primitives of Object Representation

• A voxel with its intensity value(s) (x, I)
• A landmark x
• A boundary atom b (x,n)
• A medial atom m (x,F,r,q)

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3D Shape Representations I
Raw 3D voxel model
Miller, Joshi, Christensen, Csernansky Shape
decoded in deformation field
SNAP/IRIS tool UNC
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3D Shape Representations II
SPHARM Boundary, fine scale, parametric
PDM Boundary, fine scale, sampled
Skeleton Medial, fine scale, continuous, implied
surface
M-rep Medial, coarse scale, sampled, implied
surface
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3D Shape Representations IIIManifolds for DTI
tracts?
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Modeling fiber tracts Model curve and sweeping
trajectory
Right cortico-spinal tract
Reconstruction
Callosal tract
Isabelle Corouge, UNC, ribbon bunles, MICCAI 2004
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I. Parametrized 3D surface models
Smoothed object
Raw 3D voxel model
Parametrized surface
Ch. Brechbuehler, G. Gerig and O. Kuebler,
Parametrization of closed surfaces for 3-D shape
description, CVIU, Vol. 61, No. 2, pp. 154-170,
March 1995 A. Kelemen, G. Székely, and G.
Gerig, Three-dimensional Model-based
Segmentation, IEEE TMI, 18(10)828-839, Oct. 1999
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Surface Parametrization
Mapping single faces to spherical quadrilaterals
Latitude and longitude from diffusion
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Initial Parametrization
a) Spherical parameter space with surface net, b)
cylindrical projection, c) object with coordinate
grid. Problem Distortion / Inhomogeneous
distribution
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Parametrization after Optimization
a) Spherical parameter space with surface net, b)
cylindrical projection, c) object with coordinate
grid. After optimization Equal parameter area of
elementary surface facets, reduced distortion.
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Nonlinear Optimization with Constraints
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Shape Representation by Spherical Harmonics
(SPHARM)
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Calculation of SPHARM coefficients
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Reconstruction from coefficients
Global shape description by expansion into
spherical harmonics Reconstruction of the
partial spherical harmonic series, using
coefficients up to degree 1 (a), to degree 3 (b)
and 7 (c).
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Importance of uniform parametrization
non-uniform
uniform
non-uniform
uniform
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Parametrization with spherical harmonics

• Surface Parametrization Expansion into
  spherical harmonics.
• Normalization of surface mesh (alignment to first
  ellipsoid).
• Correspondence Homology of 3D mesh points.

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Parametrization with spherical harmonics
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Correspondence through Normalization

• Normalization using first order ellipsoid
• Spatial alignment to major axes
• Rotation of parameter space.

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3D Natural Shape Variability Left Hippocampus
of 90 Subjects
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Computing the statistical model PCA
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Major Eigenmodes of Deformation by PCA

• PCA of parametric shapes ? Average Shape, Major
  Eigenmodes
• Major Eigenmodes of Deformation define shape
  space ? expected variability.

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Set of Statistical Anatomical Models
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Medial Representation

• Shape Representation
• High dimensional warping Miller,Christensen,Joshi
  / Thompson,Toga / Ayache, Thirion
• Boundary / Surface Bookstein / Cootes, Taylor /
  Duncan,Staib / Szekely, Gerig / Leventon, Grimson
  / Davatzikos
• Skeleton / Medial model Pizer / Goland /
  Bouix,Siddiqui / Kimia / Styner, Gerig

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3D Skeleton / Medial Manifold

• Generation in 3D extremly difficult, approaches
• Voronoi Diagram and pruning (Naef Szekely,
  Attali Montanari, Styner Gerig)
• Shocks of level set evolution (Siddiqi, Kimia)
• 3D skeleton to graph description not yet
  presented
• Martin Styner Pruning 3D VD
• Pizer et al. Deformation of medial template

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Model Building
VSkelTool
Medial representation for shape population
Styner, Gerig et al. , MMBIA00 / IPMI 2001 /
MICCAI 2001 / CVPR 2001/ MEDIA 2002 / IJCV 2003 /
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A medial m-rep model incorporating shape
variability in 3 steps (M. Styner)
Step 3 Computation of optimal sampling
Step 2 Computation of medial branching topology
Step 1 Definition of shape space
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Modeling of Caudate Shape
Surface Parametrization
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3b. Minimal sampling of medial sheet

• Find minimal sampling given a predefined
  approximation error

3x6
3x7
3x12
4x12
2x6
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Medial models of subcortical structures
Shapes with common m-rep model and implied
boundaries of putamen, hippocampus, and lateral
ventricles. Each structure has a single-sheet
branching topology. Medial representations
calculated automatically.
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Shape Statistics and Analysis

• Guido Gerig

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Overview

• HDLSS High Dimension and Low Sample Size
• Correspondence
• Model Quality Specificity, Compactness,
  Sensitivity
• Shape Space and Dimensionality Reduction
• Principal Component Analysis PCA
• Fisher Linear Discriminant
• M-rep
• Principal Geodesic Analysis PGA
• Metric for shape difference/distance

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Motivation

• Statistical models of anatomical shape
• Average shape
• Variability of shape
• Useful for
• Medical image segmentation
• Diagnosis of disease
• Disease type and locality

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I HDLSS High Dimension and Low Sample Size
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High Dimension and Low Sample Size (HDLSS)
Complex shape represented in a very high
dimensional space
Example

• 3D Hippocampus characterized by 169x3 (n507)
  dimensional feature vector (SPHARM order 12)
• Sample size 15 controls 15 schizophrenics
  (n30)

Common problem n ltlt d
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Classical Multivariate Analysis

• Assume multivariate data Gaussian distributed.

• Critical Assumption invertible
• Fails for HDLSS
• Estimates of are sensitive

Solution Use lower dimensional projections

• Principal component Analysis(PCA) or Eigen
  Shapes

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Eigen Shapes (Hippocampus)
Mean Difference between Schiz and controls Mapped
on Composite Control

• Fisher Linear discrimination -
• Powerful for discrimination
• between populations under
• common covariance different mean
• assumption.

First 3 Eigenshapes Shapes of the Hippocampus

• PCA - Captures the modes of
• most variation in the Ensemble.

Sarang Joshi, John G. Csernansky, Lei Wang, J.
Philip Miller, Mohktar Gado, Daniel Kido, John
Haller, Michael I. Miller
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Object Alignment / Surface Homology
MZ pair
DZ pair
Surface Correspondence
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Shape change relative to anatomical coordinates
Morphing of amygdala/hippo-campal complex between
mean shapes of NCL versus SZ (Shenton/McCarley,
BWH Boston)
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Object Alignment prior to Shape Analysis
1stelli TR, no scal
1stelli TR, vol scal
Procrustes TRS
side
top
top
side
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Correspondence through parameter space rotation
Parameters rotated to first order ellipsoids

• Normalization using first order ellipsoid
• Rotation of parameter space to align major axis
• Spatial alignment to major axes

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Correspondence ctd.

• Rhodri Davies and Chris Taylor
• MDL criterion applied to shape population
• Refinement of correspondence to yield minimal
  description
• 83 left and right hippocampal surfaces
• Initial correspondence via SPHARM normalization
• IEEE TMI August 2002

Homologous points before (blue) and after MDL
refinement (red).
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Correspondence ctd.
Homologous points before (blue) and after MDL
refinement (red).
MSE of reconstructed vs. original shapes using n
Eigenmodes (leave one out). SPHARM vs. MDL
correspondence.
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Evaluation of Correspondence

• Generalization
• Ability to describe instances outside of the
  training set
• Compactness
• Ability to use a minimal set of parameters
• Specificity
• Ability to represent only valid instances of the
  object

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SPHARM vs. MDL
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Model Compactness

• Little variance as possible
• Compactness Cumulative variance

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Model Generalization

• Capability to represent unseen instances of
  object class
• Measurement Leave-one-out reconstruction of
  objects
• Model with all-but-one member
• Fit of excluded example
• Approximation error between fit and original (MAD)

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Model Specificity

• Only generate instances of object class that are
  similar to training set objects
• Random generation of population of instances
  using the model
• Average distance to nearest member of training
  class

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Comparison of three Correspondence Schemes(M.
Styner, MICCAI03)
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IV M-rep Statistics PGA

• Acknowledgement
• Tom Fletcher
• Sarang Joshi
• Steve Pizer
• Relevant Literature CVPR03, IPMI03, Fletcher
  et al.
• Principal Geodesic Analysis for the Study
  ofNonlinear Statistics of Shape, P. Thomas
  Fletcher, Conglin Lu, Stephen M. Pizer, and
  Sarang Joshi, to appear IEEE TMI

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Modeling Anatomy

• M-rep models based on medial axis (skeleton)
• Advantages
• Intuitive shape changes (bending, widening)
• Models interior as well as boundary
• Coarse-to-fine
• Tom Fletcher PGA

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Statistics of M-reps

• M-rep parameters are not linear
• Rotations
• Scalings
• High-dimensional, curved space (Lie group)
• Standard linear statistics do not apply

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Principal Geodesic AnalysisPGA
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Example PGA of Hippocampus
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Example PGA of Hippocampus
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Example PGA of Hippocampus
Fletcher et al., TMI04, to appear
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V Shape Distance Metric
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Boundary Analysis Shape Distance Metrics

• Pairwise MSD between surfaces at corresponding
  points
• PDM Signed or unsigned distance to template at
  corresponding points

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Boundary Shape Difference
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Shape Distance Metrics using Medial Representation
Local width differences (MA_rad) Growth,
Dilation Positional differences (MA_dist)
Bending, Deformation
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Example M-rep Local Width Difference
A
A
B
B
A minus B Right Ventricles
A minus B Left Ventricles
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Summary

• Key Criteria Statistical Shape Analysis
• Choice of shape representation SPHARM, PDM,
  M-rep, etc.
• Definition of correspondence
• Compact representation of shape space HDLSS
  problem
• Non-Euclidean framework for medial primitives

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Clinical Study Hippocampal Shape in Schizophrenia

• IRIS Tool for interactive image segmentation.
• Manual contouring in all orthogonal sections.
• 2D graphical overlay and 3D reconstruction.
• Hippocampus segmentation protocol (following
  Duvernoy).
• Hippocampus reliability gt0.95 intra-, gt0.85
  inter-rater)

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Age and treatment related local hippocampal
changes in schizophrenia explained by a novel
shape analysis methodG. Gerig, K. Muller, E.
Kistner, Y. Chi, M. Chakos, M. Styner, J.
Lieberman UNC Chapel Hill, Depts. of Computer
Science, Biostatistics, Psychiatry
Healthy versus SZ

• Research Hippocampus shape change in
  schizophrenia, typical vs. atypical drug
• Novelty Modeling shape and patient variables
• Approach
• Medial representations (M-rep)
• Shape deformation and local atrophy
• Effects of age, duration of illness, treatment
• General linear multivariate model Overcomes
  multiple testing problem
• Results Effects due to aging and drug type

Deformation change with aging
Healthy 10yrs
Schizophrenics
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Hippocampal Volume Analysis

• Left smaller than right
• SZ smaller than CNTRL, both left and right
• Variability SZ larger than CNTL

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Example Hippocampal Morphometry in Schizophrenia

• Left hippocampus of 90 subjects
• 30 Controls
• 60 Schizophr.

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Hippocampal Shape Analysis
Left and right hippocampus Comparison of mean
shapes CNTL-SZ (signed distance magnitude
relative to SZ template)
Left
Right
Movie Flat tail SZ, curved tail CNTL
Movie Flat tail SZ, curved tail CNTL
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Hippocampus M-rep Global Local Statistical
Analysis
Hippocampus Integrated difference to template
shape (structures size normalized)
individual m-rep
local group discrimination statistics
Width (plt0.75)
Deformation (plt0.0001)
SZ
SZ
CNTL
CNTL
plt0.01
G. Gerig M. Styner
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Local Statistical Tests
Medial representation study confirms Hippocampal
tail is region with significant deformation.
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Statistical Analysis of M-rep Shape including
patient variables
Difference in hippocampus shape between SZ and
CNTRL as measured by M-rep deformation

• Work in progress Keith Muller, Emily Kistner, M.
  Styner, J. Lieberman, G. Gerig, UNC Chapel Hill
• Systematic embedding of interaction of age,
  duration of illness and drug type into
  statistical shape analysis
• Correction for multiple tests

Repeated measures ANOVA, cast as a General
Linear Multivariate Model, as in Muller, LaVange,
Ramey, and Ramey (1992, JASA). Exploratory
analysis included considering both the "UNIREP"
Geisser-Greenhouse test and the "MULTIREP" Wilks
test.
M-rep 3x8 mesh
Tail
Head
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Model Row x Col x Drug (y/n) x Age p 0.0097
Patient-CNTL Deformation Difference at Age 40
Deformation at mesh nodes (mm)
Patient-CNTL Deformation Difference at Age 30
AGE
Patient-CNTL Deformation Difference at Age 20
Difference in hippocampus shape between patients
and controls Located mostly in the tail of the
hippocampus, becomes more pronounced over time.
Tail
Head
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Comparison to CNTLs
Deformation at mesh nodes (mm)
Change in hippocampus shape over ten years for
controls
Tail
Head
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Patients vs. Controls Local width L/R asymmetry
analysis
Model Row x Col x Drug type x Age Left/Right
width asymmetry p 0.0097
Radius diff. at mesh nodes log (mm)
40
40
30
30
AGE
20
20
Typical Drug
Atypical Drug
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Preliminary conclusions local asymmetry of width
analysis

• Reduction in control/patient difference in
  hippocampus width asymmetry seems more pronounced
  in the atypical group.
• Differences between patients and controls in
  hippocampus width asymmetry decrease over time.
• Given the expected atrophy over time due to
  aging, it seems that the hippocampus of a young
  schizophrenic looks like the hippocampus of an
  older control.
• Atypical treated patients start (at an early age)
  less far from the normals than do those treated
  with typical drugs (TREATMENT EFFECT OR CLINICAL
  SELECTION BIAS?).

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How do different shape representations compare?
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Surface Based Analysis
Not corrected for multiple comparisons
0.001
Corrected for multiple comparisons
0.05
Posterior (L) Lateral (L) Posterior
(R) Lateral (R)
Significance maps of left (L) and right (R)
hippocampus of schizophrenic patients vs. healthy
controls
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Boundary Analysis Shape Distance Metrics

• Pairwise MSD between surfaces at corresponding
  points
• PDM Signed or unsigned distance to template at
  corresponding points

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SPHARM-PDM
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Medial Representation M-rep
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Comparison Surface-Medial
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Medial Shape Analysis
0.001
Not corrected for multiple comparisons
Corrected for multiple comparisons
0.05
Posterior (L) Lateral (L) Posterior
(R) Lateral (R)
Significance maps of left (L) and right (R)
hippocampus of schizophrenic patients vs. healthy
controls
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Application Ventricle Shape in Twin Study

• Twin Pairs
• Monozygotic (MZ) Identical twins
• Dizygotic (DZ) Nonidentical twins
• MZ-Discordant (MZ-DS) for Schizophrenia
  Identical twins one affected, co-twin at risk
• Nonrelated (NR) age/gender matched
• Ventricle size and shape
• Data D. Weinberger, NIMH

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Application Twin Study
Collection of ventricular shapes of 4 twin pairs
(unsorted)
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Twin Study ctd.
Collection of ventricular shapes of twin pairs
(4 out of 10 pairs)
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Visual Comparison Shape similarity
MZ
DZ
Size Normalization
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Clinical Study MZ twin pairs discordant for SZ
10 identical twin pairs, ventricles marker for
SZ? left co-twin at risk right schizophrenics
co-twin Data D. Weinberger, NIMH
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Twin Study Volume Analysis
MZ
DZ

• Large variability of volumes overall (CV 63)
  (All healthy)
• Considerable volume differences between twin
  pairs
• Correlation between twin pairs MZ 0.93 / DZ
  0.95

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Pairwise tests among co-twins
Trend MZ lt DZ lt NR Volume similarity correlates
with genetic difference
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Group Tests of Ventricular Volumes
All tests nonsignificant
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SPHARM Parametrization
Mono- zygotic twin pairs
T1AL / T1BL
T1BR / T1AR
T2AL / T2BL
T2BR / T2AR
Dizygotic twin pairs
T10AL / T10BL
T10BR / T10AR
T8AL / T8BL
T8BR / T8AR
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Global Shape Distance Metrics

• Pairwise MSD between surfaces
• PDM Signed or unsigned distance to template at
  corresponding points

120
Pairwise tests among co-twins
Trend MZ lt DZ lt NR Volume similarity correlates
with genetic difference
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Pairwise MSD shape differences between co-twin
ventricles
Shape similarity as pairwise co-twin difference
MZ lt DZ lt NR
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Co-twin pairwise ventricle shape difference
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Group Tests

• Both subgroups of the MZ discordant twins
  (affected and at risk) compared to healthy.
• Ventricular shape Marker for disease and
  possibly for vulnerability (?)

Healthy All
Affected At Risk
MZ discordant
Pairwise tests
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Group Tests of Ventricular Volumes
All tests nonsignificant
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Group Tests Shape Difference to Healthy
Mean difference from CNTL
CNT Affected AtRisk
CNT Affected AtRisk

• Both subgroups of MZ discordant for SZ (affected
  and at risk) differ.
• Ventricular shape seems to be marker for disease/
  vulnerability (?)
• Submitted to PNAS (Dec. 2003)

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Shape Analysis of ventricles via M-reps

• Timothy B. Terriberry

127
Analysis Performed

• Compare m-reps with geodesic distance.
• Two experiments
• Pair-based Difference between twins in a pair
• Mean-based Difference from a healthy mean
• Global and local permutation tests
• Local tests uses correction for multiple tests

128
Pair-based Analysis

• M-rep compared to that of twin.
• Mean difference compared between MZ, DS, DZ, and
  NR groups.

129
Statistics of M-reps

• M-rep parameters are not linear
• Rotations
• Scalings
• High-dimensional, curved space (Lie group)
• Standard linear statistics do not apply

130
Pair-based Results Global
M-rep shape diff. ?SL
PDM shape diff. ?SL (Styner 2004)
P-values for group difference tests (results
significant at 5 level in bold)
M-reps
PDMs (Styner 2004)
131
Conclusions

• Neuroimaging/-analysis Strong multi-disciplinary
  effort essential
• Excellent opportunities and challenges for
  research
• Shape represents changes not reflected by volume
  analysis
• Several clinical studies Shape discriminates
  better than volume
• Open issues
• Correspondence, homology
• Shape representations, invariants
• Variability/standardization of image data
• Clinical studies
• Often exploratory analysis, need replication
• Exchange of methods and test data (ITK, BIRN)
• UNC Hippocampal Dataset SPHARM, PDM, Def.Maps