Part III Statistical Characterization of Brain Structures via Mreps

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Part IIIStatistical Characterization of Brain
Structures via M-reps

• Guido Gerig
• Departments of Computer Science and Psychiatry
• UNC Chapel Hill

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Morphometry of Anatomical Structures

• UNC Chapel Hill
• Morphometry of brain structures in
• Schizophrenia
• Twin Studies (MZ/DZ/DS)
• Autism, Fragile-X
• Alzheimers Desease
• Depression
• Epilepsy

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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
Good
Function/
Psycho- pathology
Chronic/Residual
Premorbid
Prodromal
Progressive
Poor
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20
30
40
50
60
70
Gestation/ Birth
Age (Years)
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Study Structural analysis of caudate nucleus in
Schizophrenia

• Processing Steps
• Automatic whole brain tissue classification (EM
  segm.)
• User-operated masking of caudate on label image
  (intra-, interrater reliability gt 0.95)
• Surface parametrization of caudate shapes ?
  SPHARM PDM
• Alignment/Normalization Surface Correspondence
• Medial mesh generation (m-rep model)

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Modeling of Caudate Shape
PDM
M-rep
Surface Parametrization
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Basal Ganglia
Netters Atlas of Human Anatomy
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Caudate Shape Analysis

• Clinical Groups
• Healthy controls (N30)
• Typical drug treatment (30)
• Atypical drug treatment (30)
• Clinical questions
• Shape difference between groups?
• Drug/patient interaction?
• Location type of changes

Mean Shapes per Group
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Caudate volume analysis

• Significantly larger volumes of SZ versus
  controls
• Trend but not significant difference between
  Typ/Atyp
• Where and what is difference?

preliminary analysis, not controlled for age
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Mean Shapes CNTL vs. SZ
left
right
Overlay of aligned (transl/rot) original shapes
green CNTL / purple mesh SZ
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Mean Shapes CNTL vs. SZ
Overlay of size normalized shapes green CNTL
/ purple mesh SZ
shape should not reflect size change
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Alignment, Correspondence?

• Choice of alignment coordinate system?
• Establishing correspondence is a key issue for
  building statistical shape models.
• Various methods for definition of correspondence
  exist (landmarks, high dimensional warping, PDM
  w. MDL refinement, ).
• Resulting eigenmodes of deformation depend on
  these definitions.
• Scaling of objects prior to shape analysis?

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Object Alignment / Surface Homology
MZ pair
DZ pair
Surface Correspondence
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Object Alignment before 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

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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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Shape Representation Method Medial
Representation M-rep
Implied Surface
Skeletal Mesh (sampled)
Local Width (Radius)
Implied shape represents original shape with 99
volume overlap and ?0.05 MAD at boundary (M.
Styner, PhD thesis)
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Shape Difference Analysis of M-rep
Mesh Position
Local Width
Mesh distance at corresponding nodes Object
deformation, Bending
Grp A
Radius difference at corresponding nodes Local
width change
A and B aligned, superimposed
Grp B
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Statistical Analysis

• Shapes represented by m-rep Significant feature
  reduction, multi-scale
• Still Number of features ? sample size.
• Variability hides shape changes.
• Shapes not represented by scalar values Standard
  MANOVA analysis inappropriate.

• Often PCA on features, selection of small of
  Eigenmodes, Fisher linear discriminant, leave one
  out test for classification.
• But Fisher LD not robust, of features?, feature
  selection?, does PCA reflect group differences?

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Statistical Analysis
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Shape analysis using medial representations
radius

• Local width (radius) differences Growth, Atrophy
  (Loss)
• Positional differences Bending, Deformation

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Permutation Test

• Monte Carlo Sampling (mk30)
• Mean differences from 1000 permutations
• Test original difference 22.8 versus
  distribution p0.025

experiments
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Results Caudate Shape AnalysisIntegrated local
effects

• Typical group shows larger shape difference to
  controls than atypical group
• Significant shape difference between typical and
  atypical treatment group
• Shape distances not shown in combined SZ versus
  controls analysis
• Treatment effect or clinical selection bias?
• Experimental study design, result need to be
  verified in cross-validation study

Non-parametric permutation test
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Results Caudate Shape AnalysisComparison of
Surfaces

• Significant shape changes mostly in the head of
  the caudate
• Shape effect on left side larger than on right
  side
• Local significance tests in progress

CNTL Atyp Typ
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Shape Difference Where and What?Local Mesh
Deformation

• Atypical versus Typical drug treatment groups (N
  30)
• Local Deformation (Euclidean dist. between
  corresponding nodes)
• Local significance tests (nonparametric
  permutation tests)

mesh with node differences plt0.01
p-values per mesh node
mesh with nodes plt0.05
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Shape Difference Where and What?Local Mesh
Deformation

• Atypical versus Typical drug treatment groups (N
  30)
• Local Deformation (Euclidean dist. between
  corresponding nodes)

mesh with nodes plt0.05
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Shape Difference Where and What?Local Width
Difference

• Atypical versus Typical drug treatment groups
  (N_atypN_typ 30)
• Local Width Diff. (Radius diff. between
  corresponding node positions)
• Local significance tests (nonparametric
  permutation tests)

mesh with node differences plt0.05
p-values per mesh node
mesh with nodes plt0.05
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Shape Difference Where and What?Local Width
Difference

• Atypical versus Typical drug treatment groups
  (N_atypN_typ 30)
• Local Width Diff. (Radius diff. between
  corresponding node positions)

mesh with nodes plt0.05
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Shape Difference Where and What?Local Width
Difference

• Atypical versus Typical drug treatment groups
  (N_atypN_typ 30)
• Local Width Diff. (Radius diff. between
  corresponding node positions)

Morphing between Atypical (thinner) and Typical
(thicker)
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Discussion Caudate Study
Width and mesh deformation mostly in caudate
body/head. Secondary mesh deformation
posteriorly Typical treatment group differs from
Controls, but not Atypical. Clinical
implications? Study caudate shape change
relative to neighboring shapes.
Netters Atlas of Human Anatomy
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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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Hippocampal Volume Analysis

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

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3D Shape Variability Left Hippocampus of 90
Subjects
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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 representations
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 local
  statistical 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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Conclusions

• Shape represents changes not reflected by volume
  analysis
• Several clinical studies Shape discriminates
  better than volume
• M-rep superior to boundary models
• separate analysis of local width/bending
• results explained in natural language terms
• potential to analyze figure-subfigure
  relationships and figures in anatomic context
• Improved statistical framework for discrimination
  in development

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Acknowledgements

• Martin Styner
• Sean Ho
• Sampath Vetsa
• Keith Muller
• Jeffrey A. Lieberman
• Stephen M. Pizer and M-rep team
• Talk at http//midag.cs.unc.edu