Measuring Anatomy and its Deformation

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Measuring Anatomy and its Deformation Using
Deformable Shape Models
Christos Davatzikos Center for Biomedical Image
Computing Department of Radiology and
Radiological Science Johns Hopkins University
School of Medicine
http//cbic.rad.jhu.edu
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Topics

• Deformable Shape Modeling and Registration
• Modeling and Predicting Anatomical Deformations

Quantitative Morphology
Spatial normalization Data pooling Image Data
Mining
Statistical Atlases

• Biomechanical/statistical modeling of tumor
  growth
• Modeling intra-operative deformations

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• Challenges in population imaging studies
• Inter-individual anatomical variability
• Localized subtle effects of disease on structure
  or function

Brain atrophy, functional activation, or gene
expression
Need good alignment to increase sensitivity of
statistical analysis in a standardized reference
space
Before Spatial Normalization
After Spatial Normalization
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Shape-Based Elastic Transformation in 3D 1)
Shape reconstruction of a number of
structures (open or closed surfaces, curves) 2)
Match the features based on their geometric
properties (e.g. curvatures) 3) Use the
feature-to-feature map to drive an
elastic deformation transformation
Davatzikos, JCAT/CVIU, 1996/1997
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Examples of surfaces that drive the elastic
deformation
Sulcal Ribbons
Cortex
Hippocampus
Basal ganglia and ventricles
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Davatzikos, Human Brain Mapping, Jan. 1998
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Validation of the RAVENS methodology Simulation
of atrophy in precentral and superior temporal
gyri
 
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• Localized atrophy identified via t-maps of the
  RAVENS images
• Atrophy detected in the two gyri PCG and STG
• T-maps are overlaid on the average WM RAVENS map
  of 24 subjects

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• Adaptive Focus Deformable Model (AFDM)
• for shape reconstruction and mapping
• Use of an Attribute Vector on each point of the
  model
• Use of an Adaptive Deformation Approach

Attribute Vectors Affine-invariant geometric
characteristics from a local to a global scale
B
C
A
Shen et.al., IEEE-TMI April 2001
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Adaptive nature of AFDM
1. Model can zoom to small important features

• In Active Shape Models, large variable features
  dominate over small variable, yet important
  features.

Identical weighting
Large weights on eyes
mode 1
mode 2
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Different weighting for different parts of the
model
White reliable parts large weights
Black unreliable parts small weights
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Shape / Volumetric Analysis of the Hippocampus
Correlation Coefficient Averaging 0.975
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Modeling and Predicting Anatomical
Deformability with applications in image-guided
surgical planning
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Deformable Brain Atlas for Brain Tumor Patients

• Segmentation for surgical planning purposes
• Statistical atlases linking structural
  variables, surgical procedure, and surgical
  outcome

Outcome A
Outcome B
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Kyriacou et.al., IEEE-TMI, 1998
Simulation of tumor growth via a biomechanical
model
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Fundamental Limitation Estimating the inverse
deformation field is a
very ill-posed problem
Atlas Unknown normal
brain Patients brain deformed by tumor
Unknown initial tumor position
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Using shape statistics to model the deformation
between pre- and intra-operative anatomy
Pre-operative plan Intra-operative anatomy

• Need to be able to predict anatomical
  deformations in the
• planning stage
• If part of a structure is visible
  intra-operatively but another
• part is missing, the latter can be predicted

Gray predicted from green
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Generation of training samples, using
biomechanical models or available images (e.g.
intra-operative images)
s1
S
s2

• Find the principal modes of variation of s,
  which includes the principal modes of
  co-variation between s1 and s2
• Find the probability of the coefficients of each
  eigenvector
• Given s2 then estimate s1

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c12
c22
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Training stage
Biomechanical simulation
Statistical Estimation
Prediction stage
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MAP estimation framework
Fit expansion coefficients to what is known,
and estimate what is unknown
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Davatzikos 2001, IEEE-TMI
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Acknowledgements
CBIC Stelios Kyriacou Henry Li Dinggang
Shen Xiaodong Tao Ashraf Mohamed Dengfeng
Liu Donrong Xu Ahmet Genc Songyang Yu Hanchuang
Peng
Collaborators Susan Resnick Scott Moffat Jerry
Prince Eddie Herskovits Susumu Mori