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
Topics
• Deformable Shape Modeling and Registration
Quantitative Morphology
Spatial normalization
Data pooling
Statistical Atlases
Image Data Mining
•Modeling and Predicting Anatomical Deformations
- Biomechanical/statistical modeling of tumor growth
- Modeling intra-operative deformations
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
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
Examples of surfaces that drive the elastic deformation
Sulcal
Ribbons
Cortex
Hippocampus
Basal ganglia and ventricles
1
2
4
Davatzikos, Human Brain Mapping, Jan. 1998
3
Validation of the RAVENS methodology:
Simulation of atrophy in precentral and superior
temporal gyri
atrophy
original
•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
Adaptive Focus Deformable Model (AFDM)
for shape reconstruction and mapping:
1. Use of an Attribute Vector on each point of the model
2. 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
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
Different weighting for different parts of the model
White: reliable parts large weights
Black: unreliable parts small weights
Shape / Volumetric Analysis of the Hippocampus
Correlation Coefficient
Averaging 0.975
Modeling and Predicting Anatomical Deformability
with applications in image-guided surgical planning
Deformable Brain Atlas for Brain Tumor Patients
• Segmentation for surgical planning purposes
Outcome A
Outcome B
• Statistical atlases linking structural variables, surgical
procedure, and surgical outcome
Kyriacou et.al., IEEE-TMI, 1998
Simulation of tumor growth
via a biomechanical model
Fundamental Limitation: Estimating the inverse deformation
field is a very ill-posed problem
Atlas
Unknown normal brain
Patient’s brain deformed by tumor
Unknown initial tumor position
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
Generation of training samples, using biomechanical models or
available images (e.g. intra-operative images)
S=
s1
s2
s
principal modes of co-variation between s1 and s2
• Find the principal modes of variation of , which includes the
c11 c12
c22
• Find the probability of the coefficients of each eigenvector
•Given s2 then estimate s1
Training stage
Biomechanical
simulation
Statistical
Estimation
Prediction stage
MAP estimation framework:
Fit expansion
coefficients to “what is
known”, and estimate
“what is unknown”
Davatzikos 2001, IEEE-TMI
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