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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 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