1. Analysis of Longitudinal Shape Variability via Subject Specific Growth Modeling James Fishbaugh 1 Marcel Prastawa 1 Stanley Durrleman 2 Joseph Piven 3 Guido Gerig 1 1 Scientific Computing and Imaging Institute, University of Utah 2 INRIA/ICM, Pitié Salpêtrière Hospital, Paris, France 3 Carolina Institute for Developmental Disabilities, University of North Carolina

2. Longitudinal Design 1.112.6 0.7 13.424.2 0.8 12.824.4 24.8 0.6 Time (months)

3. The Problem Compare trajectories of shape change 610121824 Time (months) Trajectory A Trajectory B Normative Growth

4. Cross-sectional Extension of kernel regression to Riemannian manifolds [ Davis ICCV 2007 ] Piecewise-geodesic regression for image time-series [ Khan & Beg ISBI 2008 ] Geodesic regression [ Niethammer MICCAI 2011, Fletcher MICCAI MFCA 2011 ] Regression based on stochastic perturbations of geodesic paths [ Trouvé & Vialard Quarterly of Applied Mathematics 2012 ] Regression based on twice differentiable flows of deformation [ Fishbaugh MICCAI 2011 ] Longitudinal atlas construction Individuals modeled as spatiotemporal deformations from mean scenario [ Durrleman MICCAI 2009 ] Longitudinal atlas construction for DTI [ Hart MICCAI STIA 2010 ] and images [ Liao NeuroImage 2012 ] Background Davis ICCV 2007Niethammer MICCAI 2011Trouvé & Vialard QAM 2012 Durrleman MICCAI 2009 Liao NeuroImage 2012

5. Method Overview Framework consists of 3 main steps Estimation of a growth model by shape regression Method Overview

6. Concept: Time-indexed discrete shapes → continuous growth model Temporally smooth evolution based on controlled acceleration [ Fishbaugh MICCAI 2011 ] Shape Regression

7. Time Reference population time-series Estimate Atlas

8. 4D model of normative evolution Estimate Atlas velocity (mm/month) 0 25

9. Personalized 4D models for subjects in different groups Group BGroup A Reference Atlas Estimate Individual Trajectories

10. Surface matching [ Vaillant & Glaunes IPMI 2005 ] at specified time → homologous space for statistical analysis Group AGroup B Reference Atlas At Time t i Warp Atlas to Individuals

11. Flow of diffeomorphisms are geodesic → initial momenta parameterize deformation Group AGroup B Statistics on Diffeomorphisms Reference Atlas At Time t i

12. Experiments Synthetic database of longitudinal shapes 12 subjects in each group by randomizing growth Experimental Validation 610121824 Time (months) Group A Group B Normative Growth

13. PCA on momenta that warp atlas to each individual in Group A Hypothesis testing on magnitude of initial momenta that map reference atlas to individuals (Bonferroni correction) Experimental Validation

14. Clinical database of longitudinal shapes: Study of early brain development in autism High risk recruits: Siblings diagnosed with autism High risk & controls scanned at 6, 12, and 24 months Structures: left/right hemisphere and cerebellum Three groups: HR+: 15 high risk subjects with positive ADOS HR-: 40 high risk subjects with negative ADOS LR-: 14 low risk controls with negative ADOS 6 12 24 Time (months) Clinical Application

15. PCA showing first mode of variability per age group Hypothesis testing → no significant differences between groups at any time point Clinical Application

16. A new approach for : Analyzing longitudinal shape variability Quantifying spatiotemporal population differences Future work: Longitudinal information in atlas construction Utilize rate of change, velocity/acceleration Further clinical applications (e.g. Huntington's disease) Conclusion Time point 1Time point 2Time point 3

17. This work was supported by: Acknowledgments NIH grant U54 EB005149 NA-MIC NIH grant RO1 HD055741 Autism Center of Excellence Project IBIS