Fiber tract-oriented quantitative analysis of Diffusion Tensor MRI data

1. Fiber tract-oriented quantitative analysis of Diffusion Tensor MRI data Isabelle Corouge Postdoctoral fellow, Dept of Computer Science and Psychiatry, UNC-Chapel Hill - 1 - October 7, 2005

2. Motivations • Diffusion Tensor MRI • Study white matter structural properties • Explore relationships between diffusion properties and brain connectivity • Motivations • Inter-individual comparison • Characterization of normal variability • Atlas building • Pathology (e.g., tumor, fiber tract disruption) • Early brain development • Connectivity ? FA image - 2 - October 7, 2005

3. Clustering into bundles Fiber Extraction Fiber tract properties analysis DT images Modeling - Shape Statistics - Diffusion Tensors Statistics Fiber tract shape modeling Quantitative DTI Analysis • Spirit of our work • Alternative to voxel-based analysis • Fiber tract-based measurements: Diffusion properties within cross-sections and along bundles • Geometric modeling of fiber bundles • Fiber tract-oriented statistics of DTI • Methodology outline - 3 - October 7, 2005

4. Fiber Extraction • Extraction by tractography [Fillard’03] • High resolution DTI data (baseline + 6 directional images, 2mm3) • Principal diffusion direction tracking algorithm • Source and target regions of interest • Local continuity constraint, backward tracking, subvoxel precision • “Fibers”: streamlines through the vector field - 4 - October 7, 2005

5. A cluster C: Fi in C, at least one Fj in C, j i such that:d(Fi, Fj) < t Fiber space Fiber Clustering into Bundles • Motivation • Set of 3D curves , : 3D points • Presence of outliers (noise and ambiguities in the tensor field) • Reconstructed fibers might be part of different anatomical bundles • Clustering: based on position and shape similarity • Alternative implementation • Graph formalism & Normalized Cuts concept [C. Goodlett, PhD student] • Hierarchical, agglomerative algorithm - 5 - October 7, 2005

6. Fiber Clustering into Bundles • Examples: • 3Tesla high resolution (2x2x2 mm3) DT MRI • Cortico-spinal tract of left and right hemisphere Before… Neonate …After - 6 - October 7, 2005

7. Fiber Clustering into Bundles • Graph-theoretic approach Fornix cluster Longitudinal fasciculus 6 clusters (2312 streamlines) * Images from Casey Goodlett - 7 - October 7, 2005

8. Fiber Tract Properties Analysis • Analysis across fibers • Local shape properties: curvature/torsion • Diffusion properties: FA, MD, … • Matching scheme • Definition of a common origin for each bundle • Parameterization of the fibers: cubic B-splines • Explicit point to point matching according to arclength • Computation of pointwise mean andstandard deviation of these features - 8 - October 7, 2005

9. Adult 2 Neonate Adult 1 Local Shape Properties a c b Curvature For each curve a c a c c a b b b Mean ± σ - 9 - October 7, 2005

10. Diffusion Properties FA FA: Mean ± σ Adult Neonate - 10 - October 7, 2005

11. Geometric Modeling of Individual Fiber Tracts • Statistical modeling based on variability learning • Construction of a training set • Parametric data representation • Matching: • Dense point to point correspondence • Pose parameter estimation: Procrustes analysis • Estimation of a template curve: mean shape • Characterization of statistical shape variability • Multidimensional statistical analysis: PCA - 11 - October 7, 2005

12. Geometric Modeling • Sets of aligned shapes and estimated mean shape Right cortico spinal tract Callosal tract - 12 - October 7, 2005

13. rotated view Geometric Modeling • First and second modes of deformation • Subject 1, callosal tract Mode 2 Mode 1 - 13 - October 7, 2005

14. The tensors come in… - 14 - October 7, 2005

15. Tensor Statistics and Tensor Interpolation • Tensor: 3x3 symmetric definite-positive matrix • PD(3): space of all 3D tensors • PD(3) is NOT a vector space • Linear statistics are not appropriate ! - 15 - October 7, 2005

16. * From Tom Fletcher - 16 - October 7, 2005

17. Linear Sym. Space Properties Positive-definiteness NO YES Determinant NO YES Tensor Statistics and Tensor Interpolation • Tensor: 3x3 symmetric definite-positive matrix • PD(3): space of all 3D tensors • PD(3) is NOT a vector space • Linear statistics are not appropriate ! - 17 - October 7, 2005

18. Linear Sym. Space Properties Positive-definiteness NO YES Determinant NO YES Tensor Statistics and Tensor Interpolation • Tensor: 3x3 symmetric definite-positive matrix • PD(3): space of all 3D tensors • PD(3) is NOT a vector space • Linear operations are not appropriate ! • PD(3) is a Riemannian symmetric space - 18 - October 7, 2005

19. Geodesic distance * From Tom Fletcher • Algebraic computation - 19 - October 7, 2005

20. Tensor Statistics and Tensor Interpolation • Average of a set of tensors • Variance of a set of tensors • Interpolation of tensors: weighted-average - 20 - October 7, 2005

21. Experiments and Results • Data • 3Tesla high resolution (2x2x2 mm3) DT MRI database • 8 subjects: 4 neonates at 2 weeks-old, 4 one year-old • Fiber tracts: genu and splenium Neonate at 2 weeks-old One year-old - 21 - October 7, 2005

22. Experiments and Results • Average of diffusion tensors in cross-sections along tracts Genu Splenium 2 weeks-old One year-old - 22 - October 7, 2005

23. Experiments and Results • Diffusion properties along fiber tracts Eigenvalues Mean Diffusivity Fractional Anistropy Genu Splenium - 23 - October 7, 2005

24. Future Work • Inter-individual comparison • Fiber-tract based coordinate system • Representation of a fiber tract • Prototype curve + space trajectory • Definition of the space trajectory • Representation by cables/ribbon-bundles/manifold • Geodesic anisotropy • Hpothesis testing - 24 - October 7, 2005

25. The team Guido Gerig (UNC) Casey Goodlett (UNC) Weili Lin (UNC) Sampath Vetsa (UNC) Tom Fletcher (Utah) Rémi Jean Matthieu Jomier (France) Sylvain Gouttard (France) Clément Vachet (France) Software development ITK, VTK, Qt Julien Jomier (UNC) Acknowledgements - 25 - October 7, 2005