1. NA-MIC National Alliance for Medical Image Computing http://na-mic.org DTI atlas building for population analysis: Application to PNL SZ study Casey Goodlett, Tom Fletcher, Sarang Joshi, Guido Gerig UNC Chapel Hill, Univ. of Utah

2. National Alliance for Medical Image Computing http://na-mic.org Slide 2 Building of Population Averages Motivation: Map population into common coordinate space Learn about normal variability Describe difference from normal Use as normative atlas for segmentation Sarang Joshi, Brad Davis, Matthieu Jomier, Guido Gerig, Unbiased Diffeomorphic Atlas Construction for Computational Anatomy, vol. 23, NeuroImage 2004 B. Avants and J.C. Gee, “Geodesic estimation for large deformation anatomical shape averaging and interpolation,” Neuroimage, vol. 23, pp. 139–150, 2004.

3. National Alliance for Medical Image Computing http://na-mic.org Slide 3 Population-Based DTI Analysis Casey Goodlett, MICCAI’06

4. National Alliance for Medical Image Computing http://na-mic.org Slide 4 Atlas Formation Driving problem: DTI Population studies –Longitudinal analysis –Group hypothesis testing Desirable properties –Reliable –Separate shape from diffusion properties

5. National Alliance for Medical Image Computing http://na-mic.org Slide 5 Registration DTI Images (1:N) Scalar Images From Manifold Detector on FA Structural Average H-fields (1:N) Structural Operator Atlas (Affine, Fluid) H -1 -fields (1:N)

6. National Alliance for Medical Image Computing http://na-mic.org Slide 6 Atlas formation DTI Images Tensor Averaging DTI Atlas Rotate Tensors based on J H -1 H-fields (1:N) Riemannian Symmetric Space

7. National Alliance for Medical Image Computing http://na-mic.org Slide 7 Structural Image Want images aligned by geometry of fiber tracts FA occurs in thin manifolds –sheets –tubes FA'' highlights fiber geometry (maximum eigenvalue) FA'' does not directly optimize correspondence of tensor derived property

8. National Alliance for Medical Image Computing http://na-mic.org Slide 8 FA image and Curvature Image

9. National Alliance for Medical Image Computing http://na-mic.org Slide 9 FA image and Curvature Image

10. National Alliance for Medical Image Computing http://na-mic.org Slide 10 FA image and Curvature Image

11. National Alliance for Medical Image Computing http://na-mic.org Slide 11 Mathematics of Spatial Transformation h(x) is a mapping from R 3 to R 3. h(x) can be locally approximated as a linear function. F is the local Jacobian of the transformation and can be processed the same as for a global transformation. SVD can be used to extract the rotation component of F.

12. National Alliance for Medical Image Computing http://na-mic.org Slide 12 Processing of DTI Diffusion tensors are symmetric positive- definite matrices Riemannian symmetric spaces (Fletcher, Pennec) Log-Euclidean Framework

13. National Alliance for Medical Image Computing http://na-mic.org Slide 13

14. National Alliance for Medical Image Computing http://na-mic.org Slide 14 Average Atlases

15. National Alliance for Medical Image Computing http://na-mic.org Slide 15 Atlas: Average + Set of transformed tensor fields ROIs and tracts in atlas space transferred to every image.

16. National Alliance for Medical Image Computing http://na-mic.org Slide 16 Atlas-Based Tractography Atlas Image BImage A

17. National Alliance for Medical Image Computing http://na-mic.org Slide 17 PNL Data: Colored FA and MD Average of Control Group (N=13) Average of SZ Group (N=12) FAMD FAMD

18. National Alliance for Medical Image Computing http://na-mic.org Slide 18 Full Brain Tractography on Atlas MedINRIA Tool (Pierre Fillard, INRIA) NEW: NAMIC compatible: Reads NRRD format and writes NAMIC fiber format output, is promoted together with NAMIC FiberViewer tool.

19. National Alliance for Medical Image Computing http://na-mic.org Slide 19 Tractography in PNL Atlas Corpus Callosum middle part Cingulum full Cingulum “spine”

20. National Alliance for Medical Image Computing http://na-mic.org Slide 20 more tracts… Uncinate FasciculusUF colored with FA antpost

21. National Alliance for Medical Image Computing http://na-mic.org Slide 21 FA distributions in cross-sections

22. National Alliance for Medical Image Computing http://na-mic.org Slide 22 Tractography per Group Cingulum SZ Group Cingulum Control Group Tractography applied to tensor fields of the set of controls mapped to the atlas (left) ad the set of SZ mapped to the atlas (right).

23. National Alliance for Medical Image Computing http://na-mic.org Slide 23 Very, very preliminary tests … SZ seems to have lower FA in middle portion of cingulum. What does it mean w.r.t. diffusion properties?

24. National Alliance for Medical Image Computing http://na-mic.org Slide 24 ctd. SZ group seems to have lower lambda1 and slightly higher radial diffusion (average lambda2 + lambda3) in middle region.

25. National Alliance for Medical Image Computing http://na-mic.org Slide 25 ctd. MD seems very similar for both groups. GA shows same pattern as FA but much higher values.

26. National Alliance for Medical Image Computing http://na-mic.org Slide 26 same game with cc … Middle cc in central region shows decrease of FA and increase of MD for SZ group

27. National Alliance for Medical Image Computing http://na-mic.org Slide 27 and with uncinate fasciculus Maybe no group difference.

28. National Alliance for Medical Image Computing http://na-mic.org Slide 28 Voxel-based Analysis: FA Control AtlasSZ AtlasDifference Can we trust these difference maps? Do we see residuum of deformation or FA difference? axial low axial high

29. National Alliance for Medical Image Computing http://na-mic.org Slide 29 Voxel-based Analysis: MD ControlsSZDifference Mismatch of two atlases illustrates a problem of our atlas building: Edges of structures not well-aligned. axial low axial high

30. National Alliance for Medical Image Computing http://na-mic.org Slide 30 Problem: What is a good image match feature? Features from tensor field driving nonlinear registration?

31. National Alliance for Medical Image Computing http://na-mic.org Slide 31 Image match should consider boundaries and tract locations MaxevFAMD

32. National Alliance for Medical Image Computing http://na-mic.org Slide 32 Towards improved image match features MD does not show underlying wm structure FA shows strong wm features but not anatomical boundaries FA’’ (Hessian) emphasizes center lines → Would like measure derived from full tensor field Thick and thin structures show similar center features

33. National Alliance for Medical Image Computing http://na-mic.org Slide 33 Hessian of tensor field? Each element is matrix Choice of Norm?

34. National Alliance for Medical Image Computing http://na-mic.org Slide 34 Hessian of Tensor Field max_ev: maximum eigenvalue of each element norm: norm of each element tensor_ev: SIAM*SIAM* 3x3x(3x3) = 3*27elements *Lathauwer, SIAM J. MATRIX ANAL. APPL. Vol. 21, No. 4, pp. 1253–1278

35. National Alliance for Medical Image Computing http://na-mic.org Slide 35 Hessian of Tensor Field

36. National Alliance for Medical Image Computing http://na-mic.org Slide 36 Current Work: Towards better image match features Collaboration with Fillard/Pennec, INRIA Second derivative of tensor field (1 st ev of Hessian) tensor_evmax_evnorm

37. National Alliance for Medical Image Computing http://na-mic.org Slide 37 Conclusions Core methods: Nonlinear deformation (diffeomorphic) and “good” feature maps Atlas-building will require Slicer-3 “pipeline” (currently Linux script) After automatic construction of atlas with set of deformed tensor fields: –Efficient, user-guided analysis (15’ per tract or region) –Full set of measurements (FA, GA, MD, lambda1..3, radial diffusion etc.) Current research: Image match features Set of tracts with associated tensors from aligned images: Ready for tensor statistics (Fletcher, e.g.)

38. National Alliance for Medical Image Computing http://na-mic.org Slide 38 Conclusion PNL DTI study Low hanging fruits were not as low as expected … What was promised for Christmas is available now Encouraging results on multiple key structures (cc, UF, cingulum, fornix etc.) Plan for programmer’s week: To teach about tools and generate clinically relevant results (Goodlett, Kubicki, Bouix).