1. Generalized Tensor-Based Morphometry (TBM) for the analysis of brain MRI and DTI Natasha Leporé, Laboratory of Neuro Imaging at UCLA

2. TBM overview Source Target

3. TBM

4. TBM mathematical overview Jacobian matrix (2D)

5. Outline of talk MRI: 1. Statistical Analysis 2.Nonlinear Registration 3.Template selection DTI: 4. Extension to DTI

6. TBM

7. Volume vs shape changes But this does not take into account the direction of the changes… Usual TBM (Volume changes): So directional shrinkage and growth, but det(J) = 1 ! J = 0.5 0 0 2 0 2 (Lepore et al., TMI 2007)

8. Shape and volume statistics Multivariate statistics are computed on the 6 components of the deformation tensors Or more precisely, on their logarithm.  = (J T J) 1/2

9. Application to HIV/AIDS We are going to demonstrate our method using: ･ 26 HIV/AIDS patients + 14 controls ･ Various kinds of statistics for 1. Volume changes 1. Volume changes 2. Volume and shape changes 2. Volume and shape changes Permutation based statistics to avoid assuming a normal distribution.

10. Changes in the corpus callosum TEMPLATEDETERMINANTANGLE OF ROTATIONGEODESIC ANISOTROPY TRACEMAXIMUM EIGENVALUE EIGENVALUESDEFORMATION TENSORS Trace (  ) =  11 +  22 with N = log , I identity matrix, u 1 eigenvector, (λ 1, λ 2 ) eigenvalues  = √ (J T J) det  =  11  22 -  12 2 acos(u 1.x) √ Tr ( N – Tr ( N )* I/3 ) 2 maximum (λ 1, λ 2 )(λ 1, λ 2 )( N 11, √ 2N 12, N 22 )

11. Volume and shape statistics for the whole brain Log p-values Determinants Deformation Tensors

12. TBM

13. Fluid vs elastic registration u vΔt1vΔt1 vΔt2vΔt2 vΔtnvΔtn At each voxel, u(x,y) and v(x,y) = du/dt u analysis (elastic) and v analysis (fluid) But in fact …

14. Riemannian fluid registration (Brun et al., MICCAI 2007) ??? : Driving force from the intensity difference between images F : Driving force from the intensity difference between images Similarity term Regularization term

15. Building a Regularizer  The natural way to do the regularization in TBM is to use the deformation tensors, since they characterize the distortion of the local volume.  Since we are in the log-Euclidean framework, we want to use the matrix logarithms.  We want to use a fluid regularizer so we can have large deformations.

16. Regularizer Elastic Registration (Pennec, 2005) (Pennec, 2005) Fluid Registration Fluid Registration ∑ v : rate of strain where

17. Riemannian fluid registration : Driving force from the intensity difference between images F : Driving force from the intensity difference between images Similarity term Regularization term (Brun et al., MICCAI 2007)

18. Implementation: data  23 pairs of identical twins 23 pairs of fraternal twins 23 pairs of fraternal twins  4T MRI scans, DTI 30 directions  Data bank: 1150 healthy twins (21-27 years old) MRI, HARDI and neuropsychological measures

19. Statistics on twins Intraclass correlation: MS between - MS within MS between + MS within ICC = MS: Mean square MS: Mean square We use the ICC to compute the correlation of the deformation tensors (well, their determinants …) in twin pairs. Twin 1Twin 2 MS between MS within

20. Accuracy of the Riemannian fluid registration method Image 1 Image 2 Image 2 registered to image 1 Difference btw warped image and initial image

21. Application of the Riemannian fluid method to genetic studies Determinant of the Jacobian Tangent of the Geodesic Anisotropy Percent mean absolute difference in regional volume Identical twins Fraternal twins

22. Consistency of results: two fluid methods - genetic studies Significance of the Intraclass Correlation (ICC)

23. TBM

24. Template Template averaging  Features are typically sharper in individual brain images than in mean anatomical templates  But, we want to eliminate bias from registration to one individual  Statistics are performed on deformation tensors (Lepore et al., MICCAI 2008)

25. So... compute the average (using deformation tensors) after the registration! Template Template averaging  Features are typically sharper in individual brain images than in mean anatomical templates  But, we want to eliminate bias from registration to one individual  Statistics are performed on deformation tensors (Lepore et al., MICCAI 2008)

26. Averaging procedure data templates common space... The new deformation tensors are the (Log-Euclidean) average of the deformation tensors at each voxel in the common space. Sum over voxels to get a distance between brains.

27. p-values Identical twins Fraternal twins Significance of the Intraclass Correlation (ICC) Anatomical correlations in twins

28. Distance Number of Templates centering Template centering Distance to all the brains in the dataset using 1 to 9 templates

29. We can use almost the same procedure for DTI data! TBM for DTI (Lee et al., MICCAI 2008)

30. MRI vs. DTI 1.DTI data is harder to register, so register the MRI and apply the deformation to the DTI 2. The DTI tensors will be misaligned by the registration, so tensors need to be rotated Registration: Statistics: 1.Perform statistics on the diffusion tensors instead of the deformation tensors

32. NYCAP algorithm team External Collaborator: Xavier Pennec, INRIA Principal Investigator: Paul Thompson Graduate students: Agatha LeeCaroline Brun Research Assistants: Yi-Yu Chou Marina Barysheva Yi-Yu Chou Marina Barysheva