1. The UNIVERSITY of NORTH CAROLINA at CHAPEL HILL FADTTS: Functional Analysis of Diffusion Tensor Tract Statistics Hongtu Zhu, Ph.D. Department of Biostatistics and Biomedical Research Imaging Center, University of North Carolina at Chapel Hill

2. The UNIVERSITY of NORTH CAROLINA at CHAPEL HILL Outline Motivation Multivariate Varying Coefficient Models Simulation Studies Real Data Analysis

3. The UNIVERSITY of NORTH CAROLINA at CHAPEL HILL Motivation Functional Connectivity Structural Connectivity Anatomical MRI, DTI (HARDI) group 1 group 2 EEG, fMRI, resting fMRI

4. The UNIVERSITY of NORTH CAROLINA at CHAPEL HILL Neonatal Brain Development Knickmeyer RC, et al. J Neurosci, 2008 28: 12176-12182. Motivation PI: John H. Gilmore. www.google.com

5. The UNIVERSITY of NORTH CAROLINA at CHAPEL HILL Early Brain Development Knickmeyer RC, et al. J Neurosci, 2008 28: 12176-12182. Motivation 2 week 1 year 2 year

6. The UNIVERSITY of NORTH CAROLINA at CHAPEL HILL Diffusion Tensor Tract Statistics Motivation 2 week 1 year2 year 2 week 1 year2 year FATensor

7. The UNIVERSITY of NORTH CAROLINA at CHAPEL HILL Motivation Casey, B.J. et al. TRENDS in Cognitive Sciences, 2005 9(3): 104-110. Macaque Brain Development PI: Martin Styner & Marc Niethammer.

8. The UNIVERSITY of NORTH CAROLINA at CHAPEL HILL Motivation Casey, B.J. et al. TRENDS in Cognitive Sciences, 2005 9(3): 104-110.

9. The UNIVERSITY of NORTH CAROLINA at CHAPEL HILL Motivation Casey, B.J. et al. TRENDS in Cognitive Sciences, 2005 9(3): 104-110.

10. The UNIVERSITY of NORTH CAROLINA at CHAPEL HILL (e) Functional Analysis of Diffusion Tensor Tract Statistics Data Diffusion properties (e.g., FA, RA) Grids Covariates (e.g., age, gender, diagnostic)

11. The UNIVERSITY of NORTH CAROLINA at CHAPEL HILL FADTTS

12. The UNIVERSITY of NORTH CAROLINA at CHAPEL HILL Multivariate Varying Coefficient Model Low Frequency Signal High Frequency Noise Varying Coefficients Decomposition: Covariance operator:

13. The UNIVERSITY of NORTH CAROLINA at CHAPEL HILL Weighted Least Squares Estimate Low Frequency SignalKey Advantage

14. The UNIVERSITY of NORTH CAROLINA at CHAPEL HILL Smooth individual functions Functional Principal Component Analysis Estimated covariance operator Estimated eigenfunctions

15. The UNIVERSITY of NORTH CAROLINA at CHAPEL HILL Statistical Inferences Testing Linear Hypotheses Local Test Statistics Global Test Statistics Grid Point Whole Tract

16. The UNIVERSITY of NORTH CAROLINA at CHAPEL HILL Asymptotics Confidence Band Confidence band Critical point

17. The UNIVERSITY of NORTH CAROLINA at CHAPEL HILL Pros Directly smooth varying coefficient functions Explicitly account for functional nature of tract statistics Characterize low frequency signal Drop high frequency noise Increase statistical power Cons Complicated asymptotic results Computationally intensive Comparisons

18. The UNIVERSITY of NORTH CAROLINA at CHAPEL HILL Simulation Studies Model Setting

19. The UNIVERSITY of NORTH CAROLINA at CHAPEL HILL Simulation Studies Testing

20. The UNIVERSITY of NORTH CAROLINA at CHAPEL HILL Power Comparison between GLM and FADTTS

21. The UNIVERSITY of NORTH CAROLINA at CHAPEL HILL Real Data Analysis Casey, B.J. et al. TRENDS in Cognitive Sciences, 2005 9(3): 104-110. Early Brain Development

22. The UNIVERSITY of NORTH CAROLINA at CHAPEL HILL Real Data Analysis 128 subjects Splenium Diffusion properties = Gender + Gestational age

23. The UNIVERSITY of NORTH CAROLINA at CHAPEL HILL Real Data Analysis

24. The UNIVERSITY of NORTH CAROLINA at CHAPEL HILL Local P-values

25. The UNIVERSITY of NORTH CAROLINA at CHAPEL HILL Confidence Bands FA MD GenderAgeIntercept

26. The UNIVERSITY of NORTH CAROLINA at CHAPEL HILL Functional Principal Component Analysis FA MD Eigenvalues

27. The UNIVERSITY of NORTH CAROLINA at CHAPEL HILL FADTTS GUI Toolbox

28. The UNIVERSITY of NORTH CAROLINA at CHAPEL HILL FADTTS GUI Toolbox Input: Raw data and test data. Raw data include tract data, design data and diffusion data. Test data include test matrix and vector. All data is in.mat format. Output: Basic plots and P-value plots Basic plots include diffusion plot, coefficient plot, eigenvalue and eigenfunction plot, confidence band plot. P-value plot include local p-value (in –log10 scale) plot with global p-value. Download: FADTTS GUI Toolbox with related documents and sample data is free to download from http://www.nitrc.org/projects/fadtts/

29. The UNIVERSITY of NORTH CAROLINA at CHAPEL HILL Summary From the statistical end, we have developed a new functional analysis pipeline for delineating the structure of the variability of multiple diffusion properties along major white matter fiber bundles and their association with a set of covariates of interest. From the application end, FADTTS is demonstrated in a clinical study of neurodevelopment for revealing the complex inhomogeneous spatiotemporal maturation patterns as the apparent changes in fiber bundle diffusion properties. We developed a GUI Tool box to facilitate the application of FADTTS.

30. The UNIVERSITY of NORTH CAROLINA at CHAPEL HILL Future Research extend FADTTS to the analysis of high angular resolution diffusion image (HARDI). extend FADTTS to principal directions and full diffusion tensors on fiber bundles. extend to more complex fiber structures, such as the medial manifolds of fiber tracts. extend FADTTS to longitudinal studies and family studies.

31. The UNIVERSITY of NORTH CAROLINA at CHAPEL HILL References Zhu, H.T., Kong, L.L., Li, R.Z., Styner, M., Gerig, G., Lin, W.L., Gilmore, J. H. (2011). FADTTS: Functional Analysis of Diffiusion Tensor Tract Statistics varying coefficient models for DTI tract statistics. Neuroimage, in press. Zhu, H.T., Li, R. Z., Kong, L.L. (2011). Multivariate varying coefficient models for functional responses. Submitted. Zhu, H., Styner, M., Li, Y., Kong, L., Shi, Y., Lin, W., Coe, C., and Gilmore, J. (2010). Multivariate varying coefficient models for DTI tract statistics. In Jiang, T., Navab, N., Pluim, J., and Viergever, M., editors, Medical Image Computing and Computer-Assisted Intervention MICCAI 2010, volume 6361 of Lecture Notes in Computer Science, pages 690- 697. Springer Berlin / Heidelberg. NICTR Toolbox (2011). FADTTS: Functional Analysis of Diffusion Tensor Tract Statistics. http://www.nitrc.org/projects/fadtts/