3D space-varying coefficient models with application to diffusion tensor imaging

Computational Statistics and Data Analysis

Volumn 51, Issue 12, 2007, Pages 6212-6228

  Heim, S ^a   Fahrmeir, L ^a   Eilers, P H C ^b   Marx, B D ^c  

^a UNIVERSITY OF MUNICH   (Germany)

^b LEIDEN UNIVERSITY MEDICAL CENTER   (Netherlands)

^c LOUISIANA STATE UNIVERSITY   (United States)

Author keywords

Brain imaging; Diffusion tensor; P splines; Varying coefficient model

Indexed keywords

BRAIN; COMPUTER SIMULATION; DATA PROCESSING; DIFFUSION; IMAGE ANALYSIS; MATHEMATICAL MODELS; TISSUE;

BRAIN IMAGING; DIFFUSION TENSOR IMAGES; DIFFUSION TENSORS; VARYING COEFFICIENT MODELS;

TENSORS;

EID: 34547144842     PISSN: 01679473     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.csda.2007.01.005     Document Type: Article

References (40)

1. Assaf Y., Freidlin R.Z., Rohde G.K., and Basser P.J. New modeling and experimental framework to characterize hindered and restricted water diffusion in brain white matter. Magn. Reson. Med. 52 (2004) 965-978
2. Assunção R. Space varying coefficient models for small area data. Environmetrics 14 (2003) 453-473
3. Basser P.J., and Jones D.K. Diffusion-tensor MRI: theory, experimental design and data analysis-a technical review. NMR Biomed. 15 (2002) 456-467
4. Basser P.J., Matthiello J., and Le Bihan D. Estimation of the effective self-diffusion tensor from the NMR spin echo. J. Magn. Reson. B 103 (1994) 247-254
5. Basser P.J., and Pierpaoli C. Microstructural and physiological features of tissues elucidated by quantitative-diffusion-tensor MRI. J. Magn. Reson. B 111 (1996) 209-219
6. Behrens T., Woolrich M.W., Jenkinson M., Johansen-Berg H., Nunes R.G., Clare S., Matthews P.M., Brady J.M., and Smith S.M. Characterization and propagation of uncertainty in diffusion-weighted MR imaging. Magn. Reson. Med. 50 (2003) 1077-1088
7. Brezger, A., Fahrmeir, L., Hennerfeind, A., 2005. Locally adaptive Gaussian Markov random fields in human brain mapping. SBF386 discussion paper 456, University of Munich.
8. Brezger A., and Lang S. Generalized structured additive regression based on Bayesian p-splines. Comput. Statist. Data Anal. 50 (2006) 967-991
9. Chang L.C., Jones D.K., and Pierpaoli C. RESTORE: robust estimation of tensors by outlier rejection. Magn. Reson. Med. 53 (2005) 1088-1095
10. Currie I., Durbán M., and Eilers P. Generalized linear array models with applications to multidimendional smoothing. J. R. Stat. Soc. Ser. B Stat. Methodol. 68 (2006) 259-280
11. Dierckx P. A fast algorithm for smoothing data on a rectangular grid while using spline functions. SIAM J. Numer. Anal. 19 (1982) 1286-1304
12. Dierckx P. Curve and Surface Fitting with Splines, Monographs on Numerical Analysis (1993), Oxford University Press, Oxford
13. Ding Z., Gore J.C., and Anderson A.W. Reduction of noise in diffusion tensor images using anisotropic smoothing. Magn. Reson. Med. 53 (2005) 485-490
14. Eilers P.H.C., and Marx B.D. Multivariate calibration with temperature interaction using two-dimensional penalized signal regression. Chemom. Intell. Lab. Syst. 66 (2003) 159-174
15. Eilers, P.H.C., Heim, S., Marx, B.D., 2005. Varying coefficient tensor models for brain imaging. In: Francis, A.R., Matawie, K.M., Oshlack, A., Smyth, G.K. (Eds.), Statistical Solutions to Modern Problems. Proceedings of the 20th International Workshop on Statistical Modelling. Sydney, Australia, July 10-15, pp. 157-164.
16. Eilers P.H.C., Currie I., and Durbán M. Fast and compact smoothing on large multidimensional grids. Comput. Statist. Data Anal. 50 (2006) 61-76
17. Fahrmeir L., Kneib T., and Lang S. Penalized structured additive regression for space-time data: a Bayesian perspective. Statist. Sinica 14 (2004) 731-761
18. Gössl C., Fahrmeir L., Pütz B., Auer L.M., and Auer D.P. Fiber tracking from DTI using linear state space models: detectability of the pyramidal tract. NeuroImage 16 (2002) 378-388
19. Grimmett G., and Stirzaker D. Probability and Random Processes. third ed. (2001), Oxford University Press, Oxford
20. Hastie T., and Tibshirani R. Varying-coefficient models (with discussion). J. R. Stat. Soc. Ser. B Stat. Methodol. 55 (1993) 757-796
21. Heim, S., Hahn, K., Auer, D.P., Fahrmeir, L., 2004. Optimization of fiber tracking in human brain mapping: Statistical challenges. In: Biggeri, A., Dreassi, E., Lagazio, C., Marchi, M. (Eds.), Statistical Modelling. Proceedings of the 19th International Workshop on Statistical Modelling. Florence, Italy, July 4-8, pp. 296-300.
22. Horsfield M.A., and Jones D.K. Applications of diffusion-weighted and diffusion tensor MRI to white matter diseases-a review. NMR Biomed. 15 (2002) 570-577
23. Hutchinson M.F., and de Hoog F.R. Smoothing noisy data with spline functions. J. Numer. Math. 47 (1985) 99-106
24. Lang S., Fronk E.M., and Fahrmeir L. Function estimation with locally adaptive dynamic models. Comput. Statist. 17 (2002) 479-499
25. Le Bihan D. Looking into the functional architecture of the brain with diffusion MRI. Nat. Rev. Neurosci. 4 (2003) 469-480
26. Mangin J.F., Poupon C., Clark C., Le Bihan D., and Bloch I. Distortion correction and robust tensor estimation for MR diffusion imaging. Med. Image Anal. 6 (2002) 191-198
27. Mechelli A., Price C.J., Friston K.J., and Ashburner J. Voxel-based morphometry of the human brain: methods and applications. Curr. Med. Imag. Rev. 1 (2005) 105-113
28. Mishra A., Yonggang L., Jiingjing M., Anderson A.W., and Ding Z. Unified framework for anisotropic interpolation and smoothing of diffusion tensor images. NeuroImage 31 (2006) 1525-1535
29. Mori S., and Barker P.B. Diffusion magnetic resonance imaging: its principle and applications. Anat. Rec. 257 (1999) 102-109
30. Mori S., and van Zijl P.C.M. Fiber tracking: principles and strategies-a technical review. NMR Biomed. 15 (2002) 468-480
31. Pajevic S., Aldroubi A., and Basser P.J. A continuous tensor field approximation of discrete DT-MRI data for extracting microstructural and architectural features of tissue. J. Magnetic Resonance 154 (2002) 85-100
32. Papadakis N.G., Xing D., Huang C.L.-H., Hall L., and Carpenter T.A. A comparative study of acquisition schemes for diffusion tensor imaging using MRI. J. Magnetic Resonance 137 (1999) 67-82
33. R Development Core Team, 2006. R: A Language and Environment for Statistical Computing. R Foundation for Statistical Computing, Vienna, Austria, ISBN 3-900051-07-0. 〈URL http://www.R-project.org〉.
34. Ruppert D., and Carroll R.J. Spatially-adaptive penalties for spline fitting. Aust. N. Z. J. Stat. 42 (2000) 205-223
35. Samsonov A.A., and Johnson C.R. Noise-adaptive nonlinear diffusion filtering of MR images with spatially varying noise levels. Magn. Reson. Med. 52 (2004) 798-806
36. Sotak C.H. The role of diffusion tensor imaging in the evaluation of ischemic brain injury-a review. NMR Biomed. 15 (2002) 561-569
37. Stejskal E.O., and Tanner J.E. Spin diffusion measurements: spin echoes in the presence of time-dependent field gradient. J. Chem. Phys. 42 (1965) 288-292
38. Toledo, S., Rotkin, V., Chen, D., 2003. Taucs: A Library of Sparse Linear Solvers. Tel-Aviv University, Israel. 〈URL http://www.tau.ac.il/~stoledo/taucs/〉.
39. Tschumperlé, D., Deriche, R., 2003. Variational frameworks for DT-MRI estimation, regularization and visualization. In: IEEE International Conference on Computer Vision. Nice, France, pp. 116-121.
40. Wang Z., Vemuri B.C., Chen Y., and Mareci T.H. A constrained variational principle for direct estimation and smoothing of the diffusion tensor field from complex DWI. IEEE Trans. Med. Imaging 23 (2004) 930-939