Advertisement

International Journal of Computer Vision

, Volume 69, Issue 1, pp 77–92 | Cite as

Basis Tensor Decomposition for Restoring Intra-Voxel Structure and Stochastic Walks for Inferring Brain Connectivity in DT-MRI

  • Alonso Ramirez-Manzanares
  • Mariano Rivera
Article

Abstract

We present a regularized method for solving an inverse problem in Diffusion Tensor Magnetic Resonance Imaging (DT-MRI) data. In the case of brain images, DT-MR imagery technique produces a tensor field that indicates the local orientation of nerve bundles. Now days, the spatial resolution of this technique is limited by the partial volume effect produced in voxels that contain fiber crossings or bifurcations. In this paper, we proposed a method for recovering the intra-voxel information and inferring the brain connectivity. We assume that the observed tensor is a linear combination of a given tensor basis, therefore, the aim of our approach is the computation of the unknown coefficients of this linear combination. By regularizing the problem, we introduce the needed prior information about the piecewise smoothness of nerve bundles orientation. As a result, we recover a multi-tensor field. Moreover, for estimating the nerve bundles trajectory, we propose a method based on stochastic walks of particles through the computed multi-tensor field. The performance of the method is demonstrated by experiments in both synthetic and real data.

Keywords

DT-MRI DTI fiber tractography intra-voxel structure high angular resolution diffusion imaging multi-tensor stochastic particle walks 

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Basser, P.J., Pajevic, S., Pierpaoli, C., and Aldroubi A. 2002. Fiber tract following in the human brain using DT-MRI data. In IEICE Trans Inf Sys, vol. E85D, pp. 15–21.Google Scholar
  2. Basser, P.J., Pajevic, S., Pierpaoli, C., Duda, J., and Aldroubi, A. 1996. Microstructural and physiological features of tissues elucidated by quantitative–diffusion–tensor MRI. J. Magn.Reson., 111:209–219.CrossRefGoogle Scholar
  3. Basser, P.J., Pajevic, S., Pierpaoli, C., Duda, J., and Aldroubi, A. 2000. In Vivo Fiber Tractography Using DT-MRI Data. Magn. Reson. Med., 44: 625–632.CrossRefGoogle Scholar
  4. Björnemo, M. and Anders, B. 2002. White Matter Fiber Tracking Using Diffusion Tensor MRI. Reg nr: Liu-imt-ex-321, Linköping University.Google Scholar
  5. Buxton, R. 2002. Introduction to Functional Magnetic Resonance Imaging Principles and Techniques. Cambridge University Press.Google Scholar
  6. Gee, J.C., Alexander, D.C., Rivera, M., and Duda, J.T. 2002. Non-rigid registration of diffusion Tensor MR Images. In I. Press (ed.), IEEE International Symposium on Biomedical Imaging, pp. 477–480.Google Scholar
  7. Geman, S. and Geman, D. 1984, Stochastic relaxation, Gibbs distribution and the Bayesian restoration of images. IEEE Transactions on Pattern Analysis and Machine Intelligence, 6(6): 721–741.MATHCrossRefGoogle Scholar
  8. Hastie, T., Tibshirani, R., and Friedman, J. 2001. The Elements of Statistical Learning: Data Mining, Inference, and Prediction. Springer-Verlag.Google Scholar
  9. Lazar, M., Weinstein, D.M., Tsuruda, J.S., Hasan, K.M., Arfanakis, K., Meyerand, M.E., Badie, B., Rowley, H., Haughton, V., Field, A., and Alexander, A.L. 2003. White matter tractography using diffusion tensor deflection. Hum Brain Mapp, 18(4): 306–21.CrossRefGoogle Scholar
  10. Li, S.Z. 2001. Markov Random Field Modeling in Image Analysis. Springer Verlag.Google Scholar
  11. Mardia, K.V. 1972. Statistics of Directional Data. Academic Press.Google Scholar
  12. O’Donnell, L., Haker, S., and Westin, C.F. 2002. New Approaches to Estimation of White Matter Connectivity in Diffusion Tensor MRI: PDE-Based and Geodesics in a Tensor-Warped Space. In Fifth International Conference on Medical Image Computing and Computer-Assisted Intervention – MICCAI’02.Google Scholar
  13. Pajevic, S., Aldroubi, A., and Basserz, P.J. 2002. A Continuous Tensor Field Approximation of Discrete DT-MRI Data for Extracting Microstructural and Architectural Features of Tissue. Journal of Magnetic Resonance, 154: 85–100.CrossRefGoogle Scholar
  14. Parker, G.J.M., Wheeler-Kingshott, C.A.M., and Barker, G.J. 2002. Estimating Distributed Anatomical Brain Connectivity Using Fast Marching Methods and Diffusion Tensor Imaging. IEEE Transactions on Medical Imaging, 21(5): 505–512.CrossRefGoogle Scholar
  15. Poldrack, R.A. 2001. A structural basis for developmental dyslexia: Evidence from diffusion tensor imaging. In M. Wolf (ed.), Dyslexia, Fluency, and the Brain, pp. 213–233.Google Scholar
  16. Poupon, C., Clark, C., Frouin, V., Regis, J., Bloch, I., Bihan, D.L., and Mangin, J. 2000. Regularization of diffusionbased direction maps for the tracking of brain white matter fascicles. Neuroimage, 12: 184–195.CrossRefGoogle Scholar
  17. Ramirez-Manzanares, A. and Rivera, M. 2003. Brain Nerve Bundles Estimation by Restoring and Filtering Intra-Voxel Information in Diffusion Tensor MRI. In 2nd IEEE Workshop on Variational, Geometric and Level Sets Methods in Computer Vision (VLSM 2003), Nice France, pp. 71–80.Google Scholar
  18. Ramirez-Manzanares, A., Rivera, M., Vemuri, B., and Mareci, T. 2004. Basis Functions for Estimating Intraoxel Structure in DW–MRI. In Procc. IEEE Medical Imaging Conference 2004 (MIC 2004), Rome, Italy, 7:4207–4211, October 2004. Digital Object Identifier 10.1109/NSSMIC.2004.1466819.Google Scholar
  19. Ruiz-Alzola, J., Westin, C.F., Warfield To appear, S.K., Nabavi, A., and Kikinis, R. 2000. Nonrigid Registration of 3D Scalar, Vector and Tensor Medical Data. In MICCAI 2000, pp. 541–550.Google Scholar
  20. Tschumperlé, D. and Deriche, R. 2002. Orthonormal Vector Sets Regularization with PDE’s and Applications. In IJCV, International Journal of Computer Vision.Google Scholar
  21. Tschumperlé, D. and Deriche, R. 2003a. Tensor Field Visualization with and Application to DT-MRI Fiber Visualization. In VLSM 03, pp. 255–262.Google Scholar
  22. Tschumperlé, D. and Deriche, R. 2003b. Variational Frameworks for DT-MRI Estimation, Regularization and Visualization. In 9 th IEEE International Conference on Computer Vision, vol. 1, pp.116–121.CrossRefGoogle Scholar
  23. Tuch, D. S. 2002. Diffusion MRI of Complex Tissue Structure. Ph.D. thesis, Harvard-MIT.Google Scholar
  24. Tuch, D.S., Reese, T.G., Wiegell, M.R., Makris, N., Belliveau, J.W., and Wedeen, V.J. 2002. High angular resolution diffusion imaging reveals intravoxel white matter fiber heterogeneity. Magnetic Resonance in Medicine, 48(4): 577.CrossRefGoogle Scholar
  25. Tuch, D.S., Weisskoff, R.M., Belliveau, J.W. and Wedeen, V.J. 1999. High angular resolution diffusion imaging of the human brain. In Proc.7th Annual Meeting of ISMRM, vol. 321.Google Scholar
  26. Vigueras, F. 2001. Filtrado y segmentacion de imagenes usando difusion anisotropica. Master’s thesis, Centro de Investigacion en Matematicas (CIMAT).Google Scholar
  27. Wang, Z., Vemuri, B.C., Chen, Y., and Mareci, T. 2003. A Constrained Variational Principle for Direct Estimation and Smoothing of the Diffusion Tensor Field from DWI. In IPMI 2003, pp. 660–671.Google Scholar
  28. Westin, C., Maier, S., Mamata, H., Jolesz, F., and Kikinis, R. 2002. Processing and Visualization for Diffusion Tensor MRI. Medical Image Analysis, 6(2): 93–108.CrossRefGoogle Scholar
  29. Westin, C.F. and Maier, S.E. 2002. A dual tensor basis solution to the stejskal–tanner equations for DTMRI. In Proceedings of International Society for Magnetic Resonance in Medicine.Google Scholar
  30. Westin, C.F., Maier, S.E., Khidhir, B., Everett, P., Jolesz, F.A., and Kikinis, R. 1999. Image Processing for Diffusion Tensor Magnetic Resonance Imaging. In C. A. Taylor C (ed.), MICCAI 99, pp. 441–452.Google Scholar
  31. Wiegell, M.R., Henrik, M., Larsson, B.W., and Wedeen, V.J. 2000. Fiber Crossing in Human Brain Depicted with Diffusion Tensor MR Imaging. Radiology, 217: 897–903.Google Scholar
  32. Zhang, S., Curry, T., Morris, D.S., and Laidlaw, D.H. 2000. Streamtubes and streamsurfaces for visualizing diffusion tensor MRI volume images. In Visualization ′00 Work in Progress.Google Scholar
  33. Zhukov, L. and Barr, A. 2002. Oriented Tensor Reconstruction: Tracing Neural Pathways from Diffusion Tensor MRI. In Proceedings of IEEE Visualization 2002, pp. 387–394.Google Scholar
  34. Zhukov, L., Museth, K., Breen, D., Whitaker, R., and Barr, A. 2003. Level Set Modeling and Segmentation of DT-MRI Brain Data. Journal of Electronic Imaging, 12(1): 125–133.CrossRefGoogle Scholar

Copyright information

© Springer Science + Business Media, LLC 2006

Authors and Affiliations

  1. 1.Centro de Investigacion en Matematicas A.C.GuanajuatoMexico

Personalised recommendations