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Fuzzy Fibers: Uncertainty in dMRI Tractography

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Part of the book series: Mathematics and Visualization ((MATHVISUAL))

Abstract

Fiber tracking based on diffusion weighted Magnetic Resonance Imaging (dMRI) allows for noninvasive reconstruction of fiber bundles in the human brain. In this chapter, we discuss sources of error and uncertainty in this technique, and review strategies that afford a more reliable interpretation of the results. This includes methods for computing and rendering probabilistic tractograms, which estimate precision in the face of measurement noise and artifacts. However, we also address aspects that have received less attention so far, such as model selection, partial voluming, and the impact of parameters, both in preprocessing and in fiber tracking itself. We conclude by giving impulses for future research.

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References

  1. Alexander, D.C., Barker, G.J., Arridge, S.R.: Detection and modeling of non-gaussian apparent diffusion coefficient profiles in human brain data. Magn. Reson. Med. 48, 331–340 (2002)

    Article  Google Scholar 

  2. Behrens, T.E.J., Johansen-Berg, H., Jbabdi, S., Rushworth, M.F.S., Woolrich, M.W.: Probabilistic diffusion tractography with multiple fibre orientations: what can we gain? NeuroImage 34, 144–155 (2007)

    Article  Google Scholar 

  3. Behrens, T.E.J., Woolrich, M.W., Jenkinson, M., Johansen-Berg, H., Nunes, R.G., Clare, S., Matthews, P.M., Brady, J.M., Smith, S.M.: Characterization and propagation of uncertainty in diffusion-weighted MR imaging. Magn. Reson. Med. 50, 1077–1088 (2003)

    Article  Google Scholar 

  4. Björnemo, M., Brun, A., Kikinis, R., Westin, C.F.: Regularized stochastic white matter tractography using diffusion tensor MRI. In: Dohi, T., Kikinis, R. (eds.) Proceedings of Medical Image Computing and Computer-Assisted Intervention (MICCAI), Lecture Notes in Computer Science, vol. 2488, pp. 435–442. Springer, Berlin (2002)

    Google Scholar 

  5. Blaas, J., Botha, C.P., Peters, B., Vos, F.M., Post, F.H.: Fast and reproducible fiber bundle selection in DTI visualization. In: Silva, C., Gröller, E., Rushmeier, H. (eds) Proceedings of IEEE Visualization, pp. 59–64 (2005)

    Google Scholar 

  6. Brecheisen, R., Platel, B., ter Haar Romenij, B.M., Vilanova, A.: Illustrative uncertainty visualization for DTI fiber pathways. In: Poster Proceedings of EuroVis (2011)

    Google Scholar 

  7. Brecheisen, R., Vilanova, A., Platel, B., ter Haar Romenij, B.M.: Parameter sensitivity visualization for DTI fiber tracking. IEEE Trans. Vis. Comput. Graph. 15(6), 1441–1448 (2009)

    Google Scholar 

  8. Bretthorst, G.L., Kroenke, C.D., Neil, J.J.: Characterizing water diffusion in fixed baboon brain. In Fischer, R., Preuss, R., von Toussaint, U. (eds.) Bayesian Inference and Maximum Entropy Methods in Science and Engineering, pp. 3–15 (2004)

    Google Scholar 

  9. Bürgel, U., Mädler, B., Honey, C.R., Thron, A., Gilsbach, J., Coenen, V.A.: Fiber tracking with distinct software tools results in a clear diversity in anatomical fiber tract portrayal. Cen. Eur. Neurosurg. 70(1), 27–35 (2009)

    Article  Google Scholar 

  10. Calamante, F., Tournier, J.D., Jackson, G.D., Connelly, A.: Track-density imaging (TDI): super-resolution white matter imaging using whole-brain track-density mapping. NeuroImage 53(4), 1233–1243 (2010)

    Article  Google Scholar 

  11. Catani, M., Howard, R.J., Pajevic, S., Jones, D.K.: Virtual in vivo interactive dissection of white matter fasciculi in the human brain. NeuroImage 17, 77–94 (2002)

    Article  Google Scholar 

  12. Chung, S., Ying, L.: Comparison of bootstrap approaches for estimation of uncertainties of DTI parameters. NeuroImage 33(2), 531–541 (2006)

    Article  Google Scholar 

  13. Ciccarelli, O., Parker, G.J.M., Toosy, A.T., Wheeler-Kingshott, C.A.M., Barker, G.J., Boulby, P.A., Miller, D.H., Thompson, A.J.: From diffusion tractography to quantitative white matter tract measures: a reproducibility study. NeuroImage 18, 348–359 (2003)

    Article  Google Scholar 

  14. Ding, Z., Gore, J.C., Anderson, A.W.: Classification and quantification of neuronal fiber pathways using diffusion tensor MRI. Magn. Reson. Med. 49, 716–721 (2003)

    Article  Google Scholar 

  15. Ehricke, H.-H., Klose, U., Grodd, W.: Visualizing MR diffusion tensor fields by dynamic fiber tracking and uncertainty mapping. Comput. Graph. 30, 255–264 (2006)

    Google Scholar 

  16. Farrell, J.A.D., Landman, B.A., Jones, C.K., Smith, S.A., Prince, J.L., van Zijl, P.C.M., Mori, S.: Effects of signal-to-noise ratio on the accuracy and reproducibility of diffusion tensor imaging-derived fractional anisotropy, mean diffusivity, and principal eigenvector measurements at 1.5T. J. Magn. Reson. Imag. 26, 756–767 (2007)

    Google Scholar 

  17. Freidlin, R.Z., Özarslan, E., Komlosh, M.E., Chang, L.-C., Koay, C.G., Jones, D.K., Basser, P.J.: Parsimonious model selection for tissue segmentation and classification applications: a study using simulated and experimental DTI data. IEEE Trans. Med. Imaging 26(11), 1576–1584 (2007)

    Google Scholar 

  18. Greenspan, H., Oz, G., Kiryati, N., Peled, S.: MRI inter-slice reconstruction using super-resolution. Magn. Reson. Imaging 20, 437–446 (2002)

    Article  Google Scholar 

  19. Hagmann, P., Thiran, J.-P., Jonasson, L., Vandergheynst, P., Clarke, S., Maeder, P., Meuli, R.: DTI mapping of human brain connectivity: statistical fibre tracking and virtual dissection. NeuroImage 19, 545–554 (2003)

    Article  Google Scholar 

  20. Heidemann, R.M., Porter, D.A., Anwander, A., Feiweier, T., Calamante, F., Tournier, J.-S., Lohmann, G., Meyer, H., Knösche, T.R., Turner, R.: Whole-brain, multi-shot, diffusion-weighted imaging in humans at 7T with 1 mm isotropic resolution. In Proceedings of International Society of Magnetic Resonance in Medicine (ISMRM), p. 417 (2011)

    Google Scholar 

  21. Heiervang, E., Behrens, T.E.J., Mackay, C.E., Robson, M.D., Johansen-Berg, H.: Between session reproducibility and between subject variability of diffusion MRI and tractography measures. NeuroImage 33, 867–877 (2006)

    Article  Google Scholar 

  22. Hoeting, J.A., Madigan, D., Raftery, A.E., Volinsky, C.T.: Bayesian model averaging: a tutorial. Stat. Sci. 14(4), 382–417 (1999)

    Article  MathSciNet  MATH  Google Scholar 

  23. Hsu, E.: Generalized line integral convolution rendering of diffusion tensor fields. In Proceedings of International Society of Magnetic Resonance in Medicine (ISMRM), p. 790 (2001)

    Google Scholar 

  24. Hao, H., Zhang, J., van Zijl, P.C.m., Mori, S.: Analysis of noise effects on DTI-based tractography using the brute-force and multi-ROI approach. Magn. Reson. Med. 52, 559–565 (2004)

    Google Scholar 

  25. Hubbard, P.L., Parker, G.J.M.: Validation of tractography. In: Johansen-Berg, H., Behrens, T.E.J. (eds.) Diffusion MRI: From Quantitative Measurement to in-Vivo Neuroanatomy, pp. 353–375. Academic Press, Massachusetts (2009)

    Google Scholar 

  26. Jeurissen, B., Leemans, A., Tournier, J-D. Jones, D.K., Sijbers, J.: Estimating the number of fiber orientations in diffusion MRI voxels: a spherical deconvolution study. In Proceedings of International Society of Magnetic Resonance in Medicine (ISMRM) (2010)

    Google Scholar 

  27. Jeurissen, B., Leemans, A., Jones, D.K., Tournier, J.D., Sijbers, J.: Probabilistic fiber tracking using the residual bootstrap with constrained spherical deconvolution. Hum. Brain Mapp. 32, 461–479 (2011)

    Article  Google Scholar 

  28. Jiao, F., Phillips, J.M., Gur, Y., Johnson, C.R.: Uncertainty visualization in HARDI based on ensembles of ODFs. In: Hauser, H., Kobourov, S.G., Qu, H. (eds.) Proceedings of IEEE Pacific Visualization Symposium, pp. 193–200 (2012)

    Google Scholar 

  29. Jiao, F., Phillips, J.M., Stinstra, J., Krüger, J., Varma, R., Hsu, E., Korenberg, J., Johnson, C.R.: Metrics for uncertainty analysis and visualization of diffusion tensor images. In: Liao, H., Eddie Edwards, P.J., Pan, X., Fan, Y., Yang, G.-Z. (eds.) Proceedings of Medical Imaging and Augmented Reality. Lecture Notes in Computer Science, vol. 6326, pp. 179–190 (2010)

    Google Scholar 

  30. Jones, D.K., Travis, A.R., Eden, G., Pierpaoli, C., Basser, P.J.: Pasta: pointwise assessment of streamline tractography attributes. Magn. Reson. Med. 53(6), 1462–1467 (2005)

    Google Scholar 

  31. Jones, D.K.: Determining and visualizing uncertainty in estimates of fiber orientation from diffusion tensor MRI. Magn. Reson. Med. 49, 7–12 (2003)

    Google Scholar 

  32. Jones, D.K.: Tractography gone wild: probabilistic fibre tracking using the wild bootstrap with diffusion tensor MRI. IEEE Trans. Med. Imaging 27(9), 1268–1274 (2008)

    Article  Google Scholar 

  33. Jones, D.K.: Challenges and limitations of quantifying brain connectivity in vivo with diffusion MRI. Future Med. 2(3), 341–355 (2010)

    Google Scholar 

  34. Jones, D.K., Cercignani, M.: Twenty-five pitfalls in the analysis of diffusion MRI data. NMR Biomed. 23, 803–820 (2010)

    Article  Google Scholar 

  35. Jones, D.K., Pierpaoli, C.: Confidence mapping in diffusion tensor magnetic resonance imaging tractography using a bootstrap approach. Magn. Reson. Med. 53, 1143–1149 (2005)

    Article  Google Scholar 

  36. Kass, R.E., Raftery, A.E.: Bayes factors. J. Am. Stat. Assoc. 90(430), 773–795 (1995)

    Article  MATH  Google Scholar 

  37. Kinoshita, M., Yamada, K., Hashimoto, N., Kato, A., Izumoto, S., Baba, T., Maruno, M., Nishimura, T., Yoshimine, T.: Fiber-tracking does not accurately estimate size of fiber bundle in pathological condition: initial neurosurgical experience using neuronavigation and subcortical white matter stimulation. NeuroImage 25(2), 424–429 (2005)

    Article  Google Scholar 

  38. Koch, M.A., Norris, D.G., Hund-Georgiadis, M.: An investigation of functional and anatomical connectivity using magnetic resonance imaging. NeuroImage 16, 241–250 (2002)

    Article  Google Scholar 

  39. Lazar, M., Alexander, A.L.: Bootstrap white matter tractography (BOOT-TRAC). NeuroImage 24(2), 524–532 (2005)

    Article  Google Scholar 

  40. McGraw, T., NadarM.S.: Stochastic DT-MRI connectivity mapping on the GPU. IEEE Trans. Visual. Comput. Graph. 13(6), 1504–1511 (2007)

    Google Scholar 

  41. Nedjati-Gilani, S., Alexander, D.C.: Fanning and bending sub-voxel structures in diffusion MRI. In Proceedings International Society of Magnetic Resonance in Medicine (ISMRM), p. 1402 (2009)

    Google Scholar 

  42. Nedjati-Gilani, S., Alexander, D.C., Parker, G.J.M.: Regularized super-resolution for diffusion MRI. In Proceedings of IEEE International Symposium on Biomedical Imaging (ISBI), pp. 875–878 (2008)

    Google Scholar 

  43. Pajevic, S., Basser, P.J.: Parametric and non-parametric statistical analysis of DT-MRI data. J. Magn. Reson. 161(1), 1–14 (2003)

    Article  Google Scholar 

  44. Parker, G.J.M., Alexander, D.C.: Probabilistic monte carlo based mapping of cerebral connections utilising whole-brain crossing fibre information. In: Taylor, C.J., Noble, J.A. (eds.) Information Processing in Medical Imaging. Lecture Notes in Computer Science, vol. 2732, pp. 684–695. Springer, Berlin (2003)

    Google Scholar 

  45. Parker, G.J.M., Haroon, H.A., Wheeler-Kingshott, C.A.M.: A framework for a streamline-based probabilistic index of connectivity (pico) using a structural interpretation of MRI diffusion measurements. J. Magn. Reson. Imaging 18, 242–254 (2003)

    Google Scholar 

  46. Peled, S., Friman, O., Jolesz, F., Westin, C.-F.: Geometrically constrained two-tensor model for crossing tracts in DWI. Magn. Reson. Imaging 24(9), 1263–1270 (2006)

    Google Scholar 

  47. Peled, S., Yeshurun, Y.: Superresolution in MRI: application to human white matter fiber tract visualization by diffusion tensor imaging. Magn. Reson. Med. 45, 29–35 (2001)

    Article  Google Scholar 

  48. Peled, S., Yeshurun, Y.: Superresolution in MRI—perhaps sometimes. Magn. Reson. Med. 48, 409 (2002)

    Article  Google Scholar 

  49. Pfefferbaum, A., Adalsteinsson, E., Sullivan, E.V.: Replication of diffusion tensor imaging measurements of fractional anisotropy and trace in brain. J. Magn. Reson. Imaging 18, 427–433 (2003)

    Article  Google Scholar 

  50. Qazi, A.A., Radmanesh, A., O’Donnell, L., Kindlmann, G., Peled, S., Whalen, S., Westin, C.-F., Golby, A.J.: Resolving crossings in the corticospinal tract by two-tensor streamline tractography: method and clinical assessment using fMRI. NeuroImage, 47(Supplement 2), T98–T106 (2009, in press)

    Google Scholar 

  51. Scheffler, K.: Superresolution in MRI? Magn. Reson. Med. 48, 408 (2002)

    Article  Google Scholar 

  52. Scherrer, B., Gholipour, A., Warfield, S.K.: Super-resolution in diffusion-weighted imaging. In: Fichtinger, G., Martel, A., Peters, T. (eds.) Proceedings of Medical Image Computing and Computer-Assisted Intervention (MICCAI). Lecture Notes in Computer Science, vol. 6892, pp. 124–132. Springer, Berlin (2011)

    Google Scholar 

  53. Schultz. T.: Feature extraction for visual analysis of DW-MRI data. Ph.D. thesis, Universität des Saarlandes (2009)

    Google Scholar 

  54. Schultz, T: Learning a reliable estimate of the number of fiber directions in diffusion MRI. In: Ayache, N. et al. (eds.) Proceedings of Medical Image Computing and Computer-Assisted Intervention (MICCAI), pp. 493–500 (2012) (Part III volume 7512 of LNCS)

    Google Scholar 

  55. Schultz, T., Schlaffke, L., Schölkopf, B., Schmidt-Wilcke, T.: HiFiVE: a Hilbert space embedding of fiber variability estimates for uncertainty modeling and visualization. Comput. Graph. Forum 32(3), 121–130 (2013)

    Article  Google Scholar 

  56. Schultz, T., Seidel, H.P.: Estimating crossing fibers: a tensor decomposition approach. IEEE Trans. Visual. Comput. Graph. 14(6):1635–1642 (2008)

    Google Scholar 

  57. Schultz, T., Theisel, H., Seidel, H.P.: Topological visualization of brain diffusion MRI data. IEEE Trans. Visual. Comput. Graph. 13(6), 1496–1503 (2007)

    Google Scholar 

  58. Schultz, T., Westin, C.F., Kindlmann, G.: Multi-diffusion-tensor fitting via spherical deconvolution: a unifying framework. In Jiang, T. et al. (eds.) Proceedings of Medical Image Computing and Computer-Assisted Intervention (MICCAI), pp. 673–680. Springer, Berlin (2010) (vol. 6361 of Lecture Notes in Computer Science)

    Google Scholar 

  59. A.J. Sherbondy, R.F. Dougherty, M. Ben-Shachar, S. Napel, and B. Wandell. Contrack: Finding the most likely pathways between brain regions using diffusion tractography. Journal of Vision, 8:1, 2008.

    Google Scholar 

  60. Sotiropoulos, S.N., Jbabdi, S., Xu, J., Andersson, J.L., Moeller, S., Auerbach, E.J., Glasser, M.F., Hernandez, M., Sapiro, M., Jenkinson, M., Feinberg, D.A., Yacoub, E., Lenglet, C., Van Essen, D.C., Ugurbil, K., Behrens, T.E.J.: Advances in diffusion MRI acquisition and processing in the human connectome project. NeuroImage. doi:10.1016/j.neuroimage.2013.05.057 (2013)

  61. Tensaouti, F., Lahlou, I., Clarisse, P., Lotterie, J.A., Berry, I.: Quantitative and reproducibility study of four tractography alorithms used in clinical routine. Journal of Magnetic Resonance Imaging 34, 165–172 (2011)

    Article  Google Scholar 

  62. Tournier, J.D., Calamante, F., Connelly, A.: Non-negativity constrained super-resolved spherical deconvolution: robust determination of the fibre orientation distribution in diffusion MRI. NeuroImage 35, 1459–1472 (2007)

    Google Scholar 

  63. Voineskos, A.N., O’Donnell, L.J., Lobaugh, N.J., Markant, D., Ameis, S.H., Niethammer, M., Mulsant, B.H., Pollock, B.G., Kennedy, J.L., Westin, C.-F., Shenton, M.E.: Quantitative examination of a novel clustering method using magnetic resonance diffusion tensor tractography. NeuroImage 45(2), 370–376 (2009)

    Article  Google Scholar 

  64. Vollmar, C., O’Muircheartaigh, J., Barker, G.J., Symms, M.R., Thompson, P., Kumari, V., Duncan, J.S., Richardson, M.P., Koepp, M.J.: Identical, but not the same: intra-site and inter-site reproducibility of fractional anisotropy measures on two 3.0 T scanners. NeuroImage 51(4), 1384–1394 (2010)

    Article  Google Scholar 

  65. Wakana, S., Caprihan, A., Panzenboeck, M.M., Fallon, J.H., Perry, M., Gollub, R.L., Hua, K., Zhang, J., Jiang, H., Dubey, P., Blitz, A., van Zijl, P., Mori, S.: Reproducibility of quantitative tractography methods applied to cerebral white matter. NeuroImage 36, 630–644 (2007)

    Article  Google Scholar 

  66. Westin, C.F., Peled, S., Gubjartsson, H., Kikinis, R., Jolesz, F.A.: Geometrical diffusion measures for MRI from tensor basis analysis. In Proceedings of International Society of Magnetic Resonance in Medicine (ISMRM) (1997)

    Google Scholar 

  67. Whitcher, B., Tuch, D.S., Wisco, J.J., Gregory Sorenson, A., Wang, L.: Using the wild bootstrap to quantify uncertainty in DTI. Human Brain Map. 29(3), 346–362 (2008)

    Article  Google Scholar 

  68. Wu, J.S., Mao, Y., Zhou, L.F., Tang, W.J., Hu, J., Song, Y.Y., Hong, X.N., Du, G.H.: Clinical evaluation and follow-up outcome of diffusion tensor imaging-based functional neuronavigation: a prospective, controlled study in patients with gliomas involving pyramidal tracts. Neurosurgery 61(5), 935–949 (2007)

    Google Scholar 

  69. Zheng, X., Pang, A.: HyperLIC. In Proceedings of IEEE Visualization, pp. 249–256 (2003)

    Google Scholar 

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Schultz, T., Vilanova, A., Brecheisen, R., Kindlmann, G. (2014). Fuzzy Fibers: Uncertainty in dMRI Tractography. In: Hansen, C., Chen, M., Johnson, C., Kaufman, A., Hagen, H. (eds) Scientific Visualization. Mathematics and Visualization. Springer, London. https://doi.org/10.1007/978-1-4471-6497-5_8

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