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Visualization in Medicine and Life Sciences II pp 173–190Cite as

Enhanced DTI Tracking with Adaptive Tensor Interpolation

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

Abstract

A novel tensor interpolation method is introduced that allows Diffusion Tensor Imaging (DTI) streamlining to overcome low-anisotropy regions and permits branching of trajectories using information gathered from the neighbourhood of low-anisotropy voxels met during the tracking. The interpolation method is performed in Log-Euclidean space and collects directional information in a spherical neighbourhood of the voxel in order to reconstruct a tensor with a higher linear diffusion coefficient than the original. The weight of the contribution of a certain neighbouring voxel is proportional to its linear diffusion coefficient and inversely proportional to a power of the spatial Euclidean distance between the two voxels. This inverse power law provides our method with robustness against noise. In order to resolve multiple fiber orientations, we divide the neighbourhood of a lowanisotropy voxel in sectors, and compute an interpolated tensor in each sector. The tracking then continues along the main eigenvector of the reconstructed tensors.

We test our method on artificial, phantom and brain data, and compare it with (a) standard streamline tracking, (b) the Tensorlines method, (c) streamline tracking after an interpolationmethod based on bilateral filtering, and (d) streamline tracking using moving least square regularisation. It is shown that the new method compares favourably with these methods in artificial datasets. The proposed approach gives the possibility to explore a DTI dataset to locate singularities as well as to enhance deterministic tractography techniques. In this way it allows to immediately obtain results more similar to those provided by more powerful but computationally much more demanding methods that are intrinsically able to solve crossing fibers, such as probabilistic tracking or high angular resolution diffusion imaging.

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References

  1. Alexander, A.: Analysis of partial volume effects in diffusion tensor MRI. Magn. Reson. Med. 45(5),770-780 (2001)

    Article  Google Scholar 

  2. Alexander, D.C.: Multiple-fiber reconstruction algorithms for diffusion MRI. Annals N Y Acad Sci 1064, 113-133 (2005)

    Article  Google Scholar 

  3. Arsigny, V., Fillard, P., Pennec, X., Ayache, N.: Log-Euclidean metrics for fast and simple calculus on diffusion tensors. Magn. Reson. Med. 56(2), 411-421 (2006)

    Article  Google Scholar 

  4. Bammer, R., Acar, B., Moseley, M.E.: In vivo MR tractography using diffusion imaging. Eur. J. Radiol. 45(3), 223-234 (2003)

    Article  Google Scholar 

  5. Basser, P.J., Mattiello, J., Bihan, D.L.: Estimation of the effective self-diffusion tensor from the NMR spin-echo. J. Magn. Reson. 103(3), 247-254 (1994)

    Article  Google Scholar 

  6. Basser, P.J., Pajevic, S., Pierpaoli, C., Duda, J., Aldroubi, A.: In vivo fiber tractography using DT-MRI data. Magn. Reson. Med. 44(4), 625-632 (2000)

    Article  Google Scholar 

  7. Basser, P.J., Pierpaoli, C.: Microstructural and physiological features of tissues elucidated by quantitative-diffusion-tensor MRI. J. Magn. Reson. 111(3), 209-219 (1996)

    Article  Google Scholar 

  8. Beaulieu, C.: The basis of anisotropic water diffusion in the nervous system - a technical review. Nucl. Magn. Res. in Biomed. 15(7-8), 435-455 (2002)

    Google Scholar 

  9. Behrens, T., Johansen-Berg, H., Jabdi, S., Rushworth, M.F., Woolrich, M.W.: Probabilistic diffusion tractography with multiple fibre orientations: What can we gain? Neuroimage 34(1), 144-155 (2007)

    Article  Google Scholar 

  10. 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. in Medicine 50(5), 1077-1088 (2003)

    Article  Google Scholar 

  11. Bergmann, O., Kindlmann, G., Peled, S., Westin, C.F.: Two-tensor fiber tractography. In: Proc. ISBI, 796-799 (2007)

    Google Scholar 

  12. Castano-Moraga, C., Rodrigues-Florido, M.A., Alvarez, L., Westin, C.F., Ruiz-Alzola, J.: Anisotropic interpolation of DT-MRI data. In: Proc. MICCAI, 343-350 (2004)

    Google Scholar 

  13. Chefd’hotel, C., Tschumperlé, D., Deriche, R., Faugeras, O.: Regularizing flows for constrained matrix-valued images. J. Math. Imaging Vision 20(1-2), 147-162 (2004). DOI http://dx.doi.org/10.1023/B:JMIV.0000011324.14508.fb

    Article  MathSciNet  Google Scholar 

  14. Conturo, T.E., Lori, N.F., Cull, T.S., Akbudak, E., Snyder, A.Z., Shimony, J.S., McKinstry, R.C., Burton, H., Raichle, M.E.: Tracking neuronal fiber pathways in the living human brain. Proc. Natl. Acad. Sci. USA 96(18), 10,422-10,427 (1999)

    Article  Google Scholar 

  15. Corouge, I., Fletcher, P., Joshi, S., Gouttard, S., Gerig, G.: Fiber tract-oriented statistics for quantitative diffusion tensor MRI analysis. Med. Image Anal. 10(5), 786-798 (2006)

    Article  Google Scholar 

  16. Coulon, O., Alexander, D.C., Arridge, S.A.: A regularization scheme for diffusion tensor magnetic resonance images. In: Proc. of the 17th Int. Conf. Inf. Proc. Med. Imag., vol. 2082, 92-105 (2001)

    Google Scholar 

  17. Feddern, C., Weickert, J., Burgeth, B., Welk, M.: Curvature-driven PDE methods for matrix- valued images. Int. J. Comput. Vision 69(1), 93-107 (2006). DOI http://dx.doi.org/10.1007/s11263-006-6854-8

  18. Hahn, K., Pigarin, S., Putz, B.: Edge preserving regularization and tracking for diffusion tensor imaging. In: MICCAI, vol. 2208, 195-203 (2001)

    Google Scholar 

  19. Hamarneh, G., Hradsky, J.: Bilateral filtering of diffusion tensor magnetic resonance images. IEEE Trans Image Process. 16(10), 2463-2475 (2007)

    Google Scholar 

  20. Hlawitschka, M., Scheuermann, G.: HOT- Lines: Tracking lines in higher order tensor fields. In: Proc. IEEE Visualization, 27-34 (2005)

    Google Scholar 

  21. Jalba, A., Roerdink, J.B.T.M.: Efficient surface reconstruction using generalized Coulomb potentials. IEEE Trans. Vis. Comput. Graph. 13(6), 1512-1519 (2007)

    Article  Google Scholar 

  22. Jones, D.K.: Determining and visualizing uncertainty in estimates of fiber orientation from diffusion tensor MRI. Magn. Reson. Med. 49(1), 7-12 (2003)

    Article  Google Scholar 

  23. Jones, D.K.: Studying connections in the living human brain with diffusion MRI. Cortex 44(8), 936-952 (2008)

    Article  Google Scholar 

  24. Jones, D.K., Simmons, A., Williams, S.C.R., Horsfield, M.A.: Non-invasive assessment of axonal fiber connectivity in the human brain via diffusion tensor MRI. Magn. Res. Med. 42(1), 37-41 (1999)

    Article  Google Scholar 

  25. Kanaan, R.A.A., Kim, J.S., Kaufmann, W.E., Pearlson, G.D., Barker, G.J., McGuire, P.K.: Diffusion tensor imaging in schizophrenia. Bio. Psychiatry 58(12), 921-929 (2005)

    Google Scholar 

  26. Kingsley, P.B.: Introduction to diffusion tensor imaging mathematics: Part I. tensors, rotations, and eigenvectors. Concepts in Magn. Reson 28A(2), 101-122 (2005)

    Google Scholar 

  27. Koch, M.A., Norris, D.G., Hund-Georgiadis, M.: An investigation of functional and anatomical connectivity using magnetic resonance imaging. NeuroImage 16(1), 241-250 (2002)

    Article  Google Scholar 

  28. Lazar, M., Weinstein, D.M., Tsuruda, J.S., Hasan, K.M., Arfanakis, K., Meyerand, M.E., Badie, B., Rowley, H.A., Haughton, V., Field, A., Alexander, L.A.: White matter tractography using diffusion tensordeflection. Human Brain Ma 18(4), 306-321 (2003)

    Article  Google Scholar 

  29. McGraw, T., Nadar, M.: Stochastic DT-MRI connectivity mapping on the GPU. IEEE Trans. Vis. Comp. Graphics 13(6), 1504-1511 (2007)

    Article  Google Scholar 

  30. Mori, S., Crain, B.J., Chacko, V.P., vanZijl, P.C.: Three dimensional tracking of axonal projections in the brain by magnetic resonance imaging. Ann. Neurol. 45(2), 265-269 (1999)

    Google Scholar 

  31. Parker, G.J., Haroon, H.A., Wheeler-Kingshott, C.A.: 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)

    Article  Google Scholar 

  32. Parker, G.J.M., Stephan, K.E., Barker, G.J., Rowe, J.B., MacManus, D.G., Wheeler-Kingshott, C.A.M., Ciccarelli, O., Passingham, R.E., Spinks, R.L., Lemon, R.N., Turner, R.: Inizial demonstration of in vivo tracing of axonal projections in the macaque brain and comparison with the human brain using tensor imaging and fast marching tractography. NeuroImage 15(4), 797-809 (2002)

    Article  Google Scholar 

  33. Parker, G.J.M., Wheeler-Kingshott, C.A.M., Barker, G.J.: Estimating distributed anatomical connectivity using fast marching methods and diffusion tensor imaging. IEEE Trans. Med. Imaging 21(5), 505-51 (2002)

    Article  Google Scholar 

  34. Pennec, X., Fillard, P., Ayache, N.: A Riemannian framework for tensor computing. Int. J. Comput. Vis. 66(1), 41-66 (2004)

    Article  Google Scholar 

  35. Pierpaoli, C., Jezzard, P., Basser, P.J., Barnett, A., DiChiro, G.: Diffusion tensor MR imaging of the human brain. Radiology 201(3), 637-648 (1996)

    Google Scholar 

  36. Poupon, C., Mangin, J., Frouin, V., Regis, J., Poupon, F., Pachot-Clouard, M., Bihan, D.L., Bloch, I.: Regularization of MR diffusion tensor maps for tracking brain white matter bundles. In: MICCAI, 489-498 (1998)

    Google Scholar 

  37. Poupon, C., Mangin, J.F., Clark, C.A., Frouin, V., Regis, J., Bihan, D.L., Bloch, I.: Towards inference of human brain connectivity from MR diffusion tensor data. Med. Image Anal. 5(2), 1-15 (2001)

    Article  Google Scholar 

  38. Sethian, A.: A fast marching level set method for monotonically advancing fronts. Prod. Natl. Acad. Sci. USA 93(4), 1591-1955 (1996)

    Article  MathSciNet  MATH  Google Scholar 

  39. Smith, S.M., Jenkinson, M., Woolrich, M.W., Beckmann, C.F., Behrens, T.E., Johansen-Berg, H., Bannister, P.R., Luca, M.D., Drobnjak, I., Flitney, D.E., Niazy, R.K., Saunders, J., Vickers, J., Zhang, Y., Stefano, N.D., Brady, J.M., Matthews, P.M.: Advances in functional and structural MR image analysis and implementation as FSL. NeuroImage 23(Supplement 1), 208-219 (2004). Mathematics in Brain Imaging

    Google Scholar 

  40. Sotiropoulos, S., Bai, L., Morgan, P.S., Auer, D.P., Constantinescu, C.S., Tench, C.R.: A regularized two-tensor model fit to low angular resolution diffusion images using basis directions. J. Magn. Reson. Imag. 28(1), 199-209 (2008)

    Google Scholar 

  41. Staempfli, P., Jaermann, T., Crelier, G.R., Kollias, S., Valavanis, A., Boesiger, P.: Resolving fiber crossing using advanced fast marching tractography based on diffusion tensor imaging. NeuroImage 30(1), 110-120 (2006)

    Google Scholar 

  42. Tschumperlé, D., Deriche, R., Deriche, R.: Diffusion tensor regularization with constraint spreservation. In: IEEE Computer Society Conference on Computer Vision and Pattern Recognition, vol. 1, 948-953 (2001)

    Google Scholar 

  43. Tuch, D.S.: Q-ball imaging. Magn. Reson. Med. 52(6), 1358-1372 (2004)

    Article  Google Scholar 

  44. Tuch, D.S., Reese, T.G., Wiegell, M.R., Makris, N., Belliveau, J.W., Wedeen, V.J.: High angular resolution diffusion imaging reveals intra voxel white matter fiber heterogeneity. Magn. Reson. Med. 48, 577-582 (2002)

    Article  Google Scholar 

  45. Walker, J.C., Guccione, J.M., Jiang, Y., Zhang, P., Wallace, A.W., Hsu, E.W., Ratcliffe, M.B.: Helical myofiber orientation after myocardial infraction and left ventricular surgical restoration in sheep. J. Thoracic Cardiov. Surgery 129(2), 382-390 (2005)

    Google Scholar 

  46. Watts, R., Liston, C., Niogi, S., Ulug, A.M.: Fiber tracking using magnetic resonance diffusion tensor imaging and its applications to human brain development. Ment. Retar. Dev. Disabil. Res. Rev. 9(3), 168-177 (2003)

    Article  Google Scholar 

  47. Wedeen, V.J., Hagmann, P., Tseng, W.Y., Reese, T.G., Weisskoff, R.M.: Mapping complex tissue architecture with diffusion spectrum magnetic resonance imaging. Magn. Res. Med. 54 (6),1377-1386 (2005)

    Article  Google Scholar 

  48. Weinstein, D.M., Kindlmann, G.L., Lundberg, E.C.: Tensorlines: Advection-diffusion based propagation through diffusion tensor fields. In: IEEE Visualization, 249-253 (1999)

    Google Scholar 

  49. Welk, M., Weickert, J., Becker, F., Schorr, C., Feddern, C., Burgeth, B.: Median and related local filters for tensor-valued images. Signal Process. 87(2), 291-308 (2007)

    Article  MATH  Google Scholar 

  50. Westin, C.F., Knutson, H.: Tensor field regularization using normalized convolution. In: Proc. 9th Int. Conf. Computer Aided Systems Theory, 564-572 (2003)

    Google Scholar 

  51. Wiegell, M.R., Larsson, H.B., Wedeen, V.J.: Fiber crossing in human brain depicted with diffusion tensor MR imaging. Radiology 217, 897-903 (2000)

    Google Scholar 

  52. Wimberger, D.M., Roberts, T.P., Barkovich, A.J., Prayer, L.M., Moseley, M.E.,, Kucharczyk, J.: Identification of premyelination by diffusion-weighted MRI. J. Comp. Assist. Tomogr. 19 (1),28-33 (1995)

    Article  Google Scholar 

  53. Zhukov, L., Barr, A.H.: Oriented tensor reconstruction: Tracing neural pathways from diffusion tensor MRI. In: Proc. IEEE Visualization, 378-394 (2002)

    Google Scholar 

  54. Zhukov, L., Barr, A.H.: Heart-muscle fiber reconstruction from diffusion tensor MRI. In: Proc. IEEE Visualization, 79-84 (2003)

    Google Scholar 

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Author information

Authors and Affiliations

  1. Johann Bernoulli Institute for Mathematics and Computer Science, University of Groningen, 407, 9700 AK, Groningen, The Netherlands

    Alessandro Crippa & Jos B. T. M. Roerdink

  2. Institute for Mathematics and Computing Science, Eindhoven University of Technology, 513, 5600 MB, Eindhoven, The Netherlands

    Andrei C. Jalba

Authors
  1. Alessandro Crippa
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  2. Andrei C. Jalba
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  3. Jos B. T. M. Roerdink
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Corresponding author

Correspondence to Jos B. T. M. Roerdink .

Editor information

Editors and Affiliations

  1. Bremen School of Engineering and Science, Jacobs University, 75 05 61, 28725, Bremen, Germany

    Lars Linsen

  2. FB Informatik, Universität Kaiserslautern, 30 49, 67653, Kaiserslautern, Germany

    Hans Hagen

  3. Institute for Data Analysis and Visualization Department of Computer Science, University of California, Davis, One Shields Avenue, Davis, CA, 95616-8562, USA

    Bernd Hamann

  4. Visualization and Data Analysis, Zuse Institute Berlin (ZIB), Takustr. 7, 14195, Berlin, Germany

    Hans-Christian Hege

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Crippa, A., Jalba, A.C., Roerdink, J.B.T.M. (2012). Enhanced DTI Tracking with Adaptive Tensor Interpolation. In: Linsen, L., Hagen, H., Hamann, B., Hege, HC. (eds) Visualization in Medicine and Life Sciences II. Mathematics and Visualization. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-21608-4_10

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