Magnetic Resonance Imaging
Volume 24, Issue 5 , Pages 569-582 , June 2006

A statistical framework for the classification of tensor morphologies in diffusion tensor images

  • Hongtu Zhu

      Affiliations

    • MRI Unit, Department of Psychiatry, Columbia University Medical Center, USA
    • Department of Child Psychiatry, The New York State Psychiatric Institute, New York, NY 10032, USA
    • Corresponding Author InformationCorresponding author. Department of Child Psychiatry, The New York State Psychiatric Institute, New York, NY 10032, USA. Tel.: +1 212 543 5207; fax: +1 212 543 6660.
  • ,
  • Dongrong Xu

      Affiliations

    • MRI Unit, Department of Psychiatry, Columbia University Medical Center, USA
    • Department of Child Psychiatry, The New York State Psychiatric Institute, New York, NY 10032, USA
  • ,
  • Amir Raz

      Affiliations

    • MRI Unit, Department of Psychiatry, Columbia University Medical Center, USA
    • Department of Child Psychiatry, The New York State Psychiatric Institute, New York, NY 10032, USA
  • ,
  • Xuejun Hao

      Affiliations

    • MRI Unit, Department of Psychiatry, Columbia University Medical Center, USA
    • Department of Child Psychiatry, The New York State Psychiatric Institute, New York, NY 10032, USA
  • ,
  • Heping Zhang

      Affiliations

    • Department of Epidemiology and Public Health, Yale University School of Medicine, New Haven, CT 06520-8034, USA
  • ,
  • Alayar Kangarlu

      Affiliations

    • MRI Unit, Department of Psychiatry, Columbia University Medical Center, USA
    • Department of Child Psychiatry, The New York State Psychiatric Institute, New York, NY 10032, USA
  • ,
  • Ravi Bansal

      Affiliations

    • MRI Unit, Department of Psychiatry, Columbia University Medical Center, USA
    • Department of Child Psychiatry, The New York State Psychiatric Institute, New York, NY 10032, USA
  • ,
  • Bradley S. Peterson

      Affiliations

    • MRI Unit, Department of Psychiatry, Columbia University Medical Center, USA
    • Department of Child Psychiatry, The New York State Psychiatric Institute, New York, NY 10032, USA

Received 22 October 2005 ,Accepted 16 January 2006.

References 

  1. Basser PJ, Mattiello J, LeBihan D. Estimation of the effective self-diffusion tensor from the NMR spin echo. J Magn Reson B. 1994;103:247–254
  2. Basser PJ, Mattiello J, LeBihan D. MR diffusion tensor spectroscopy and imaging. Biophys J. 1994;66:259–267
  3. Mori S. Principles, methods, and applications of diffusion tensor imaging. In:  Toga AW,  Mazziotta JC editor. Brain mapping: the methods. 2nd ed.. San Diego: Academic Press; 2002;p. 379–397
  4. Conturo TE, Lori NF, Cull TS, Akbudak E, Snyder AZ, Shimony JS, et al. Tracking neuronal fiber pathways in the living human brain. Proc Natl Acad Sci U S A. 1999;96:10422–10427
  5. Xue R, van Zijl PC, Crain BJ, Solaiyappan M, Mori S. In vivo three-dimensional reconstruction of rat brain axonal projections by diffusion tensor imaging. Magn Reson Med. 1999;42:1123–1127
  6. Xu D, Mori S, Solaiyappan M, van Zijl PC, Davatzikos C. A framework for callosal fiber distribution analysis. Neuroimage. 2002;17:1131–1143
  7. Catani M, Howard RJ, Pajevic S, Jones DK. Virtual in vivo dissection of white matter fasciculi in the human brain. Neuroimage. 2002;17:77–94
  8. Poupon C, Clark A, Frouin V, Regis J, Bihan DL, Bloch I, et al. Regularization of diffusion-based direction maps for the tracking of brain white matter fascicles. Neuroimage. 2000;12:184–195
  9. Stieltjes B, Kaufmann WE, van Zijl PCM, Fredericksen K, Pearlson GD, Solaiyappan M, et al. Diffusion tensor imaging and axonal tracking in the human brainstem. Neuroimage. 2001;14:723–735
  10. Lazar M, Weinstein DM, Tsuruda JS, Hasan KM, Arfanakis K, Meyerand EM, et al. White matter tractography using tensor deflection. Hum Brain Mapp. 2003;18:306–321
  11. Behrens TEJ, Johansen-Berg H, Woolrich MW, Smith SM, Wheeler-Kingshott CAM, Boulby PA, et al. Noninvasive mapping of connections between human thalamus and cortex using diffusion imaging. Nat Neurosci. 2003;6:750–757
  12. Pierpaoli C, Basser PJ. Toward a quantitative assessment of diffusion anisotropy. Magn Reson Med. 1996;36:893–906
  13. Martin KM, Papadakis NG, Huang CLH, Hall LD, Carpenter TA. The reduction of the sorting bias in the eigenvalues of the diffusion tensor. Magn Reson Imaging. 1999;17:893–901
  14. Basser PJ, Pajevic S. Dealing with uncertainty in diffusion tensor MR data. Isr J Chem. 2003;43:129–144
  15. Skare S, Li TQ, Nordell B, Ingvar M. Noise considerations in the determination of diffusion tensor anisotropy. Magn Reson Imaging. 2000;18:659–669
  16. Jones DK. Determining and visualizing uncertainty in estimates of fiber orientation from diffusion tensor MRI. Magn Reson Med. 2003;49:7–12
  17. Jones DK. The effect of gradient sampling schemes on measures derived from diffusion tensor MRI: a Monte Carlo study. Magn Reson Med. 2004;51:807–815
  18. Barrick TR, Clark CA. Singularities in diffusion tensor fields and their relevance in white matter fiber tractography. Neuroimage. 2004;22:481–491
  19. Basser PJ. New histological and physiological stains derived from diffusion-tensor MR images. Ann N Y Acad Sci. 1997;820:123–138
  20. Hasan KM, Basser PJ, Parker DL, Alexander AL. Analytical computation of the eigenvalues and eigenvectors in DT-MRI. J Magn Reson. 2001;152:41–47
  21. Wu YC, Field AS, Chung MK, Badie B, Alexander AL. Quantitative analysis of diffusion tensor orientation: theoretical framework. Magn Reson Med. 2004;52:1146–1155
  22. Westin CF, Peled S, Gudbjartsson H, Kikinis R, Jolesz FA. Geometrical diffusion measures for MRI from tensor basis analysis. In: Proceedings of the 5th Annual Meeting of ISMRM, Vancouver. 1997;p. 1742
  23. Mori S, van Zijl PCM. Fiber tracking: principles and strategies — a technical review. NMR Biomed. 2002;15:468–480
  24. Anderson AW. Theoretical analysis of the effects of noise on diffusion tensor imaging. Magn Reson Med. 2001;46:1174–1188
  25. Stejskal EO, Tanner JE. Spin diffusion measurements: spin echoes in the presence of a time-dependent field gradient. J Chem Phys. 1965;42:288–292
  26. Henkelman RM. Measurement of signal intensities in the presence of noise in MR images. Med Phys. 1985;12:232–233[Erratum. Med Phys 1986;13:544]
  27. Gudbjartsson H, Patz S. The Rician distribution of noisy MRI data. Magn Reson Med. 1995;34:910–914[Letter, response, and erratum. Magn Reson Med 1996;36:331-333]
  28. White H. A heteroskedasticity-consistent covariance matrix estimator and a direct test for heteroskedasticity. Econometrica. 1980;48:817–838
  29. MacKinnon JG, White H. Some heteroskedasticity consistent covariance matrix estimators with improved finite sample properties. J Econom. 1985;29:305–325
  30. Borisenko AI, Tarapov IE. Vector and tensor analysis with applications. Dover: New York; 1968;
  31. Hasan KM, Narayana PA. Computation of the fractional anisotropy and mean diffusivity maps without tensor decoding and diagonalization: theoretical analysis and validation. Magn Reson Med. 2003;50:589–598
  32. Alexander AL, Hasan K, Kindlmann G, Parker DL, Tsuruda JS. A geometric analysis of diffusion tensor measurements of the human brain. Magn Reson Med. 2000;44:283–291
  33. Hardin RH, Sloane NJA, Smith WD. Minimal energy arrangements of points on a sphere with minimal 1/r potential. http://www.research.att.com/~njas/electrons/
  34. Tuch DS, Reese TG, Wiegell MR, Makris N, Belliveau JW, Wedeen VJ. High angular resolution diffusion imaging reveals intravoxel white matter fiber heterogeneity. Magn Reson Med. 2002;48:577–582
  35. Alexander AL, Hasan KM, Lazar M, Tsuruda JS, Parker DL. Analysis of partial volume effects in diffusion-tensor MRI. Magn Reson Med. 2001;45:770–780
  36. Alexander DC, Barker GJ, Arridge SR. Detection and modelling of non-Gaussian apparent diffusion coefficient profiles in human brain data. Magn Reson Med. 2002;48:331–340
  37. Frank LR. Characterization of anisotropy in high angular resolution diffusion-weighted MRI. Magn Reson Med. 2002;47:1083–1099
  38. Frank LR. Anisotropy in high angular resolution diffusion weighted MRI. Magn Reson Med. 2001;45:935–939
  39. Smith SM. Fast robust automated brain extraction. Human Brain Mapp. 2002;17:143–155
  40. Efron B. Bootstrap methods: another look at the jacknife. Ann Stat. 1979;7:1–26
  41. Efron B, Tibshirani RJ. An Introduction to the Bootstrap. London: Chapman and Hall; 1993;
  42. Pajevic S, Basser PJ. Parametric and non-parametric statistical analysis of DT-MRI data. J Magn Reson. 2003;161:1–14
  43. Boos DD. Introduction to the Bootstrap world. Stat Sci. 2003;18:168–174
  44. Papadakis NG, Xing D, Houston GC, Smith JM, Smith MI, James F, et al. A study of rotationally invariant and symmetric indices of diffusion anisotropy. Magn Reson Imaging. 1999;17:881–892
  45. Eicker F. Asymptotic normality and consistency of the least squares estimators for families of linear regressions. Ann Math Stat. 1963;34:447–456
  46. van der Vaart AW. Asymptotic statistics. Cambridge: Cambridge University Press; 1998;
  47. Chou CP, Bentler PM, Satorra A. Scaled test statistics and robust standard errors for non-normal data in covariance structure analysis: a Monte Carlo study. Br J Math Stat Psychol. 1991;44:347–357

PII: S0730-725X(06)00031-2

doi: 10.1016/j.mri.2006.01.004

Magnetic Resonance Imaging
Volume 24, Issue 5 , Pages 569-582 , June 2006