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Diffusion-tensor MRI: theory, experimental design and data analysis – a technical review

  1. Peter J. Basser1,*,
  2. Derek K. Jones2

Article first published online: 5 DEC 2002

DOI: 10.1002/nbm.783

Issue

NMR in Biomedicine

NMR in Biomedicine

Special Issue: Diffusion tensor imaging and axonal mapping - state of the art

Volume 15, Issue 7-8, pages 456–467, November - December 2002

Additional Information

How to Cite

Basser, P. J. and Jones, D. K. (2002), Diffusion-tensor MRI: theory, experimental design and data analysis – a technical review. NMR Biomed., 15: 456–467. doi: 10.1002/nbm.783

Author Information

  1. 1

    Section on Tissue Biophysics and Biomimetics, NICHD, National Institutes of Health, Bethesda, MD, USA

  2. 2

    Section of Old Psychiatry, Institute of Psychiatry, London, UK

*Section on Tissue Biophysics and Biomimetics, NICHD, National Institutes of Health, Bethesda, Maryland, 20892, USA

Publication History

  1. Issue published online: 5 DEC 2002
  2. Article first published online: 5 DEC 2002
  3. Manuscript Accepted: 9 JAN 2002
  4. Manuscript Revised: 8 JAN 2002
  5. Manuscript Received: 16 NOV 2001

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REFERENCES

  • 1
    Basser PJ. Inferring microstructural features and the physiological state of tissues from diffusion-weighted images. NMR Biomed. 1995; 8: 333–344.
    Direct Link:
  • 2
    Basser PJ. New histological and physiological stains derived from diffusion-tensor MR images. Ann. NY Acad. Sci. 1997; 820: 123–138.
    Direct Link:
  • 3
    Mori S, Barker PB. Diffusion magnetic resonance imaging: its principle and applications. Anat. Rec. 1999; 257(3): 102–109.
    Direct Link:
  • 4
    Le Bihan D. Diffusion and Perfusion Magnetic Resonance Imaging. Raven Press: New York, 1995.
  • 5
    Le Bihan D, Mangin JF, Poupon C, Clark CA, Pappata S, Molko N, Chabriat H. Diffusion tensor imaging: concepts and applications. J. Magn. Reson. Imag. 2001; 13(4): 534–546.
    Direct Link:
  • 6
    Cleveland GG, Chang DC, Hazlewood CF, Rorschach HE. Nuclear magnetic resonance measurement of skeletal muscle: anisotropy of the diffusion coefficient of the intracellular water. Biophys. J. 1976; 16(9): 1043–1053.
  • 7
    Garrido L, Wedeen VJ, Kwong KK, Spencer UM, Kantor HL. Anisotropy of water diffusion in the myocardium of the rat. Circul. Res. 1994; 74(5): 789–793.
  • 8
    Tanner JE. Self diffusion of water in frog muscle. Biophys. J. 1979; 28: 107–116.
  • 9
    Henkelman RM, Stanisz GJ, Kim JK, Bronskill MJ. Anisotropy of NMR properties of tissues. Magn. Reson. Med. 1994; 32(5): 592–601.
    Direct Link:
  • 10
    Moseley ME, Cohen Y, Kucharczyk J, Mintorovitch J, Asgari HS, Wendland MF, Tsuruda J, Norman D. Diffusion-weighted MR imaging of anisotropic water diffusion in cat central nervous system. Radiology 1990; 176(2): 439–445.
  • 11
    Moseley ME, Kucharczyk J, Asgari HS, Norman D. Anisotropy in diffusion-weighted MRI. Magn. Reson. Med. 1991; 19(2): 321–326.
    Direct Link:
  • 12
    Crank J. The Mathematics of Diffusion. Oxford University Press: Oxford, 1975.
  • 13
    Torrey HC. Bloch equations with diffusion terms. Phys. Rev. 1956; 104(3): 563–565.
  • 14
    Bloch F. Nuclear induction. Phys. Rev. 1946; 70: 460–474.
  • 15
    Douglass DC, McCall DW. Diffusion in paraffin hydrocarbons. J. Phys. Chem. 1958; 62: 1102.
  • 16
    Neuman CH. Spin echo of spins diffusing in a bounded medium. J. Chem. Phys. 1974; 60: 4508–4511.
  • 17
    Stejskal EO. Use of spin echoes in a pulsed magnetic-field gradient to study restricted diffusion and flow. J. Chem. Phys. 1965; 43(10): 3597–3603.
  • 18
    Wayne RC, Cotts RM. Nuclear-magnetic-resonance study of self-diffusion in a bounded medium. Phys. Rev. 1966; 151(1): 264–272.
  • 19
    Stejskal EO, Tanner JE. Spin diffusion measurements: spin echoes in the presence of time-dependent field gradient. J. Chem. Phys. 1965; 42(1): 288–292.
  • 20
    Basser PJ, Mattiello J, Le Bihan D. Estimation of the effective self-diffusion tensor from the NMR spin echo. J. Magn. Reson. B 1994; 103(3): 247–254.
  • 21
    Basser PJ, Mattiello J, Le Bihan D. MR diffusion tensor spectroscopy and imaging. Biophys. J. 1994; 66(1): 259–267.
  • 22
    Mattiello J, Basser PJ, Le Bihan D. Analytical expression for the b matrix in NMR diffusion imaging and spectroscopy. J. Magn. Reson. A 1994; 108: 131–141.
  • 23
    Neeman M, Freyer JP, Sillerud LO. Pulsed-gradient spin-echo studies in NMR imaging. Effects of the imaging gradients on the determination of diffusion coefficients. J. Magn. Reson. 1990; 90: 303–312.
  • 24
    Mattiello J, Basser PJ, Le Bihan D. The b matrix in diffusion tensor echo-planar imaging. Magn. Reson. Med. 1997; 37(2): 292–300.
    Direct Link:
  • 25
    Mattiello J, Basser PJ, Le Bihan D. Analytical calculation of the b matrix in diffusion imaging. In Diffusion and Perfusion Magnetic Resonance Imaging, BihanDL. (ed.). Raven Press: New York, 1995; 77–90.
  • 26
    Le Bihan D, Breton E. Imagerie de diffusion in-vivo par resonance magnetique nucleaire. Cr. Acad. Sci. (Paris) 1985; 301: 1109–1112.
  • 27
    Tanner JE. Transient diffusion in system partitioned by permeable barriers. Application to NMR measurements with a pulsed field gradient. J. Chem. Phys. 1978; 69(4): 1748–1754.
  • 28
    Pajevic S, Aldroubi A, Basser PJ. A continuous tensor field approximation of discrete DT-MRI data for extracting microstructural and architectural features of tissues. J. Magn. Reson. 2002; 154(1): 85–100.
  • 29
    Basser PJ, Le Bihan D. Fiber orientation mapping in an anisotropic medium with NMR diffusion spectroscopy. 11th Annual Meeting of the SMRM, Berlin, 1992; 1221.
  • 30
    Kärger J, Pfeifer H, Heink W. Principles and applications of self-diffusion measurements by nuclear magnetic resonance. In Advances in Magnetic Resonance, WaughJ (ed.). Academic Press: New York, 1988; 1–89.
  • 31
    Pierpaoli C, Jezzard P, Basser PJ, Barnett A, Di Chiro G. Diffusion tensor MR imaging of the human brain. Radiology 1996; 201(3): 637–648.
  • 32
    van Gelderen P, Vleeschouwer MHMd, DesPres D, Pekar J, Zijl PCMv, Moonen CTW. Water diffusion and acute stroke. Magn. Reson. Med. 1994; 31: 154–163.
    Direct Link:
  • 33
    Pierpaoli C, Baratti C, Jezzard P. Fast tensor imaging of water diffusion changes in gray and white matter following cardiac arrest in cats. In: Proceedings of the ISMRM, 1–5 April, New York, 1996; 314.
  • 34
    Pierpaoli C, Basser PJ. Toward a quantitative assessment of diffusion anisotropy. [Published erratum appears in Magn. Reson. Med. 1997; 37(6): 972.] Magn. Reson. Med. 1996; 36(6): 893–906.
    Direct Link:
  • 35
    Ulug AM, Beauchamp N, Bryan RN, van Zijl PCM. Absolute quantitation of diffusion constants in human stroke. Stroke 1997; 28: 483–490.
  • 36
    Wong EC, Cox RW. Single-shot imaging with isotropic diffusion weighting. Second Annual Meeting of the SMR, San Francisco, 1994; 136.
  • 37
    Wong EC, Cox RW, Song AW. Optimized isotropic diffusion weighting. Magn. Reson. Med. 1995; 34(2): 139–143.
    Direct Link:
  • 38
    Mori S, van Zijl PC. Diffusion weighting by the trace of the diffusion tensor within a single scan. Magn. Reson. Med. 1995; 33(1): 41–52.
    Direct Link:
  • 39
    Sands DE. Vectors and Tensors in Crystallography, Dover, 1995.
  • 40
    Westin C-F, Maier S, Khidir B, Everett P, Jolesz FA, Kikinis R. Image processing for diffusion tensor magnetic resonance imaging. MICCAI'99, Cambridge, UK. Springer: Berlin, 1994; 441–452.
  • 41
    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.
    Direct Link:
  • 42
    Frank LR. Anisotropy in high angular resolution diffusion-weighted MRI. Magn. Reson. Med. 2001; 45(6): 935–939.
    Direct Link:
  • 43
    Jones DK, Williams SCR, Horsfield MA. Full representation of white-matter fibre direction on one map via diffusion tensor analysis. 5th ISMRM Meeting, Vancouver, 1997; 1743.
  • 44
    Pierpaoli C. Oh no! One more method for color mapping of fiber tract direction using diffusion MR imaging data. 5th ISMRM, Vancouver, 1997; 1741.
  • 45
    Pajevic S, Pierpaoli C. Color schemes to represent the orientation of anisotropic tissues from diffusion tensor data: application to white matter fiber tract mapping in the human brain. Magn. Reson. Med. 2000; 43(6): 921.
    Direct Link:
  • 46
    Makris N, Worth AJ, Sorensen AG, Papadimitriou GM, Wu O, Reese TG, Wedeen VJ, Davis TL, Stakes JW, Caviness VS. and others. Morphometry of in vivo human white matter association pathways with diffusion-weighted magnetic resonance imaging. Ann. Neurol. 1997; 42(6): 951–962.
    Direct Link:
  • 47
    Basser PJ, Pajevic S, Pierpaoli C, Duda J, Aldroubi A. In vivo fiber-tractography in human brain using diffusion tensor MRI (DT-MRI) data. Magn. Reson. Med. 2000; 44(4): 625–632.
    Direct Link:
  • 48
    Basser PJ. Fiber-tractography via diffusion tensor MRI (DT-MRI). 6th ISMRM, Sydney, 1998; 1226.
  • 49
    Wedeen VJ, Davis TL, Weisskoff RM, Tootell R, Rosen BR, Belliveau JW. White matter connectivity explored by MRI. Proceedings of the First International Conference for Functional Mapping of the Human Brain, Paris, 1995; P1.36.
  • 50
    Wedeen VJ. Diffusion anisotropy and white matter tracts. Second Brain Map Meeting, Boston, 1996; P1A4-021.
  • 51
    Mori S, Crain BJ, van Zijl PC. 3D brain fiber reconstruction from diffusion MRI. Proceedings of International Conference on Functional Mapping of the Human Brain, Montreal, 1998.
  • 52
    Jones DK, Simmons A, Williams SCR, Horsfield MA. Non-invasive assessment of structural connectivity in white matter by diffusion tensor MRI. Sixth Annual Meeting of the International Society for Magnetic Resonance in Medicine, ISMRM, 1998; 531.
  • 53
    Jones DK, Simmons A, Williams SC, Horsfield MA. Non-invasive assessment of axonal fiber connectivity in the human brain via diffusion tensor MRI. Magn. Reson. Med. 1999; 42(1): 37–41.
    Direct Link:
  • 54
    Mori S, Crain BJ, Chacko VP, van Zijl PC. Three-dimensional tracking of axonal projections in the brain by magnetic resonance imaging. Ann. Neurol. 1999; 45(2): 265–269.
    Direct Link:
  • 55
    Mori S, Xue R, Crain B, Solaiyappan M, Chacko VP, Zijl PCMv. 3D reconstruction of axonal fibers from diffusion tensor imaging using fiber assignment by continuous tracking (FACT). 8th Annual Meeting of the ISMRM, Philadelphia, 1999; 320.
  • 56
    Mori S, Kaufmann WE, Pearlson GD, Crain BJ, Stieltjes B, Solaiyappan M, van Zijl PC. In vivo visualization of human neural pathways by magnetic resonance imaging. Ann. Neurol. 2000; 47(3): 412–414.
    Direct Link:
  • 57
    Poupon C, Mangin J-F, Frouin V, Regis F, Poupon C, Pachot-Clouard M, Bihan DL, Bloch I. Regularization of MR diffusion tensor maps for tracking brain white matter bundles. Proceedings of MICCAI'98. Springer: Berlin, 1998; 489–498.
  • 58
    Poupon C, Clark CA, Frouin V, Bloch I, Bihan DL, Mangin J-F. Tracking white matter fascicles with diffusion tensor imaging. 8th Annual Meeting of the ISMRM, Philadelphia, 1999; 325.
  • 59
    Poupon C, Mangin J, Clark CA, Frouin V, Regis J, Le Bihan D, Bloch I. Towards inference of human brain connectivity from MR diffusion tensor data. Med. Image Anal. 2001; 5(1): 1–15.
  • 60
    Conturo TE, Lori NF, Cull TS, Akbudak E, Snyder AZ, Shimony JS, McKinstry RC, Burton H, Raichle ME. Tracking neuronal fiber pathways in the living human brain. Proc. Natl Acad. Sci. USA 1999; 96(18): 10422–10427.
  • 61
    Pierpaoli C, Barnett A, Virta A, Penix L, Chen R. Diffusion MRI of Wallerian degeneration. A new tool to investigate neural connectivity in vivo? 6th ISMRM, Sydney, 1998; 1247.
  • 62
    Pierpaoli C, Barnett AS, Pajevic S, Virta A, Basser PJ. Validation of DT-MRI tractography in the descending motor pathways of human subjects. ISMRM, Glasgow, 2001; 501.
  • 63
    Aldroubi A, Basser PJ. Reconstruction of vector and tensor fields from sampled discrete data. In Contemporary Mathematics, BaggettLW, LarsonDR (eds). AMS: Providence, RI, 1999; 1–15.
  • 64
    Jones DK. A least squares continuous diffusion tensor field approximation. NeuroImage 2001; 13: S168.
  • 65
    Zhang S, Curry C, Morris DS, Laidlaw DH. Visualizing diffusion tensor MR images using streamtubes and streamsurfaces. Proceedings of the IEEE Visualization Conference, Utah, 2000.
  • 66
    Tuch DS, Wiegell MR, Reese TG, Belliveau JW, Wedeen VJ. Measuring cortice-cortical connectivity matrices with diffusion spectrum imaging. ISMRM, Glasgow, 2001; 502.
  • 67
    Struik DJ. Lectures on Classical Differential Geometry. Dover: New York, 1961.
  • 68
    Anderson AW, Gore JC. Analysis and correction of motion artifacts in diffusion weighted imaging. Magn. Reson. Med. 1994; 32(3): 379–387.
    Direct Link:
  • 69
    Ordidge RJ, Helpern JA, Qing ZX, Knight RA, Nagesh V. Correction of motional artifacts in diffusion-weighted MR images using navigator echoes. Magn. Reson. Imag. 1994; 12(3): 455–460.
  • 70
    Alexander AL, Tsuruda JS, PD L. Elimination of eddy current artifacts in diffusion-weighted echo-planar images: the use of bipolar gradients. Magn. Reson. Med. 1997; 38: 1016–1021.
    Direct Link:
  • 71
    Papadakis NG, Martin KM, Pickard JD, Hall LD, Carpenter TA, Huang CL. Gradient pre-emphasis calibration in diffusion-weighted echo-planar imaging. Magn. Reson. Med. 2000; 44(4): 616–624.
    Direct Link:
  • 72
    Haselgrove JC, Moore JR. Correction for distortion of echo-planar images used to calculate the apparent diffusion coefficient. Magn. Reson. Med. 1996; 36(6): 960–964.
    Direct Link:
  • 73
    Bastin ME. Correction of eddy current-induced artefacts in diffusion tensor imaging using iterative cross-correlation. Magn. Reson. Imag. 1999; 17(7): 1011–1024.
  • 74
    Jones DK, Horsfield MA, Simmons A. Optimal strategies for measuring diffusion in anisotropic systems by magnetic resonance imaging. Magn. Reson. Med. 1999; 42(3): 515–525.
    Direct Link:
  • 75
    Jezzard P, Barnett AS, Pierpaoli C. Characterization of and correction for eddy current artifacts in echo planar diffusion imaging. Magn. Reson. Med. 1998; 39(5): 801–812.
    Direct Link:
  • 76
    Bammer R, Keeling SL, Augustin M, Pruessman KP, Wolf R, Stollberger R, Hartung H, Fazekas P. Improved diffusion-weighted single-shot echo-planar imaging (EPI) in stroke using sensitivity encoding (SENSE). Magn. Reson. Med. 2001; 46: 548–554.
    Direct Link:
  • 77
    Horsfield MA. Mapping eddy current induced fields for the correction of diffusion-weighted echo planar images. Magn. Reson. Imag. 1999; 17: 1335–1345.
  • 78
    Bastin ME, Armitage PA. On the use of water phantom images to calibrate and correct eddy current induced artefacts in MR diffusion tensor imaging. Magn. Reson. Imag. 2000; 18: 681–687.
  • 79
    Clark CA, Barker GJ, Tofts PS. An in vivo evaluation of the effects of local magnetic susceptibility-induced gradients on water diffusion measurements in human brain. J. Magn. Reson. 1999; 141(1): 52–61.
  • 80
    Basser PJ, Pajevic S. Method to reduce eigenvalue sorting bias in DT-MRI. 7th Annual ISMRM, Philadelphia, 1999; 1788.
  • 81
    Martin KM, Papadakis NG, Huang CL, Hall LD, Carpenter TA. The reduction of the sorting bias in the eigenvalues of the diffusion tensor. Magn. Reson. Imag. 1999; 17(6): 893–901.
  • 82
    Ahrens ET, Laidlaw DH, Readhead C, Brosnan CF, Fraser SE, Jacobs RE. MR microscopy of transgenic mice that spontaneously acquire experimental allergic encephalomyelitis. Magn. Reson. Med. 1998; 40(1): 119–132.
    Direct Link:
  • 83
    Jara H, Wehrli FW. Determination of background gradients with diffusion MR imaging. J. Magn. Reson. Imag. 1994; 4(6): 787–797.
    Direct Link:
  • 84
    Basser PJ. A sensitive method to calibrate magnetic field gradients using the diffusion tensor. Third Meeting of the SMR, Nice, 1995; 308.
  • 85
    Basser PJ, Mattiello J, Le Bihan D. Method and system for measuring the diffusion tensor and for diffusion tensor imaging. US Patent 5,539,310, 23 July 1996.
  • 86
    Papadakis NG, Xing D, Huang CL, Hall LD, Carpenter TA. A comparative study of acquisition schemes for diffusion tensor imaging using MRI. J. Magn. Reson. 1999; 137(1): 67–82.
  • 87
    Hsu EW, Mori S. Analytical expressions for the NMR apparent diffusion-coefficients in an anisotropic system and a simplified method for determining fiber orientation. Magn. Reson. Med. 1995; 32(4): 194–200.
    Direct Link:
  • 88
    Bossart EL, Inglis BA, Buckley DL, Wirth III ED, Mareci TH. Multiple component diffusion tensor imaging in excised fixed CNS tissue. ISMRM, Philadelphia, 1999; 328.
  • 89
    Tuch DS, Weiskoff RM, Belliveau JW, Wedeen VJ. High angular resolution diffusion imaging of the human brain. ISMRM, Philadelphia, 1999; 321.
  • 90
    Le Bihan D, Delannoy J, Levin RL. Temperature mapping with MR imaging of molecular diffusion: application to hyperthermia. Radiology 1989; 171(3): 853–857.
  • 91
    Mills R. Self-diffusion in normal and heavy water in the range ­1–45∞. J. Phys. Chem. 1973; 77(5): 685–688.
  • 92
    Simpson JH, Carr HY. Diffusion and nuclear spin relaxation in water. Phys. Rev. 1958; 111(5): 1201–1202.
  • 93
    Neil JJ, Shiran SI, McKinstry RC, Schefft GL, Snyder AZ, Almli CR, Akbudak E, Aronovitz JA, Miller JP, Lee BC. and others. Normal brain in human newborns: apparent diffusion coefficient and diffusion anisotropy measured by using diffusion tensor MR imaging. Radiology 1998; 209(1): 57–66.
  • 94
    Beaulieu C, Allen PS. Water diffusion in the giant axon of the squid: implications for diffusion-weighted MRI of the nervous system. Magn. Reson. Med. 1994; 32(5): 579–583.
    Direct Link:
  • 95
    Beaulieu C, Allen PS. Determinants of anisotropic water diffusion in nerves. Magn. Reson. Med. 1994; 31(4): 394–400.
    Direct Link:
  • 96
    Wimberger DM, Roberts TP, Barkovich AJ, Prayer LM, Moseley ME, Kucharczyk J. Identification of premyelination by diffusion-weighted MRI. J. Comput. Assist. Tomogr. 1995; 19(1): 28–33.
  • 97
    Le Bihan D, Turner R, Douek P. Is water diffusion restricted in human brain white matter? An echo-planar NMR imaging study. Neuroreport 1993; 47: 887–890.
  • 98
    Clark CA, Le Bihan D. Water diffusion compartmentation and anisotropy at high b values in the human brain. Magn. Reson. Med. 2000; 44(6): 852–859.
    Direct Link:
  • 99
    Mulkern RV, Gudbjartsson H, Westin CF, Zengingonul HP, Gartner W, Guttmann CR, Robertson RL, Kyriakos W, Schwartz R, Holtzman D. and others. Multi-component apparent diffusion coefficients in human brain. NMR Biomed. 1999; 12(1): 51–62.
    Direct Link:
  • 100
    Peled S, Cory DG, Raymond SA, Kirschner DA, Jolesz FA. Water diffusion, T(2), and compartmentation in frog sciatic nerve. Magn. Reson. Med. 1999; 42(5): 911–8.
    Direct Link:
  • 101
    Callaghan PT. Principles of Nuclear Magnetic Resonance Microscopy. Oxford University Press: Oxford 1991.
  • 102
    Callaghan PT, Eccles CD, Xia Y. NMR microscopy of dynamic displacements: k-space and q-space imaging. J. Phys. E: Sci. Instrum. 1988; 21: 820–822.
  • 103
    Tuch DS, Wedeen VJ, Dale AM, George JS, Belliveau JW. Conductivity tensor mapping of the human brain using diffusion tensor MRI. Proc. Natl Acad. Sci. USA 2001; 98(20): 11697–11701.
  • 104
    Pajevic S, Basser PJ. Parametric description of noise in diffusion tensor MRI. 8th Annual Meeting of the ISMRM, Philadelphia, 1999; 1787.
  • 105
    Basser PJ, Pajevic S. Quantitative statistical tests for assessing changes in the trace of the diffusion tensor: clinical and biological implications. 7th Annual ISMRM, Philadelphia, 1999; 1789.
  • 106
    Pajevic S, Basser PJ. Non-parametric statistical analysis of diffusion tensor MRI data using the bootstrap method. 8th Annual Meeting of the ISMRM, Philadelphia, 1999; 1790.
  • 107
    Alexander DC, Basser PJ, Pierpaoli C, Gee JC. Spatial transformations of diffusion tensor Images. IEEE Trans. Med. Imag. 20(11): 1131–1139.
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