Review Article
Free Access
Diffusion-tensor MRI: theory, experimental design and data analysis – a technical review
Peter J. Basser,
Derek K. Jones,
Corresponding Author
Peter J. Basser
Section on Tissue Biophysics and Biomimetics, NICHD, National Institutes of Health, Bethesda, MD, USA
Section on Tissue Biophysics and Biomimetics, NICHD, National Institutes of Health, Bethesda, Maryland, 20892, USASearch for more papers by this authorDerek K. Jones
Section of Old Psychiatry, Institute of Psychiatry, London, UK
Search for more papers by this authorPeter J. Basser,
Derek K. Jones,
Corresponding Author
Peter J. Basser
Section on Tissue Biophysics and Biomimetics, NICHD, National Institutes of Health, Bethesda, MD, USA
Section on Tissue Biophysics and Biomimetics, NICHD, National Institutes of Health, Bethesda, Maryland, 20892, USASearch for more papers by this authorDerek K. Jones
Section of Old Psychiatry, Institute of Psychiatry, London, UK
Search for more papers by this authorAbstract
This article treats the theoretical underpinnings of diffusion-tensor magnetic resonance imaging (DT-MRI), as well as experimental design and data analysis issues. We review the mathematical model underlying DT-MRI, discuss the quantitative parameters that are derived from the measured effective diffusion tensor, and describe artifacts thet arise in typical DT-MRI acquisitions. We also discuss difficulties in identifying appropriate models to describe water diffusion in heterogeneous tissues, as well as in interpreting experimental data obtained in such issues. Finally, we describe new statistical methods that have been developed to analyse DT-MRI data, and their potential uses in clinical and multi-site studies. Copyright © 2002 John Wiley & Sons, Ltd.
REFERENCES
- 1Basser PJ. Inferring microstructural features and the physiological state of tissues from diffusion-weighted images. NMR Biomed. 1995; 8: 333–344.
- 2Basser PJ. New histological and physiological stains derived from diffusion-tensor MR images. Ann. NY Acad. Sci. 1997; 820: 123–138.
- 3Mori S, Barker PB. Diffusion magnetic resonance imaging: its principle and applications. Anat. Rec. 1999; 257(3): 102–109.
- 4Le Bihan D. Diffusion and Perfusion Magnetic Resonance Imaging. Raven Press: New York, 1995.
- 5Le 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.
- 6Cleveland 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.
- 7Garrido 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.
- 8Tanner JE. Self diffusion of water in frog muscle. Biophys. J. 1979; 28: 107–116.
- 9Henkelman RM, Stanisz GJ, Kim JK, Bronskill MJ. Anisotropy of NMR properties of tissues. Magn. Reson. Med. 1994; 32(5): 592–601.
- 10Moseley 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.
- 11Moseley ME, Kucharczyk J, Asgari HS, Norman D. Anisotropy in diffusion-weighted MRI. Magn. Reson. Med. 1991; 19(2): 321–326.
- 12Crank J. The Mathematics of Diffusion. Oxford University Press: Oxford, 1975.
- 13Torrey HC. Bloch equations with diffusion terms. Phys. Rev. 1956; 104(3): 563–565.
- 14Bloch F. Nuclear induction. Phys. Rev. 1946; 70: 460–474.
- 15Douglass DC, McCall DW. Diffusion in paraffin hydrocarbons. J. Phys. Chem. 1958; 62: 1102.
- 16Neuman CH. Spin echo of spins diffusing in a bounded medium. J. Chem. Phys. 1974; 60: 4508–4511.
- 17Stejskal 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.
- 18Wayne RC, Cotts RM. Nuclear-magnetic-resonance study of self-diffusion in a bounded medium. Phys. Rev. 1966; 151(1): 264–272.
- 19Stejskal EO, Tanner JE. Spin diffusion measurements: spin echoes in the presence of time-dependent field gradient. J. Chem. Phys. 1965; 42(1): 288–292.
- 20Basser 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.
- 21Basser PJ, Mattiello J, Le Bihan D. MR diffusion tensor spectroscopy and imaging. Biophys. J. 1994; 66(1): 259–267.
- 22Mattiello 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.
- 23Neeman 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.
- 24Mattiello J, Basser PJ, Le Bihan D. The b matrix in diffusion tensor echo-planar imaging. Magn. Reson. Med. 1997; 37(2): 292–300.
- 25Mattiello J, Basser PJ, Le Bihan D. Analytical calculation of the b matrix in diffusion imaging. In Diffusion and Perfusion Magnetic Resonance Imaging, DL Bihan. (ed.). Raven Press: New York, 1995; 77–90.
- 26Le Bihan D, Breton E. Imagerie de diffusion in-vivo par resonance magnetique nucleaire. Cr. Acad. Sci. (Paris) 1985; 301: 1109–1112.
- 27Tanner 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.
- 28Pajevic 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.
- 29Basser PJ, Le Bihan D. Fiber orientation mapping in an anisotropic medium with NMR diffusion spectroscopy. 11th Annual Meeting of the SMRM, Berlin, 1992; 1221.
- 30Kärger J, Pfeifer H, Heink W. Principles and applications of self-diffusion measurements by nuclear magnetic resonance. In Advances in Magnetic Resonance, J Waugh (ed.). Academic Press: New York, 1988; 1–89.
- 31Pierpaoli C, Jezzard P, Basser PJ, Barnett A, Di Chiro G. Diffusion tensor MR imaging of the human brain. Radiology 1996; 201(3): 637–648.
- 32van Gelderen P, Vleeschouwer MHMd, DesPres D, Pekar J, Zijl PCMv, Moonen CTW. Water diffusion and acute stroke. Magn. Reson. Med. 1994; 31: 154–163.
- 33Pierpaoli 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.
- 34Pierpaoli 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.
- 35Ulug AM, Beauchamp N, Bryan RN, van Zijl PCM. Absolute quantitation of diffusion constants in human stroke. Stroke 1997; 28: 483–490.
- 36Wong EC, Cox RW. Single-shot imaging with isotropic diffusion weighting. Second Annual Meeting of the SMR, San Francisco, 1994; 136.
- 37Wong EC, Cox RW, Song AW. Optimized isotropic diffusion weighting. Magn. Reson. Med. 1995; 34(2): 139–143.
- 38Mori 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.
- 39Sands DE. Vectors and Tensors in Crystallography, Dover, 1995.
- 40Westin 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.
- 41Alexander 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.
- 42Frank LR. Anisotropy in high angular resolution diffusion-weighted MRI. Magn. Reson. Med. 2001; 45(6): 935–939.
- 43Jones 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.
- 44Pierpaoli C. Oh no! One more method for color mapping of fiber tract direction using diffusion MR imaging data. 5th ISMRM, Vancouver, 1997; 1741.
- 45Pajevic 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.
- 46Makris 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.
- 47Basser 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.
- 48Basser PJ. Fiber-tractography via diffusion tensor MRI (DT-MRI). 6th ISMRM, Sydney, 1998; 1226.
- 49Wedeen 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.
- 50Wedeen VJ. Diffusion anisotropy and white matter tracts. Second Brain Map Meeting, Boston, 1996; P1A4-021.
- 51Mori 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.
- 52Jones 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.
- 53Jones 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.
- 54Mori 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.
- 55Mori 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.
- 56Mori 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.
- 57Poupon 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.
- 58Poupon 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.
- 59Poupon 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.
- 60Conturo 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.
- 61Pierpaoli 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.
- 62Pierpaoli 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.
- 63Aldroubi A, Basser PJ. Reconstruction of vector and tensor fields from sampled discrete data. In Contemporary Mathematics, LW Baggett, DR Larson (eds). AMS: Providence, RI, 1999; 1–15.
- 64Jones DK. A least squares continuous diffusion tensor field approximation. NeuroImage 2001; 13: S168.
- 65Zhang S, Curry C, Morris DS, Laidlaw DH. Visualizing diffusion tensor MR images using streamtubes and streamsurfaces. Proceedings of the IEEE Visualization Conference, Utah, 2000.
- 66Tuch DS, Wiegell MR, Reese TG, Belliveau JW, Wedeen VJ. Measuring cortice-cortical connectivity matrices with diffusion spectrum imaging. ISMRM, Glasgow, 2001; 502.
- 67Struik DJ. Lectures on Classical Differential Geometry. Dover: New York, 1961.
- 68Anderson AW, Gore JC. Analysis and correction of motion artifacts in diffusion weighted imaging. Magn. Reson. Med. 1994; 32(3): 379–387.
- 69Ordidge 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.
- 70Alexander 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.
- 71Papadakis 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.
- 72Haselgrove 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.
- 73Bastin ME. Correction of eddy current-induced artefacts in diffusion tensor imaging using iterative cross-correlation. Magn. Reson. Imag. 1999; 17(7): 1011–1024.
- 74Jones 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.
- 75Jezzard 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.
- 76Bammer 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.
- 77Horsfield MA. Mapping eddy current induced fields for the correction of diffusion-weighted echo planar images. Magn. Reson. Imag. 1999; 17: 1335–1345.
- 78Bastin 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.
- 79Clark 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.
- 80Basser PJ, Pajevic S. Method to reduce eigenvalue sorting bias in DT-MRI. 7th Annual ISMRM, Philadelphia, 1999; 1788.
- 81Martin 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.
- 82Ahrens 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.
- 83Jara H, Wehrli FW. Determination of background gradients with diffusion MR imaging. J. Magn. Reson. Imag. 1994; 4(6): 787–797.
- 84Basser PJ. A sensitive method to calibrate magnetic field gradients using the diffusion tensor. Third Meeting of the SMR, Nice, 1995; 308.
- 85Basser 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.
- 86Papadakis 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.
- 87Hsu 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.
- 88Bossart EL, Inglis BA, Buckley DL, Wirth III ED, Mareci TH. Multiple component diffusion tensor imaging in excised fixed CNS tissue. ISMRM, Philadelphia, 1999; 328.
- 89Tuch DS, Weiskoff RM, Belliveau JW, Wedeen VJ. High angular resolution diffusion imaging of the human brain. ISMRM, Philadelphia, 1999; 321.
- 90Le Bihan D, Delannoy J, Levin RL. Temperature mapping with MR imaging of molecular diffusion: application to hyperthermia. Radiology 1989; 171(3): 853–857.
- 91Mills R. Self-diffusion in normal and heavy water in the range 1–45∞. J. Phys. Chem. 1973; 77(5): 685–688.
- 92Simpson JH, Carr HY. Diffusion and nuclear spin relaxation in water. Phys. Rev. 1958; 111(5): 1201–1202.
- 93Neil 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.
- 94Beaulieu 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.
- 95Beaulieu C, Allen PS. Determinants of anisotropic water diffusion in nerves. Magn. Reson. Med. 1994; 31(4): 394–400.
- 96Wimberger 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.
- 97Le 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.
- 98Clark 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.
- 99Mulkern 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.
- 100Peled 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.
- 101Callaghan PT. Principles of Nuclear Magnetic Resonance Microscopy. Oxford University Press: Oxford 1991.
- 102Callaghan 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.
- 103Tuch 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.
- 104Pajevic S, Basser PJ. Parametric description of noise in diffusion tensor MRI. 8th Annual Meeting of the ISMRM, Philadelphia, 1999; 1787.
- 105Basser 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.
- 106Pajevic 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.
- 107Alexander DC, Basser PJ, Pierpaoli C, Gee JC. Spatial transformations of diffusion tensor Images. IEEE Trans. Med. Imag. 20(11): 1131–1139.
Abbreviations used:
-
- ADC
-
apparent diffusion coefficient
-
- CSF
-
cerebrospinal fluid
-
- DT-MRI
-
diffusion tensor MRI
-
- DI
-
diffusion imaging
-
- DWI
-
diffusion-weighted imaging
-
- EPI
-
echo-planar imaging
-
- FA
-
fractional anisotropy
-
- RA
-
relative anisotropy
-
- RMS
-
root mean square
-
- SNR
-
signal to noise ratio
Citing Literature
Special Issue: Diffusion tensor imaging and axonal mapping ‐ state of the art
November ‐ December 2002
Pages 456-467
