Biexponential and diffusional kurtosis imaging, and generalised diffusion-tensor imaging (GDTI) with rank-4 tensors: a study in a group of healthy subjects

  • Ludovico Minati
  • Domenico Aquino
  • Stefano Rampoldi
  • Sergio Papa
  • Marina Grisoli
  • Maria Grazia Bruzzone
  • Elio Maccagnano
Research Article



Clinical diffusion imaging is based on two assumptions of limited validity: that the radial projections of the diffusion propagator are Gaussian, and that a single directional diffusivity maximum exists in each voxel. The former can be removed using the biexponential and diffusional kurtosis models, the latter using generalised diffusion-tensor imaging. This study provides normative data for these three models.

Materials and methods

Eighteen healthy subjects were imaged. Maps of the biexponential parameters D fast, D slow and f slow, of D and K from the diffusional kurtosis model, and of diffusivity D-were obtained. Maps of generalised anisotropy (GA) and scaled entropy(SE) were also generated, for second and fourth rank tensors. Normative values were obtained for 26 regions.


In grey versus white matter, D slow and D-were higher and D fast, f slow and K were lower. With respect to maps of D- anatomical contrast was stronger in maps of D slow and K. Elevating tensor rank increased SE, generally more significantly than GA, in: anterior limb of internal capsule, corpus callosum, deep frontal and subcortical white matter, along superior longitudinal fasciculus and cingulum.


The values reported herein can be used for reference in future studies and in clinical settings.


Diffusion-tensor imaging (DTI) Biexponential model Diffusional kurtosis imaging (DKI) High angular resolution diffusion imaging (HARDI) Generalised DTI (GDTI) 


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    Niendorf T, Dijkhuizen RM, Norris DG, van Lookeren Campagne M and Nicolay K (1996). Biexponential diffusion attenuation in various states of brain tissue: implications for diffusion-weighted imaging. Magn Reson Med 36: 847–857 CrossRefPubMedGoogle Scholar
  2. 2.
    Mulkern RV, Gudbjartsson H, Westin CF, Zengingonul HP, Gartner W, Guttmann CR, Robertson RL, Kyriakos W, Schwartz R, Holtzman D, Jolesz FA and Maier SE (1999). Multi-component apparent diffusion coefficients in human brain. NMR Biomed 12: 51–62 CrossRefPubMedGoogle Scholar
  3. 3.
    Clark CA and Le Bihan D (2000). Water diffusion compartmentation andanisotropy at high b values in the human brain. Magn Reson Med 44: 852–859 CrossRefPubMedGoogle Scholar
  4. 4.
    Wiegell M, Larsson HB and Wedeen J (2000). Fiber crossing in human brain depictedwith diffusion tensor MR imaging. Radiology 217: 897–903 PubMedGoogle Scholar
  5. 5.
    Tuch DS, Reese TG, Wiegell MR, Makris N, Belliveau JW and Wedeen VJ (2002). High angular resolution diffusion imaging reveals intravoxel white matter fiber heterogeneity. Magn Reson Med 48: 577–582 CrossRefPubMedGoogle Scholar
  6. 6.
    Minati L, Banasik T, Brzezinski J, Mandelli ML, Bizzi A, BruzzoneMG, Konopka M, Jasinski A (2007) Elevating tensor rank increasesanisotropy in brain areas associated with orientationalheterogeneity (IVOH): a generalised DTI (GDTI) study. NMR Biomed(in press)Google Scholar
  7. 7.
    Ozarslan E and Mareci TH (2003). Generalized diffusion tensor imaging and analytical relationships between diffusion tensor imaging and high angular resolution diffusion imaging. Magn Reson Med 50: 955–965 CrossRefPubMedGoogle Scholar
  8. 8.
    Jensen JH, Helpern JA, Ramani A, Lu H and Kaczynski K (2005). Diffusional kurtosis imaging: the quantification of non-gaussian water diffusion by means of magnetic resonance imaging. Magn Reson Med 53: 1432–1440 CrossRefPubMedGoogle Scholar
  9. 9.
    Frohlich AF, Ostergaard L and Kiselev VG (2005). Effect of impermeable interfaces on apparent diffusion coefficient in heterogeneous media. Appl Magn Reson 28: 123–137 CrossRefGoogle Scholar
  10. 10.
    Frohlich AF, Ostergaard L and Kiselev VG (2006). Effect of impermeable boundaries on diffusion-attenuated MR signal. J Magn Reson 179: 223–233 CrossRefPubMedGoogle Scholar
  11. 11.
    Joanes DN and Gill CA (1998). Comparing measures of sample skewness andkurtosis. J R Stat Soc D 47: 183–189 CrossRefGoogle Scholar
  12. 12.
    Abramowitz M, Stegun IA (1972) Handbook of mathematical functionswith formulas, graphs, and mathematical tables. Dover, New York, p 928Google Scholar
  13. 13.
    Ozarslan E, Vemuri BC and Mareci T (2005). Generalized scalar measures for diffusion MRI using trace, variance, and entropy. Magn Reson Med 53: 866–876 CrossRefPubMedGoogle Scholar
  14. 14.
    Maier SE, Bogner P, Bajzik G, Mamata H, Mamata Y, Repa I, Jolesz FA and Mulkern RV (2001). Normal brain and brain tumor: multicomponent apparent diffusion coefficient line scan imaging. Radiology 219: 842–849 PubMedGoogle Scholar
  15. 15.
    Brugieres P, Thomas P, Maraval A, Hosseini H, Combes C, Chafiq A, Ruel L, Breil S, Peschanski M and Gaston A (2004). Water diffusion compartmentation at highb values in ischemic human brain. AJNR Am JNeuroradiol 25: 692–698 Google Scholar
  16. 16.
    Reese TG, Heid O, Weissko RM and Wedeen VJ (2003). Reduction of eddy-current-induced distortion in diffusion MRI using a twice-refocused spin echo. Magn Reson Med 49: 177–182 CrossRefPubMedGoogle Scholar
  17. 17.
    Jenkinson M, Bannister PR, Brady JM and Smith SM (2002). Improved optimisation for the robust and accurate linear registration and motion correction of brain images. NeuroImage 17: 825–841 CrossRefPubMedGoogle Scholar
  18. 18.
    Niewenhuys R (1996). Thehuman central nervous system: a synopsis and atlas. Springer, New York Google Scholar
  19. 19.
    Wakana S, Jiang H, Nagae-Poetscher LM, Mori S and van Zijl PC(2004). Fiber tract-based atlas of human white matter anatomy. Radiology 230: 77–87 CrossRefPubMedGoogle Scholar
  20. 20.
    Brodmann K (1909) Vergleichende Lokalisationslehre der Grosshirnrinde inihren Prinzipien dargestellt auf Grund des Zellenbaues. Barth,LeipzigGoogle Scholar
  21. 21.
    Mai JK, Paxinos G and Assheuer JK (2003). Atlasof the human brain. Academic, New York Google Scholar
  22. 22.
    Martin J (1996). Neuroanatomy: text and atlas. McGraw-Hill, New York Google Scholar
  23. 23.
    Helenius J, Soinne L, Perkio J, Salonen O, Kangasmaki A, Kaste M, Carano RA, Aronen HJ and Tatlisumak T (2001). Diffusion-weighted MR imaging in normal human brains in various age groups. AJNR Am J Neuroradiol 23: 194–199 Google Scholar
  24. 24.
    Beaulieu C (2002). The basis of anisotropic water diffusionin the nervous system—a technical review. NMRBiomed 15: 435–455 Google Scholar
  25. 25.
    Pilatus U, Shim H, Artemov D, Davis D, Glickson JD and van Zijl PC (1997). Intracellular volume and apparent diffusion constants of perfused cancer cell cultures, as measured by NMR. Magn Reson Med 37: 825–832 CrossRefPubMedGoogle Scholar
  26. 26.
    Sukstanskii AL, Ackerman JJH and Yablonskiy DA (2002). Effects of restricted diffusion on MR signal formation. J Magn Reson 157: 95–105 CrossRefGoogle Scholar
  27. 27.
    Schwarcz A, Bogner P, Meric P, Correze J, Berente Z, Pal J, Gallyas F, Doczi T, Gillet B and Beloeil J (2004). The existence of biexponential signal decay in magnetic resonance diffusion-weighted imaging appears to be independent of compartmentalization. Magn Reson Med 51: 278–285 CrossRefPubMedGoogle Scholar
  28. 28.
    Sukstanskii AL, Yablonskiy DA and Ackerman JJH (2004). Effects of permeable boundaries on the diffusion-attenuated MR signal: insight from a one-dimensional model. J Magn Reson 170: 56–66 CrossRefPubMedGoogle Scholar
  29. 29.
    Kiselev VG and Il’yasov KA (2007). Is the “biexponential diffusion-biexponential. Magn Reson Med 57: 464–469 CrossRefPubMedGoogle Scholar
  30. 30.
    Minati L, Bruzzone MG, Grisoli G, Maccagnano C, Rampoldi S, BanasikT, Mandelli ML, Farina L (2006) Preliminary findings withDiffusional Kurtosis Imaging (DKI) of brain tumours. In: EPOS#574, 23rd Meeting of the European Society for Magnetic Resonancein Medicine and Biology, WarsawGoogle Scholar
  31. 31.
    Lu H, Jensen JH, Ramani A and Helpern JA (2006). Three-dimensional characterization of non-gaussian water diffusion in humans using diffusion kurtosis imaging. NMR Biomed 19: 236–247 CrossRefPubMedGoogle Scholar
  32. 32.
    Le Bihan D, Turner R and Douek P (1993). Is water diffusion restricted in human brain white matter? An echo planar NMR imaging study. NeuroReport 4: 887–890 PubMedCrossRefGoogle Scholar
  33. 33.
    Koch M and Norris DG (2000). An assessment of eddy current sensitivity and correction in single-shot diffusion weighted imaging. Phys Med Biol 45: 3821–3832CrossRefPubMedGoogle Scholar
  34. 34.
    Skare S and Andersson JL (2001). On the effects of gating in diffusion imaging of the brain using single-shot EPI. Magn Reson Imag 19: 1125–1128 CrossRefGoogle Scholar

Copyright information

© ESMRMB 2007

Authors and Affiliations

  • Ludovico Minati
    • 1
    • 2
  • Domenico Aquino
    • 2
  • Stefano Rampoldi
    • 3
  • Sergio Papa
    • 3
  • Marina Grisoli
    • 2
  • Maria Grazia Bruzzone
    • 2
  • Elio Maccagnano
    • 2
    • 3
  1. 1.Scientific Direction UnitFondazione Istituto Nazionale Neurologico “Carlo Besta”MilanItaly
  2. 2.Neuroradiology DepartmentFondazione Istituto Nazionale Neurologico “Carlo Besta”MilanItaly
  3. 3.Diagnostic Imaging DepartmentCentro Diagnostico Italiano CDIMilanItaly

Personalised recommendations