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Diffusional Kurtosis Imaging

Diffusional kurtosis imaging (DKI) extends conventional diffusion tensor imaging (DTI) by estimating the kurtosis of the water diffusion probability distribution function.‎1-‎4 The kurtosis is a general, dimensionless statistic for quantifying the non-Gaussianity of any distribution.‎5 A positive kurtosis means the distribution is more strongly peaked and has heavier tails than a Gaussian distribution with the same variance. Water diffusion in biological tissues is non-Gaussian due to the effects of cellular microstructure (e.g., cell membranes and organelles). This is particularly evident in brain, where water diffusion is strongly restricted by myelinated axons. Qualitatively, a large diffusional kurtosis suggests a high degree of diffusional heterogeneity and microstructural complexity.

Because diffusion in brain is anisotropic, DKI requires the introduction of a diffusional kurtosis tensor in addition to the diffusion tensor used in DTI. From the diffusion and diffusional kurtosis tensors (which are calculated together from a single diffusion-weighted imaging dataset), several rotationally invariant metrics can be computed. These include standard DTI metrics, such as the mean diffusivity and fractional anisotropy, as well as metrics reflecting the diffusional kurtosis, such as the mean, axial, and radial kurtoses. The diffusional kurtosis metrics are strongly linked to cellular microstructure, as this is the main source of diffusional non-Gaussianity in tissues. The extra information provided by DKI can also resolve intra-voxel fiber crossings and thus be used to improve fiber tractography of white matter.‎6

An advantage of DKI is that it is relatively simple to implement for human imaging on conventional MRI clinical scanners. DKI protocols differ from DTI protocols in requiring at least 3 b-values (as compared to 2 b-values for DTI) and at least 15 independent diffusion gradient directions (as compared to 6 for DTI). Typical protocols for brain have b-values of 0, 1000, 2000 s/mm2 with 30 diffusion directions. Image post-processing requires the use of specialized algorithms.‎4,‎7

DKI has been most commonly used for the study of brain,‎8-‎18 although applications to lung,‎19 to head and neck tumors,‎20 and to prostate cancer‎21 have also been investigated.



  1. Jensen JH, Helpern JA. Quantifying non-Gaussian water diffusion by means of pulsed-field-gradient MRI. In: Proceedings of the International Society for Magnetic Resonance in Medicine eleventh scientific meeting. 2154, 2003.
  2. Jensen JH, Helpern JA, Ramani A, Lu H, Kaczynski K. Diffusional kurtosis imaging: the quantification of non-Gaussian water diffusion by means of MRI. Magn Reson Med 2005;53:1432-1440.
  3. Lu H, Jensen JH, Ramani A, Helpern JA. Three-dimensional characterization of non-Gaussian water diffusion in humans using diffusion kurtosis imaging (DKI). NMR Biomed 2006;19:236-247.
  4. Jensen JH, Helpern JA. MRI Quantification of non-Gaussian water diffusion by kurtosis analysis. NMR Biomed 2010; 23:698-710.
  5. DeCarlo LT. On the meaning and use of kurtosis. Psychological Methods 1997; 2:292-307.
  6. Lazar M, Jensen JH, Xuan L, Helpern JA. Estimation of the orientation distribution function from diffusional kurtosis imaging. Magn Reson Med 2008;60:774-781.
  7. Tabesh A, Jensen JH, Ardekani BA, Helpern JA. Estimation of tensors and tensor-derived measures in diffusional kurtosis imaging. Magn Reson Med 2011; 65:823-836.
  8. Falangola MF, Jensen JH, Babb JS, Hu C, Castellanos FX, DiMartino A, Ferris SH, Helpern JA. Age-related non-Gaussian diffusion patterns in the prefrontal brain. J Magn Reson Imaging 2008;28:1345-1350.
  9. Hui ES, Cheung MM, Qi L, Wu EX. Towards better MR characterization of neural tissues using directional diffusion kurtosis analysis. Neuroimage 2008; 42:122-134.
  10. Cheung MM, Hui ES, Chan KC, Helpern JA, Qi L, Wu EX. Does diffusion kurtosis imaging lead to better neural tissue characterization? A rodent brain maturation study. Neuroimage 2009; 45:386-392
  11. Raab P, Hattingen E, Franz K, Zanella FE, Lanfermann H. Cerebral gliomas: diffusional kurtosis imaging analysis of microstructural differences. Radiology 2010; 254:876-881.
  12. Wu EX, Cheung MM. MR diffusion kurtosis imaging for neural tissue characterization. NMR Biomed 2010; 23:836-848.
  13. Helpern JA, Adisetiyo V, Falangola MF, Hu C, Di Martino A, Williams K, Castellanos FX, Jensen JH. Preliminary evidence of altered gray and white matter microstructural development in the frontal lobe of adolescents with ADHD: a diffusional kurtosis imaging study. J Magn Reson Imaging 2011; 33:17-23.
  14. Jensen JH, Falangola MF, Hu C, Tabesh A, Rapalino O, Lo C, Helpern JA. Preliminary observations of increased diffusional kurtosis in human brain following recent cerebral infarction. NMR Biomed 2011; 24:452-457.
  15. Grossman EJ, Ge Y, Jensen JH, Babb JS, Miles L, Reaume J, Silver JM, Grossman RI, Inglese M. Thalamus and cognitive impairment in mild traumatic brain injury: a diffusional kurtosis imaging study. J Neurotrauma 2011.
  16. Fieremans E, Jensen JH, Helpern JA. White matter characterization with diffusional kurtosis imaging. Neuroimage 2011; 58:177-188.
  17. Zhuo J, Xu S, Proctor JL, Mullins RJ, Simon JZ, Fiskum G, Gullapalli RP. Diffusion kurtosis as an in vivo imaging marker for reactive astrogliosis in traumatic brain injury. Neuroimage 2012; 59:467-477.
  18. Van Cauter S, Veraart J, Sijbers J, Peeters RR, Himmelreich U, De Keyzer F, Van Gool SW, Van Calenbergh F, De Vleeschouwer S, Van Hecke W, Sunaert S. Gliomas: diffusion kurtosis MR imaging in grading. Radiology 2012; 263:492-501.
  19. Trampel R, Jensen JH, Lee RF, Kamenetskiy I, McGuinness G, Johnson G. Diffusional kurtosis imaging in the lung using hyperpolarized 3He. Magn Reson Med 2006;56:733-737.
  20. Jansen JF, Stambuk HE, Koutcher JA, Shukla-Dave A. Non-gaussian analysis of diffusion-weighted MR imaging in head and neck squamous cell carcinoma: a feasibility study. AJNR Am J Neuroradiol 2010; 31:741-748.
  21. Rosenkrantz AB, Sigmund EE, Johnson G, Babb JS, Mussi TC, Melamed J, Taneja SS, Lee VS, Jensen JH. Prostate cancer: feasibility and preliminary experience of a diffusional kurtosis model for detection and assessment of aggressiveness of peripheral zone cancer. Radiology 2012.

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