**An Overview
** Diffusion Kurtosis Imaging (DKI) extends conventional diffusion tensor imaging (DTI) by estimating the kurtosis of the water diffusion probability distribution function1-4. The kurtosis is a general, dimensionless statistic for quantifying the non-Gaussianity of any distribution5. 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 complexity2,4.

Because diffusion in brain is anisotropic, DKI requires the introduction of a diffusion 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.

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.

**Links**

Software for DKI post-processing (Diffusion Kurtosis Estimator

**References
**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.

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.

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.

Jensen JH, Helpern JA. MRI Quantification of non-Gaussian water diffusion by kurtosis analysis. NMR Biomed 2010; 23:698-710.

DeCarlo LT. On the meaning and use of kurtosis. Psychological Methods 1997; 2:292-307.

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.

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.