Hi Laura,

Great question.

Kmean (MK) is the average kurtosis over all directions (in theory an infinite amount). MK requires knowledge of both the diffusion and kurtosis tensors. Practically speaking, we advise gathering at least 30 directions at both b = 1000 and 2000 s/mm^2 (more often we gather 64 or 128 directions). 

MKT is the mean kurtosis tensor which is a bit different from MK. The kurtosis tensor, W, can be calculated (with the omission of a scaling factor) and then averaged. So, MKT is really the mean (of the) kurtosis tensor. Explicitly, MKT only approximates MK. However, if diffusion tensor were to be completely isotropic then MKT and MK would be equal.

The paper for MKT is: Hansen B, Lund TE, Sangill R, Jespersen SN. Experimentally and computationally fast method for estimation of mean kurtosis. Magn Reson. Med 2013; 69:1754-1760.

MK and MKT have shown to have similar information in this publication: Glenn GR, Helpern JA, Tabesh A, Jensen JH. Quantitative assessment of diffusional kurtosis anisotropy. NMR Biomed 2015;28:448–459.

I hope this answers your question but if not, please feel free to ask for more clarification.

Thanks for using DKE!

-Hunter