Comparison of cumulant expansion and q-space imaging estimates for diffusional kurtosis in brain

To compare estimates for the diffusional kurtosis in brain as obtained from a cumulant expansion (CE) of the diffusion MRI (dMRI) signal and from q-space (QS) imaging.

For the CE estimates of the kurtosis, the CE was truncated to quadratic order in the b-value and fit to the dMRI signal for b-values from 0 up to 2000s/mm². For the QS estimates, b-values ranging from 0 up to 10,000s/mm² were used to determine the diffusion displacement probability density function (dPDF) via Stejskal's formula. The kurtosis was then calculated directly from the second and fourth order moments of the dPDF. These two approximations were studied for in vivo human data obtained on a 3T MRI scanner using three orthogonal diffusion encoding directions.

The whole brain mean values for the CE and QS kurtosis estimates differed by 16% or less in each of the considered diffusion encoding directions, and the Pearson correlation coefficients all exceeded 0.85. Nonetheless, there were large discrepancies in many voxels, particularly those with either very high or very low kurtoses relative to the mean values.

Estimates of the diffusional kurtosis in brain obtained using CE and QS approximations are strongly correlated, suggesting that they encode similar information. However, for the choice of b-values employed here, there may be substantial differences, depending on the properties of the diffusion microenvironment in each voxel.