Precision and accuracy of diffusion kurtosis estimation and the influence of b-value selection

Diffusion kurtosis imaging (DKI) is an extension of diffusion tensor imaging that accounts for leading non-Gaussian diffusion effects. In DKI studies, a wide range of different gradient strengths (b-values) is used, which is known to affect the estimated diffusivity and kurtosis parameters. Hence there is a need to assess the accuracy and precision of the estimated parameters as a function of b-value. This work examines the error in the estimation of mean of the kurtosis tensor (MKT) with respect to the ground truth, using simulations based on a biophysical model for both gray (GM) and white (WM) matter. Model parameters are derived from densely sampled experimental data acquired in ex vivo rat brain and in vivo human brain. Additionally, the variability of MKT is studied using the experimental data. Prevalent fitting protocols are implemented and investigated. The results show strong dependence on the maximum b-value of both net relative error and standard deviation of error for all of the employed fitting protocols. The choice of b-values with minimum MKT estimation error and standard deviation of error was found to depend on the protocol type and the tissue. Protocols that utilize two terms of the cumulant expansion (DKI) were found to achieve minimum error in GM at b-values less than 1 ms/μm² , whereas maximal b-values of about 2.5 ms/μm² were found to be optimal in WM. Protocols including additional higher order terms of the cumulant expansion were found to provide higher accuracy for the more commonly used b-value regime in GM, but were associated with higher error in WM. Averaged over multiple voxels, a net average error of around 15% for both WM and GM was observed for the optimal b-value choice. These results suggest caution when using DKI generated metrics for microstructural modeling and when comparing results obtained using different fitting techniques and b-values.