Fast and robust estimation of diffusional kurtosis imaging (DKI) parameters by general closed-form expressions and their extensions.

Diffusional kurtosis imaging (DKI) for clinical imaging involves time-consuming computation and demonstrates low robustness. Standard estimation of DKI parameters is based on an extension of Stejskal-Tanner's signal model with squared b-value term and is a least-squares fitting problem. The use of numerical methods for computation requires time, and estimation of DKI parameters is noise sensitive and often produces noisy results, such as images with pepper noise.In this study, we propose general closed-form solutions for DKI parameters to avoid numerical computation for least-squares fitting, solutions that can be applied to diffusion weighted imaging (DWI) datasets with any number of b-values more than three. Solutions are obtained through stationary-point conditions of an objective function that are minimized for fitting. We use 3 techniques to extend the solutions to increase robustness-b-value-dependent weighting in fitting, removal of outliers, and addition of neighbor sampling. Based on synthetic datasets and clinical datasets that both consist of 6 b-value and 3 b-value datasets, we detail and compare the 3 methods including a method by Jensen et al. are compared and investigated in detail. The synthetic data consist of several combinations of DKI parameters and some Rician noise. In addition to visually assessing result images, we also performed quantitative evaluation using a range of estimated parameters, positive-definiteness of the objective function for fitting, and root-mean-square error including estimation bias from the true value (synthetic data only). Methods that added neighbor sampling outperformed others in terms of low errors and visual smoothness. Though the solution by our method is to estimate DKI parameters in a single MPG direction, it can contribute to anisotropic analysis of diffusional kurtosis such as kurtosis tensor. More robust estimation is expected by combining techniques.