A Bayesian approach to diffusional kurtosis imaging

Purpose: Diffusional kurtosis metrics show high performance for detecting pathological changes and are therefore expected to be disease biomarkers. Kurtosis maps, however, tend to be noisy. The maps’ visual quality is crucial for disease diagnosis, even when kurtosis is being used quantitatively. A Bayesian method was proposed to curtail the large statistical error inherent in kurtosis estimation while maintaining potential application to biomarkers. Theory: Gaussian priors are determined from first-step estimations implemented using the least-square method (LSM). The likelihood-function variance is determined from the residuals of the estimation. Although the proposed approach is similar to a regularized LSM, regularization parameters do not have to be artificially adjusted. An appropriate balance between denoising and preventing false shrinkages of metric dispersions is automatically achieved. Methods: Map qualities achieved using the conventional and proposed methods were compared. The receiver-operating characteristic analysis was performed for glioma-grade differentiation using simulated low- and high-grade glioma DWI datasets. Noninferiority of the proposed method was tested for areas under the curves (AUCs). Results: The noisier the conventional maps, the better the proposed Bayesian method improved them. Noninferiority of the proposed method was confirmed by AUC tests for all kurtosis-related metrics. Superiority of the proposed method was also established for several metrics. Conclusions: The proposed approach improved noisy kurtosis maps while maintaining their performances as biomarkers without increasing data acquisition requirements or arbitrarily choosing LSM regularization parameters. This approach may enable the use of higher-order terms in diffusional kurtosis imaging (DKI) fitting functions by suppressing overfitting, thereby improving the DKI-estimation accuracy.