Using the Wild Bootstrap to Quantify Uncertainty in Mean Apparent Propagator MRI

Purpose: Estimation of uncertainty of MAP-MRI metrics is an important topic, for several reasons. Bootstrap derived uncertainty, such as the standard deviation, provides valuable information, and can be incorporated in MAP-MRI studies to provide more extensive insight. Methods: In this paper, the uncertainty of different MAP-MRI metrics was quantified by estimating the empirical distributions using the wild bootstrap. We applied the wild bootstrap to both phantom data and human brain data, and obtain empirical distributions for the MAP-MRI metrics return-to-origin probability (RTOP), non-Gaussianity (NG), and propagator anisotropy (PA). Results: We demonstrated the impact of diffusion acquisition scheme (number of shells and number of measurements per shell) on the uncertainty of MAP-MRI metrics. We demonstrated how the uncertainty of these metrics can be used to improve group analyses, and to compare different preprocessing pipelines. We demonstrated that with uncertainty considered, the results for a group analysis can be different. Conclusion: Bootstrap derived uncertain measures provide additional information to the MAP-MRI derived metrics, and should be incorporated in ongoing and future MAP-MRI studies to provide more extensive insight.