Using the residual bootstrap to quantify uncertainty in mean apparent propagator MRI

Estimation of noise-induced variability in MAP-MRI is needed to properly characterize the amount of uncertainty in quantities derived from the estimated MAP-MRI coefficients. Bootstrap metrics, such as the standard deviation, provides additional valuable diffusion information in addition to common MAP-MRI parameters, and can be incorporated in MAP-MRI studies to provide more extensive insight. To the best of our knowledge, this is the first paper to study the uncertainty of MAP-MRI derived metrics. The noise variability of quantities of MAP-MRI have been quantified using the residual bootstrap, in which the residuals are resampled using two sampling schemes. The residual bootstrap method can provide empirical distributions for MAP-MRI derived quantities, even when the exact distributions are not easily derived. The residual bootstrap methods are applied to SPARC data and HCP-MGH data, and empirical distributions are obtained for the zero-displacement probabilities. Here, we compare and contrast the residual bootstrap schemes using all shells and within the same shell. We show that residual resampling within each shell generates larger uncertainty than using all shells for the HCP-MGH data. Standard deviation and quartile coefficient maps of the estimated variability are provided.