Estimating Uncertainty in White Matter Tractography Using Wild Non-local Bootstrap.

Statistics derived from diffusion MRI data, especially those related to tractography, are often highly non-linear and non-Gaussian with unknown complex distributions. In estimating the sampling distributions of these statistics, many existing techniques are limited by their reliance on models that assume normality and that are yet to be verified in complex situations where various noise sources, such as physiologic variation, scanner instability, and imaging noise, might be simultaneously present. In complex conditions as such, a viable solution is the bootstrap, which due to its distribution-independent nature is an appealing tool for the estimation of the variability of almost any statistic, without relying on complicated theoretical calculations, but purely on computer simulation. In this paper, we will examine whether a new bootstrap scheme, called the wild non-local bootstrap (W-NLB), is effective in estimating the uncertainty in tractography data. In contrast to the residual or wild bootstrap, which relies on a predetermined data model, or the repetition bootstrap, which requires repeated signal measurements, W-NLB does not assume a predetermined form of data structure and obviates the need for time-consuming multiple acquisitions. W-NLB hinges on the observation that local imaging information recurs in the image. This self-similarity implies that imaging information coming from spatially distant (non-local) regions can be exploited for more effective estimation of statistics of interest. In silico evaluations indicate that W-NLB produces distribution estimates that are in closer agreement to those generated using Monte Carlo simulations, compared with the conventional residual bootstrap. Evaluations using in vivo data show that W-NLB produces results that are in agreement with our knowledge on the white matter connection architecture.