Tractography Gone Wild: Probabilistic Fibre Tracking Using the Wild Bootstrap With Diffusion Tensor MRI

Diffusion tensor magnetic resonance imaging (DT-MRI) permits the noninvasive assessment of tissue microstructure and, with fibre-tracking algorithms, allows for the 3-D trajectories of white matter fasciculi to be reconstructed noninvasively. Probabilistic algorithms allow one to assign a ldquoconfidencerdquo to a given reconstructed pathway - but often rely on a priori assumptions about sources of uncertainty in the data. Bootstrap methods have been proposed as a way of circumventing this problem, deriving the uncertainty from the data themselves - but acquisition times for data amenable to precise and robust bootstrapping are clinically prohibitive. By combining the wild bootstrap, recently introduced to the DT-MRI literature, with tractography, we show how confidence can be assigned to reconstructed trajectories using data collected in a fraction of the time required for regular bootstrapping. We compare in vivo wild bootstrap tracking results with regular tracking results and show that results are comparable. This approach therefore allows users who have collected data sets for use with deterministic tracking algorithms, rather than those specifically designed for bootstrapping, to be able to apply bootstrap analyses and retrospectively assign confidence to their reconstructed trajectories with minimum additional effort.

I. Introduction

In diffusion tensor magnetic resonance imaging (DT-MRI), a set of diffusion-weighted (DW) MR images is collected and used to form estimates of the self-diffusion tensor in each voxel of the imaged volume [1], [2]. The diffusion tensor model yields estimates of mean diffusivity, diffusion anisotropy, and fibre orientation. This information has been employed over the last nine years in various attempts to reconstruct noninvasively the pathways of white matter fasciculi within the brain using a variety of algorithms that are generically referred to as fibre-tracking or tractography (e.g., [3]–[13]).