Dealing with Uncertainty in Diffusion Tensor MR Data

This paper explains how radio frequency (RF) background noise produces uncertainty in measured diffusion tensor MRI (DT-MRI) data, how this noise can be modeled, and how its effects can be mitigated. DT-MRI data are derived from a series of magnitude diffusion-weighted images (DWI) in which RF noise is rectified. A new Gaussian distribution is proposed that describes the vari- ability of the estimated diffusion tensor, D, in an ideal experiment in which RF noise is the only artifact present. We show how to improve the design of DT-MRI experiments by requiring that the statistical distribution of D be independent of the laboratory coordinate system. Non-parametric empirical methods of analyzing un- certainty in DT-MRI experiments are also described. Monte Carlo simulations are useful in designing and interpreting DT-MRI experiments. Bootstrap methods help us measure the true variability of D (and quantities derived from it), and assess the quality of DT-MRI data. Matrix Perturbation techniques predict how the uncertainty in D propagates to its eigenvalues and eigenvectors. A method for obtaining a continuous diffusion tensor field from the measured discrete noisy DT-MRI data also reduces the uncertainty of D and quantities derived from it. Finally, we describe schemes that use wavelets to remove noise from DWI and DT-MRI data while preserving boundaries between different tissue regions. Collectively, these paramet- ric and nonparametric methods provide a unified statistical framework to improve the design of DT-MRI experiments and their subsequent analysis.