Accurate free-water estimation in white matter from fast diffusion MRI acquisitions using the spherical means technique

Abstract

Purpose: To accurately estimate the partial volume fraction of free water in the white matter from diffusion MRI acquisitions not demanding strong sensitizing gradients and/or large collections of different b-values. Data sets considered comprise $\sim$ 32-64 gradients near $b=1000s/{\mathrm{mm}}^2$ plus $\sim$ 6 gradients near $b=500s/{\mathrm{mm}}^2$ .

Theory and methods: The spherical means of each diffusion MRI set with the same b-value are computed. These means are related to the inherent diffusion parameters within the voxel (free- and cellular-water fractions; cellular-water diffusivity), which are solved by constrained nonlinear least squares regression.

Results: The proposed method outperforms those based on mixtures of two Gaussians for the kind of data sets considered. W.r.t. the accuracy, the former does not introduce significant biases in the scenarios of interest, while the latter can reach a bias of 5%-7% if fiber crossings are present. W.r.t. the precision, a variance near $10\%$ , compared to 15%, can be attained for usual configurations.

Conclusion: It is possible to compute reliable estimates of the free-water fraction inside the white matter by complementing typical DTI acquisitions with few gradients at a lowb-value. It can be done voxel-by-voxel, without imposing spatial regularity constraints.

Keywords: diffusion MRI; free water; spherical means; white matter.