Extremely efficient and deterministic approach to generating optimal ordering of diffusion MRI measurements

Abstract

Diffusion MRI measurements are typically acquired sequentially with unit gradient directions that are distributed uniformly on the unit sphere. The ordering of the gradient directions has significant effect on the quality of dMRI-derived quantities. Even though several methods have been proposed to generate optimal orderings of gradient directions, these methods are not widely used in clinical studies because of the two major problems. The first problem is that the existing methods for generating highly uniform and antipodally symmetric gradient directions are inefficient. The second problem is that the existing methods for generating optimal orderings of gradient directions are also highly inefficient. In this work, the authors propose two extremely efficient and deterministic methods to solve these two problems. The method for generating nearly uniform point set on the unit sphere (with antipodal symmetry) is based upon the notion that the spacing between two consecutive points on the same latitude should be equal to the spacing between two consecutive latitudes. The method for generating optimal ordering of diffusion gradient directions is based on the idea that each subset of incremental sample size, which is derived from the prescribed and full set of gradient directions, must be as uniform as possible in terms of the modified electrostatic energy designed for antipodally symmetric point set. The proposed method outperformed the state-of-the-art method in terms of computational efficiency by about six orders of magnitude. Two extremely efficient and deterministic methods have been developed for solving the problem of optimal ordering of diffusion gradient directions. The proposed strategy is also applicable to optimal view-ordering in three-dimensional radial MRI.