Minimal number of sampling directions for robust measures of the spherical mean diffusion weighted signal: Effects of sampling directions, b-value, signal-to-noise ratio, hardware, and fitting strategy

Abstract

Several recent multi-compartment diffusion MRI investigations and modeling strategies have utilized the orientationally-averaged, or spherical mean, diffusion-weighted signal to study tissue microstructure of the central nervous system. Most experimental designs sample a large number of diffusion weighted directions in order to calculate the spherical mean signal, however, sampling a subset of these directions may increase scanning efficiency and enable either a decrease in scan time or the ability to sample more diffusion weightings. Here, we aim to determine the minimum number of gradient directions needed for a robust measurement of the spherical mean signal. We used computer simulations to characterize the variation of the measured spherical mean signal as a function of the number of gradient directions, while also investigating the effects of diffusion weighting (b-value), signal-to-noise ratio (SNR), available hardware, and spherical mean fitting strategy. We then utilize empirically acquired data in the brain and spinal cord to validate simulations, showing experimental results are in good agreement with simulations. We summarize these results by providing an intuitive lookup table to facilitate the determination of the minimal number of sampling directions needed for robust spherical mean measurements, and give recommendations based on SNR and experimental conditions.

Keywords: Diffusivity; Optimal sampling; Spherical mean signal; Volume fraction.