Minimal number of gradient directions for robust measurement of spherical mean diffusion weighted signal

Abstract

PurposeDetermination of the minimum number of gradient directions (Nmin) for robust measurement of spherical mean diffusion weighted signal (S¯). MethodsComputer simulations were employed to characterize the relative standard deviation (RSD) of the measured spherical mean signal as a function of the number of gradient directions (N). The effects of diffusion weighting b-value and signal-to-noise ratio (SNR) were investigated. Multi-shell high angular resolution Human Connectome Project diffusion data were analyzed to support the simulation results. ResultsRSD decreases with increasing N, and the minimum number of N needed for RSD ≤ 5% is referred to as Nmin. At high SNRs, Nmin increases with increasing b-value to achieve sufficient sampling. Simulations showed that Nmin is linearly dependent on the b-value. At low SNRs, Nmin increases with increasing b-value to reduce the noise. RSD can be estimated as σS¯N, where σ = 1/SNR is the noise level. The experimental results were in good agreement with the simulation results. The spherical mean signal can be measured accurately with a subset of gradient directions. ConclusionAs Nmin is affected by b-value and SNR, we recommend using 10 × b / b1 (b1 = 1 ms/μm2) uniformly distributed gradient directions for typical human diffusion studies with SNR ~ 20 for robust spherical mean signal measurement.