Abstract
PURPOSE: Determination of the minimum number of gradient directions (N(min)) for robust measurement of spherical mean diffusion weighted signal (S¯). METHODS: Computer 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. RESULTS: RSD decreases with increasing N, and the minimum number of N needed for RSD ≤ 5% is referred to as N(min). At high SNRs, N(min) increases with increasing b-value to achieve sufficient sampling. Simulations showed that N(min) is linearly dependent on the b-value. At low SNRs, N(min) 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. CONCLUSION: As N(min) is affected by b-value and SNR, we recommend using 10 × b / b(1) (b(1) = 1 ms/μm(2)) uniformly distributed gradient directions for typical human diffusion studies with SNR ~ 20 for robust spherical mean signal measurement.