PURPOSE Determination of the minimum number of gradient directions (Nmin) 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 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. CONCLUSION As 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.

中文翻译：

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最小数目的梯度方向，可稳定地测量球形平均扩散加权信号。

目的确定用于球形平均扩散加权信号（S′）的稳健测量的最小梯度方向数（Nmin）。方法采用计算机模拟来表征测得的球面平均信号的相对标准偏差（RSD），该相对标准偏差是梯度方向数（N）的函数。研究了扩散加权b值和信噪比（SNR）的影响。多壳高角度分辨率人类Connectome项目扩散数据进行了分析，以支持模拟结果。结果RSD随着N的增加而降低，并且RSD≤5％所需的最小N数称为Nmin。在高SNR时，Nmin随着b值的增加而增加，以实现足够的采样。仿真表明，Nmin线性依赖于b值。在低SNR的情况下，Nmin随着b值的增加而增加，以降低噪声。RSD可以估计为σSSN，其中σ= 1 / SNR是噪声水平。实验结果与仿真结果吻合良好。可以使用梯度方向的子集准确地测量球形平均信号。结论由于Nmin受b值和SNR的影响，我们建议使用10×b / b1（b1 = 1 ms /μm2）均匀分布的梯度方向进行典型的人体扩散研究，而SNR〜20则用于可靠的球形均值信号测量。