Hua Li1, Ho Ming Chow2, Diane C Chugani3, Harry T Chugani4. 1. Katzin Diagnostic & Research PET/MR Center, Nemours - Alfred I. duPont Hospital for Children, Wilmington, DE 19803, USA. Electronic address: hua.li@nemours.org. 2. Katzin Diagnostic & Research PET/MR Center, Nemours - Alfred I. duPont Hospital for Children, Wilmington, DE 19803, USA. 3. Katzin Diagnostic & Research PET/MR Center, Nemours - Alfred I. duPont Hospital for Children, Wilmington, DE 19803, USA; College of Health Sciences, University of Delaware, Newark, DE 19716, USA. 4. Katzin Diagnostic & Research PET/MR Center, Nemours - Alfred I. duPont Hospital for Children, Wilmington, DE 19803, USA; Department of Neurology, Thomas Jefferson University, Philadelphia, PA 19107, USA.
Abstract
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.
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.
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