Reci A, Sederman A J, Gladden L F
Department of Chemical Engineering and Biotechnology, University of Cambridge, Philippa Fawcett Drive, Cambridge CB3 0AS, United Kingdom.
Department of Chemical Engineering and Biotechnology, University of Cambridge, Philippa Fawcett Drive, Cambridge CB3 0AS, United Kingdom.
J Magn Reson. 2018 Sep;294:35-43. doi: 10.1016/j.jmr.2018.06.010. Epub 2018 Jun 19.
Sampling strategies are often central to experimental design. Choosing efficiently which data to acquire can improve the estimation of parameters and reduce the acquisition time. This work is focused on designing optimal sampling patterns for Nuclear Magnetic Resonance (NMR) applications, illustrated with respect to the best estimate of the parameters characterising a lognormal distribution. Lognormal distributions are commonly used as fitting models for distributions of spin-lattice relaxation time constants, spin-spin relaxation time constants and diffusion coefficients. A method for optimising the choice of points to be sampled is presented which is based on the Cramér-Rao Lower Bound (CRLB) theory. The method's capabilities are demonstrated experimentally by applying it to the problem of estimating the emulsion droplet size distribution from a pulsed field gradient (PFG) NMR diffusion experiment. A difference of <5% is observed between the predictions of CRLB theory and the PFG NMR experimental results. It is shown that CLRB theory is stable down to signal-to-noise ratios of ∼10. A sensitivity analysis for the CRLB theory is also performed. The method of optimizing sampling patterns is easily adapted to distributions other than lognormal and to other aspects of experimental design; case studies of optimising the sampling scheme for a fixed acquisition time and determining the potential for reduction in acquisition time for a fixed parameter estimation accuracy are presented. The experimental acquisition time is typically reduced by a factor of 3 using the proposed method compared to a constant gradient increment approach that would usually be used.
采样策略通常是实验设计的核心。有效地选择要采集的数据可以改善参数估计并减少采集时间。这项工作专注于为核磁共振（NMR）应用设计最佳采样模式，并以表征对数正态分布的参数的最佳估计为例进行说明。对数正态分布通常用作自旋晶格弛豫时间常数、自旋 - 自旋弛豫时间常数和扩散系数分布的拟合模型。提出了一种基于克拉美 - 罗下界（CRLB）理论的优化采样点选择的方法。通过将其应用于从脉冲场梯度（PFG）NMR扩散实验估计乳液液滴尺寸分布的问题，实验证明了该方法的能力。在CRLB理论的预测和PFG NMR实验结果之间观察到小于5%的差异。结果表明，CLRB理论在信噪比低至约10时仍保持稳定。还对CRLB理论进行了灵敏度分析。优化采样模式的方法很容易适用于除对数正态分布以外的其他分布以及实验设计的其他方面；给出了针对固定采集时间优化采样方案以及确定在固定参数估计精度下减少采集时间潜力的案例研究。与通常使用的恒定梯度增量方法相比，使用所提出的方法通常可将实验采集时间减少三分之一。
