Katz Yaniv, Nevo Uri
Department of Biomedical Engineering, The Iby and Aladar Fleischman Faculty of Engineering, Tel-Aviv University, Tel-Aviv, Israel.
J Chem Phys. 2014 Apr 28;140(16):164201. doi: 10.1063/1.4871193.
Pulsed field gradient (PFG) diffusion NMR experiments are sensitive to restricted diffusion within porous media and can thus reveal essential microstructural information about the confining geometry. Optimal design methods of inverse problems are designed to select preferred experimental settings to improve parameter estimation quality. However, in pore size distribution (PSD) estimation using NMR methods as in other ill-posed problems, optimal design strategies and criteria are scarce. We formulate here a new optimization framework for ill-posed problems. This framework is suitable for optimizing PFG experiments for probing geometries that are solvable by the Multiple Correlation Function approach. The framework is based on a heuristic methodology designed to select experimental sets which balance between lowering the inherent ill-posedness and increasing the NMR signal intensity. This method also selects favorable discrete pore sizes used for PSD estimation. Numerical simulations performed demonstrate that using this framework greatly improves the sensitivity of PFG experimental sets to the pores' sizes. The optimization also sheds light on significant features of the preferred experimental sets. Increasing the gradient strength and varying multiple experimental parameters is found to be preferable for reducing the ill-posedness. We further evaluate the amount of pore size information that can be obtained by wisely selecting the duration of the diffusion and mixing times. Finally, we discuss the ramification of using single PFG or double PFG sequences for PSD estimation. In conclusion, the above optimization method can serve as a useful tool for experimenters interested in quantifying PSDs of different specimens. Moreover, the applicability of the suggested optimization framework extends far beyond the field of PSD estimation in diffusion NMR, and reaches design of sampling schemes of other ill-posed problems.
脉冲场梯度（PFG）扩散核磁共振实验对多孔介质内的受限扩散敏感，因此可以揭示有关限制几何结构的基本微观结构信息。反问题的优化设计方法旨在选择最佳实验设置以提高参数估计质量。然而，与其他不适定问题一样，在使用核磁共振方法进行孔径分布（PSD）估计时，优化设计策略和标准却很少。我们在此为不适定问题制定了一个新的优化框架。该框架适用于优化PFG实验，以探测可通过多重相关函数方法求解的几何结构。该框架基于一种启发式方法，旨在选择在降低固有不适定性和增加核磁共振信号强度之间取得平衡的实验集。该方法还选择用于PSD估计的有利离散孔径。进行的数值模拟表明，使用该框架可大大提高PFG实验集对孔径的灵敏度。优化还揭示了优选实验集的重要特征。发现增加梯度强度并改变多个实验参数对于降低不适定性更可取。我们进一步评估了通过明智地选择扩散和混合时间的持续时间可获得的孔径信息的量。最后，我们讨论了使用单PFG或双PFG序列进行PSD估计的影响。总之，上述优化方法可为有兴趣量化不同样品PSD的实验人员提供有用的工具。此外，所建议的优化框架的适用性远远超出了扩散核磁共振中PSD估计的领域，并延伸到其他不适定问题的采样方案设计。
