Istituto Sistemi Complessi, Consiglio Nazionale delle Ricerche, UOS Sapienza, 00185, Rome, Italy.
Istituto Sistemi Complessi, Consiglio Nazionale delle Ricerche, via dei Taurini 19, 00185, Rome, Italy.
Sci Rep. 2023 Jan 30;13(1):1703. doi: 10.1038/s41598-023-27389-7.
The diffusion-weighted NMR signal acquired using Pulse Field Gradient (PFG) techniques, allows for extrapolating microstructural information from porous materials and biological tissues. In recent years there has been a multiplication of diffusion models expressed by parametric functions to fit the experimental data. However, clear-cut criteria for the model selection are lacking. In this paper, we develop a theoretical framework for the interpretation of NMR attenuation signals in the case of Gaussian systems with stationary increments. The full expression of the Stejskal-Tanner formula for normal diffusing systems is devised, together with its extension to the domain of anomalous diffusion. The range of applicability of the relevant parametric functions to fit the PFG data can be fully determined by means of appropriate checks to ascertain the correctness of the fit. Furthermore, the exact expression for diffusion weighted NMR signals pertaining to Brownian yet non-Gaussian processes is also derived, accompanied by the proper check to establish its contextual relevance. The analysis provided is particularly useful in the context of medical MRI and clinical practise where the hardware limitations do not allow the use of narrow pulse gradients.
使用脉冲梯度（PFG）技术获得的扩散加权 NMR 信号，可以从多孔材料和生物组织中推断出微观结构信息。近年来，用于拟合实验数据的扩散模型已经通过参数函数呈指数式增长。然而，对于模型选择，还缺乏明确的标准。在本文中，我们为高斯系统中具有固定增量的 NMR 衰减信号的解释开发了一个理论框架。设计了正态扩散系统的 Stejskal-Tanner 公式的完整表达式，并将其扩展到反常扩散的领域。相关参数函数的适用范围可以通过适当的检查来确定，以确保拟合的正确性，从而完全确定拟合 PFG 数据的适用性。此外，还推导了与布朗运动而非高斯过程相关的扩散加权 NMR 信号的精确表达式，并进行了适当的检查以确定其上下文相关性。所提供的分析在医学 MRI 和临床实践中特别有用，在这些领域中，硬件限制不允许使用窄脉冲梯度。
