Université Paris-Est, UMR Navier, LCPC-ENPC-CNRS, Champs sur Marne, France.
J Magn Reson. 2011 Jan;208(1):4-19. doi: 10.1016/j.jmr.2010.09.007. Epub 2010 Oct 1.
The form of the two-dimensional (2D) NMR-relaxation spectra--which allow to study interstitial fluid dynamics in diffusive systems by correlating spin-lattice (T(1)) and spin-spin (T(2)) relaxation times--has given rise to numerous conjectures. Herein we find analytically a number of fundamental structural properties of the spectra: within the eigen-modes formalism, we establish relationships between the signs and intensities of the diagonal and cross-peaks in spectra obtained by various 1 and 2D NMR-relaxation techniques, reveal symmetries of the spectra and uncover interdependence between them. We investigate more specifically a practically important case of porous system that has sets of T(1)- and T(2)-eigenmodes and eigentimes similar to each other by applying the perturbation theory. Furthermore we provide a comparative analysis of the application of the, mathematically more rigorous, eigen-modes formalism and the, rather more phenomenological, first-order two-site exchange model to diffusive systems. Finally we put the results that we could formulate analytically to the test by comparing them with computer-simulations for 2D porous model systems. The structural properties, in general, are to provide useful clues for assignment and analysis of relaxation spectra. The most striking of them--the presence of negative peaks--underlines an urgent need for improvement of the current 2D Inverse Laplace Transform (ILT) algorithm used for calculation of relaxation spectra from NMR raw data.
二维（2D）NMR 弛豫谱的形式——通过关联自旋晶格（T(1)）和自旋自旋（T(2)）弛豫时间来研究扩散系统中的间质流体动力学——引起了许多猜测。在这里，我们通过解析方法找到了谱的一些基本结构性质：在本征模式形式中，我们建立了通过各种 1 和 2D NMR 弛豫技术获得的谱中对角和交叉峰的符号和强度之间的关系，揭示了谱的对称性，并揭示了它们之间的相互依赖性。我们通过应用微扰理论更具体地研究了多孔系统的一个实际重要情况，该系统具有一组 T(1)-和 T(2)-本征模式和相似的本征时间。此外，我们还对应用数学上更严格的本征模式形式和更具唯象性的一阶双位点交换模型进行了扩散系统的比较分析。最后，我们将能够通过与二维多孔模型系统的计算机模拟进行比较来对我们可以通过解析方法得到的结果进行测试。这些结构性质通常为弛豫谱的分配和分析提供有用的线索。其中最引人注目的是负峰的存在，这突出表明需要改进当前用于从 NMR 原始数据计算弛豫谱的二维逆拉普拉斯变换（ILT）算法。
