Fourier and Laplace-like low-field NMR spectroscopy: The perspectives of multivariate and artificial neural networks analyses

Low field Nuclear Magnetic Resonance (LF-NMR) is a rich source of information for a wide range of samples types. These can be hard or soft solids, such as plastics or elastomers; bulk liquids or liquids absorbed in porous materials, and can come from biomaterials, biological tissues, archaeological artifacts, cultural heritage objects. LF-NMR instruments present a significant advance especially for in situ, ex situ and in vivo measurement of relaxation and diffusion. Moreover, high resolution 1D and 2D spectroscopy, as well as magnetic resonance (MR) imaging are available in these fields. In this work we discuss the advanced analysis of the data measured in LF-NMR from the perspectives of tertiary level that implies the analysis on principal components (PCA), and on the quaternary analysis that uses an artificial neural network (ANN). The principles of PCA and ANN are largely discussed. For the PCA analysis, a series of 52 spectra were analyzed, having been recorded in vivo by LF-NMR. Of these spectra, 38 were generated from normal uterus, 7 by uterus tissue with endometrial cancer, and another 7 were obtained from tissues of women with uterine cervical cancer. The PC1 vs PC2 plot was further analyzed using an artificial neural network, and the results are presented as 2D maps of probability. Furthermore, the perspectives of applying an ANN to solve the problem of Laplace-like inversion are discussed. An example of such ANN was presented and the performance was discussed. Finally, a model of complex ANN, capable to sequentially solve this kind of problems specific to LF-NMR is proposed and discussed.