Estimation of NMR signals in the time domain: methodology, applications and software

Thesis

Nuclear magnetic resonance (NMR) spectroscopy is an analytical technique employed in many scientific disciplines that is able to provide insights into the structures and dynamics of chemical species. To maximise the utility of NMR, appropriate data treatment and analysis is necessary. The conventional route to extracting quantitative information from the raw experimental data — the free induction decay (FID) — is to convert it to an NMR spectrum, through application of the Fourier transform (FT). NMR spectra provide a human-interpretable representation of data; trained practitioners are able to rationalise the appearance of a given spectrum by mapping its component peaks to chemical environments in the sample from which the dataset was acquired. However, the FT suffers from poor resolution, with peaks of similar frequencies exhibiting over- lap. Disentangling the information associated with such peaks is not feasible using typical methods such as integrating user-defined regions of the spectrum. As an alternative approach, parametric estimation techniques aim to provide a detailed description of each signal which contributes to the FID. These methods have been shown to perform effectively even in scenarios where significant spectral peak overlap exists.

This thesis focusses on the development of a parametric estimation method for the analysis of FIDs derived from solution-state NMR experiments. The guiding principle behind the method is that it should require as little user input as possible, while being able to provide accurate and reliable signal estimates. Beyond simply providing a breakdown of individual signal components, many useful applications may be realised when estimation techniques are employed. The initial motivation for this work was to develop a procedure for the generation of broadband homode- coupled (pure shift) NMR spectra with desirable properties from 2DJ datasets. Furthermore, a means of analysing datasets such as those from inversion recovery (Τ₁), Carr-Purcell-Meiboom- Gill (CPMG) (T₂), and diffusion experiments, in which each FID exhibits a variation in its amplitude, is presented. The last application described is a means of producing phased, ultra-broadband NMR spectra from an experiment comprising a single frequency-swept (chirp) excitation pulse.

The methods presented in this thesis are incorporated into a software package written in the Python programming language, called NMR estimation in Python (NMR-EsPy), of which more information can be found at https://github.com/foroozandehgroup/NMR-EsPy.

Authors: Hulse, SG

• DOI: 10.5287/ora-bpdg8rr9k
• Type of award: DPhil
• Level of award: Doctoral
• Awarding institution: University of Oxford
• Language: English
• Keywords: signal processing; python programming; chirp pulse; NMR; numerical optimisation; diffusion NMR; 2D J-resolved NMR; matrix pencil method
• Subjects: Mathematical optimization--Data processing; Analytical chemistry--Data processing; Nuclear magnetic resonance