Bayesian Approach for Automated Quantitative Analysis of Benchtop NMR Data

Abstract Low-cost, user-friendly benchtop NMR instruments are often touted as a “one-click” solution for data acquisition, however insufficient peak dispersion in their spectra often reduces the accuracy of quantification and requires user expertise with sophisticated processing tools. Our work aims to facilitate the wide acceptance of benchtop NMR instruments as a viable and effective substitute for cryogenic magnets. We propose an algorithmic approach that completely automates the routine analysis of sets of samples with similar compositions – the problem that often underlies many industrial applications concerned with reaction and process monitoring and quality control. Our solution is rooted in the idea of parametric modelling formulated in terms of Bayesian statistics, which effectively incorporates prior knowledge about the studied system (such as concentration-dependent chemical shift changes) that is usually available in industrial applications. Furthermore, the use of quantum mechanical models for chemical species makes our approach invariant to the spectrometer field strength – a necessary prerequisite for the successful analysis of benchtop data. We demonstrate the performance of our method with two representative sets of samples: mixtures of alcohols and acetates, and aqueous mixtures of biologically relevant species. In these examples, our fully automated analysis of benchtop spectra achieves average errors in concentrations of 0.01 mol/mol and 0.02 mol/mol respectively. Our method is competitive with the traditional processing approaches of well resolved high-field data and has the potential to bring the benefits of NMR even to a small chemistry laboratory.