An experimental validation of a Bayesian model for quantification in NMR spectroscopy

Improving the Accuracy of Model-based Quantitative NMR

“…It is instructive to look at the possible improvement of the least squares fitting results with more representative lineshape models. Specifically, we include second and third order terms in the real and complex-valued decay model of FID as done in (Matviychuk et al, 2017), which contribute additional weighting parameters to be fitted; we observe that the second order FIDs correspond to linear combinations of Lorentzian and Gaussian lines in the spectrum, while complex-valued polynomial decay models allow us to address peaks asymmetry. Furthermore, we consider a custom-written version of the reference deconvolution method (Metz et al, 2000), in which we estimate the convolution kernel given a Lorentzian model fitted to the experimental data as described above.…”

“…Based on the idea that an experimental spectrum can be represented as a collection of parametric lineshapes, e.g. Lorentzians with certain positions, widths, and heights, they offer a principled mechanism to resolve overlapping peaks and are less susceptible to noise (Matviychuk et al, 2017). By adjusting its parameters, the model is fitted to match experimental data, which eventually determines the sought concentrations of chemical species in the analysed sample.…”

“…However, we note that when the model fitting is performed in the least squares sense -as done most commonly -both variants of the problem formulations are equivalent and result in the same solution. Thus, even though explicit data preprocessing steps can be often obviated by timedomain methods, they inevitably include the phasing parameters in a certain form, either as angles of complex-valued intensity estimates for separate resonances (Krishnamurthy, 2013;Rubtsov and Griffin, 2007;Kung et al, 1983) or as independently optimized parameters of a linear phasing model (Matviychuk et al, 2017). On the other hand, the phasing parameters can also be estimated from the complex-valued frequency domain data (Sokolenko et al, 2019).…”

Calibration‐Free Chemical Process and Quality Control Units as Enablers for Modular Production

“…Using a Bayesian approach, a general model for an NMR signal was published that considers the effects of chemical shifts, relaxation, line shape imperfections, phasing, and baseline distortions 33, 34. Indirect hard modeling (IHM) enables the analysis of complex spectra acquired on low‐field instruments (Fig.…”

Digitalization in Thermodynamics

“…New methods have become available not only for carrying out the NMR experiments but also for the evaluation of the spectra. They include applications of Bayesian statistics [51] and indirect hard modeling [52]. Spectra from series of experiments need to be evaluated automatically.…”