A Monte Carlo Method for Analyzing Systematic and Random Uncertainty in Quantitative Nuclear Magnetic Resonance Measurements

Quantitative nuclear magnetic resonance (qNMR) is a powerful analytical technology that is capable of quantifying the concentration of any analyte with exquisite accuracy and precision so long as it contains at least one nonlabile nuclear magnetic resonance (NMR)-active nucleus. Unlike with traditional analytical technologies, the concentrations of analytes do not directly influence the uncertainty in the quantification of NMR signals because an ideal NMR response depends only on the nature and amount of the nucleus being observed. Rather, in the absence of spectral artifacts and under favorable experimental conditions, the measurement uncertainty may be influenced by the following factors: (1) spectroscopic parameters such as the spectral width, number of time domain points, and acquisition time; (2) postacquisition data processing, such as apodization and zero-filling; (3) the signal-to-noise ratios (SNRs) and lineshapes of the two signals being used in a qNMR measurement; and (4) the method of signal quantification employed, such as numerical integration or lineshape fitting (LF). Here, a general Monte Carlo (MC) method that considers these factors is presented, with which the random and systematic contributions to qNMR measurement uncertainty may be calculated. Autocorrelation analysis of synthetic and experimental noise is used in a fingerprint-like approach to demonstrate the validity of the simulations. The MC method allows for a general quantitative assessment of measurement uncertainty without the need to acquire spectral replicates and without reference to the molecular structures and concentrations of analytes. Representative examples of qNMR measurement uncertainty simulations are provided in which the metrological performances of integration and LF are contrasted for signal pairs obtained using various acquisition and processing schemes in the low-SNR regime.an area where application of the proposed MC method may prove to be particularly salient.

Automated summary

Quantitative nuclear magnetic resonance (qNMR) is a powerful analytical technology that can quantify the concentration of any analyte with high accuracy, with the uncertainty influenced by various factors such as spectroscopic parameters, data processing, signal-to-noise ratios, and signal quantification methods. The Monte Carlo (MC) method provides a way to calculate the contributions to qNMR measurement uncertainty and allows for a general quantitative assessment without the need for spectral replicates or reference to molecular structures.