Multicomponent Quantitative Analysis Using Second-Order Nonbilinear Data: Theory and Simulations

The application of rank annihilation to a class of instruments generating data which can be classified as second-order nonbilinear is described. This method permits determining the concentration of an analyte of interest even in the presence of spectral interferents unknown and unaccounted for during calibration. The primary difficulty in applying rank annihilation to nonbilinear data is that multiple, different concentration estimates are obtained; it is shown that, for two-dimensional mass spectrometry and absolute value mode two-dimensional nuclear magnetic resonance spectroscopy, the correct concentration estimate should be the smallest of those obtained. The method provides a back-estimate of the calibration matrix, which can be used as an indication of the accuracy of the resulting concentration estimate, as well as a diagnostic for the presence of matrix effects between the calibration and unknown samples. In this paper, the theory and motivation for rank annihilation is presented, and the application to nonbilinear data is presented using computer simulations and a test system consisting of 2D j-coupled NMR spectra (COSY) of six sugars in D₂O.