Strategy To Obtain Accurate Analytical Solutions in Second-Order Multivariate Calibration with Curve Resolution Methods

Abstract

A novel procedure is described for processing the second-order data matrices with multivariate curve resolution-alternating least-squares; while the data set is nontrilinear and severe profile overlapping occurs in the instrumental data modes. The area of feasible solutions can be reduced to a unique solution by including/considering the area correlation constraint, besides the traditional constraints (i.e., non-negativity, unimodality, species correspondence, etc.). The latter is implemented not only for the unknown samples but also for all calibration samples, regardless of their interferent content. The area of correlation constraint was specially designed to remove rotational ambiguity in the chemical data sets when information about calibration samples is at hand. In this contribution a comprehensive strategy is developed to uniquely unravel nontrilinear data sets or data sets with severely overlapped profiles in the instrumental data modes. The approach is illustrated with simulated and experimental data sets. Borgen plots are employed to adequately visualize the extent of rotational ambiguity under non-negativity constraint.

Application of the area correlation constraint in the MCR-ALS quantitative analysis of complex mixture samples

“…Therefore, this procedure has been recently proposed to be implemented as a new constraint (area correlation constraint) during the ALS optimization. In this way, the results resulted to be optimal from a least-squares criterion, and the concentration profiles of the analytes were recovered in their proper quantitative units [30][31][32]. As shown in Fig.…”

“…In this case, a new different constraint named "area correlation constraint"hasbeenproposedfortheMC-ALS quantitative calibration of the analytes in the presence of interferences during the ALS optimization [30]. In this way, not only the concentrations of the analytes can be recovered in real concentration units, but also more accurate quantifications can be achieved, and rotation ambiguities associated with the bilinear model can be diminished [31,32].…”

“…In the present work, the application of the recently developed area correlation constraint in MCR-ALS is shown for the improvement of quantitative results in two data examples [30][31][32]. Firstly, MCR-ALS with the area correlation constraint is tested for the analysis of PAH mixtures using Excitation-Emission (EEM) fluorescence second-order data in laboratory and river water samples and the results are compared with those obtained using the trilinear decomposition model.…”

Second‐order multivariate calibration with the extended bilinear model: Effect of initialization, constraints, and composition of the calibration set on the extent of rotational ambiguity

“…The presence of RA in these systems was later confirmed . Recently, a new constraint was proposed to remove RA in analytical systems of this kind, by adding calibration samples of known analyte content but containing the interferents, and forcing the area under the analyte concentration profile to follow its known nominal concentration . The question remains whether it is possible to develop a successful calibration protocol based on bilinear decomposition of an augmented data matrix, even when a remaining RA exists, and to balance the pros and cons of some available resources to reduce or remove the ambiguity.…”

“…17 Recently, a new constraint was proposed to remove RA in analytical systems of this kind, by adding calibration samples of known analyte content but containing the interferents, and forcing the area under the analyte concentration profile to follow its known nominal concentration. 18 The question remains whether it is possible to develop a successful calibration protocol based on bilinear decomposition of an augmented data matrix, even when a remaining RA exists, and to balance the pros and cons of some available resources to reduce or remove the ambiguity. Three different scenarios are considered, all of them involving basic constraints such as nonnegativity and species correspondence: (a) different initialization schemes, (b) application of local rank constraints, and (c) use of new constraints based on a calibration design containing interferents.…”