Three-point multivariate calibration models by correlation constrained MCR-ALS: A feasibility study for quantitative analysis of complex mixtures

When it comes to address quantitative analysis in complex mixtures, Partial Least Squares (PLS) is often referred to as a standard first-order multivariate calibration method. The set of samples used to build the PLS regression model should ideally be large and representative to produce reliable predictions. In practice, however, the large number of calibration samples is not always affordable and the choice of these samples should be handled with care as it can significantly affect the accuracy of the predictive model. Correlation constrained multivariate curve resolution (CC-MCR) is an alternative regression method for first-order datasets where, unlike PLS, calibration and prediction stages are performed iteratively and optimized under constraints until the decomposition meets the convergence criterion. Both calibration and test samples are fitted into a unique bilinear model so that the number of calibration samples is no longer a critical issue. In this paper we demonstrate that under certain conditions CC-MCR models can provide for reasonable predictions in quantitative analysis of complex mixtures even when only three calibration samples are employed. The latter are defined as samples having the minimum, the maximum and the average concentration, providing for a simple and rapid strategy to build reliable calibration model. The feasibility of three-point multivariate calibration approach was assessed with several case studies featuring mixtures of different analytes in presence of interfering species. Satisfactory predictions with relative errors in the range 3-15% were achieved and good agreement with classical PLS models built from a larger set of calibration samples was observed.