The inversion of multiresponse partial least squares models, a useful tool to improve analytical methods in the framework of analytical quality by design

Analytical Quality by Design (AQbD) is the adaptation of Quality by Design (QbD) when it is applied to the development of an analytical method. The main idea is to develop the analytical method in such a way that the desired quality of the Critical Quality Attributes (CQAs), stated via the analytical target profile (ATP), is maintained while allowing some variation in the Control Method Parameters (CMPs). The paper presents a general procedure for selecting factor levels in the CMPs to achieve the desired responses, characterized by the CQAs, when liquid chromatographic methods are to be used for the simultaneous determination of several analytes. In such a case, the CMPs are usually the composition of the ternary mobile phase, its flow rate, column temperature, etc., while typical CQAs refer to the quality of the chromatograms in terms of the resolution between each pair of consecutive peaks, initial and final chromatographic time, etc. The analytical target profile in turn defines the desired characteristics for the CQAs, the reason for the whole approach. The procedure consists of four steps. The first is to construct a D-optimal combined design (mixture-process design) to select the domain and levels of the CMPs. The second step is to fit a PLS2 model to predict the analytical responses expressed in the ATP (the good characteristics of the chromatogram) as a function of the CMPs. The third step is the inversion of the PLS2 model to obtain the conditions necessary to obtain the preset ATP in the corresponding CQAs. The inversion is performed computationally in order to estimate the Pareto front of these responses, namely, a set of experimental conditions to perform the chromatographic determination for which the desired critical quality attributes are met. The fourth final step is to obtain the Method Operable Design Region (MODR), that is, the region where the CMPs can vary while maintaining the quality of the CQAs. The procedure has been applied to some cases involving different analytes, all of which are regulated by the European Union due to their toxicity to human health, namely five bisphenols and ten polycyclic aromatic hydrocarbons. [Display omitted] •Method Operable Design Region obtained with a Partial Least Squares model inversion.•Finding, by PLS2, Control Method Parameters to fulfil Critical Quality Attributes.•A computational algorithm to invert a PLS2 model to get Method Operable Design Region.•D-optima criteria used to reduce experiments