Modeling of HILIC retention behavior with theoretical models and new spline interpolation technique

Abstract

When it is taken into account that hydrophilic interaction liquid chromatography (HILIC) as an analytical method is relatively young compared with the other techniques, retention modeling could still bring scientifically valuable data to the field. Therefore, in this paper, olanzapine and its 8 impurities were selected as a test mixture, considering that they have never been analyzed in HILIC before. Their investigation on 4 different HILIC columns (bare silica, cyanopropyl, diol and zwitterionic) has been performed. The mixture of 9 structurally similar substances allows the examination of complex HILIC retention behavior depending on the chemical properties of the analytes, as well as of the stationary phase. To describe the nature of the relationship between the retention and the stronger eluent content in the mobile phase, we fitted experimentally obtained data to several theoretical (localized adsorption, nonlocalized partition, quadratic, and mixed) models. Results show that the best fit is the quadratic model with the highest R 2 and cross-validated coefficient of determination (Q 2 ) values, but its usage has some drawbacks. With the aim to improve the possibility to predict retention behavior in HILIC, a new empirical model was proposed. For that purpose, a spline interpolation technique was performed, by dividing the experimental range into several subdivisions. This type of interpolation was performed for the first time in the chromatographic field.The estimation of the polynomial equations was performed using Q 2 values. Obtained Q 2 values pointed out the goodness of fit of the model, as well as its good predictive capabilities. In the end, the prediction capabilities were experimentally verified, under randomly chosen conditions from the experimental range. The errors in prediction were all under 10%, which is satisfying for HILIC.

Quality-by-design in pharmaceutical development: From current perspectives to practical applications

“…In all cases, DoE experiments are for HPLC method fine-tuning, previously reported methods or preliminary experiments being the starting point. Numerous reverse phase HPLC methods optimized using AQbD are published, but there are several using gradient HILIC (hydrophilic interaction chromato graphy) methods as well (53). Using isocratic HPLC methods, the most frequent CMPs are the aforementioned input variables (54,55).…”

Recent applications of retention modelling in liquid chromatography

“…For that reason, Tumpa et al. divided the experimental space into different segments with an interpolated polynomial for each part, which is known as spline interpolation [157]. The MM, Q, ADS, and LSS model were tested in this study.…”

Prediction of Analyte Retention Time in Liquid Chromatography

“…To enhance the accuracy of retention models in HILIC, Tumpa et al 137 have demonstrated the construction of polynomial models using a spline interpolation technique based on olanzapine and its impurities on various HILIC stationary phases. High Q 2 values indicated the good predictive ability of the polynomial equations, with the most accurate model giving errors of prediction below 10% over all studied HILIC systems in comparison to the LSSM, adsorption, mixed-mode, and quadratic models.…”

“…The experimental data describing the relationship of ln k versus φ fit quite well to a quadratic relationship (eq ). The mixed-mode model (eq ), which combines eq and eq by considering both partitioning and adsorption mechanisms is more suitable to describe HILIC retention than linear models over a wider φ range. where c 1 expresses the interaction between analytes and the SP and c 2 the interaction between analytes and MP solvents.…”

“…To enhance the accuracy of retention models in HILIC, Tumpa et al . have demonstrated the construction of polynomial models using a spline interpolation technique based on olanzapine and its impurities on various HILIC stationary phases.…”