Combination of partial least squares regression and design of experiments to model the retention of pharmaceutical compounds in supercritical fluid chromatography.

This work presents a first attempt to establish a model of the retention behaviour for pharmaceutical compounds in gradient mode SFC. For this purpose, multivariate statistics were applied on the basis of data gathered with the Design of Experiment (DoE) methodology. It permitted to build optimally the experiments needed, and served as a basis for providing relevant physicochemical interpretation of the effects observed. Data gathered over a broad experimental domain enabled the establishment of well-fit linear models of the retention of the individual compounds in presence of methanol as co-solvent. These models also allowed the appreciation of the impact of each experimental parameter and their factorial combinations. This approach was carried out with two organic modifiers (i.e. methanol and ethanol) and provided comparable results. Therefore, it demonstrates the feasibility to model retention in gradient mode SFC for individual compounds as a function of the experimental conditions. This approach also permitted to highlight the predominant effect of some parameters (e.g. gradient slope and pressure) on the retention of compounds. Because building of individual models of retention was possible, the next step considered the establishment of a global model of the retention to predict the behaviour of given compounds on the basis of, on the one side, the physicochemical descriptors of the compounds (e.g. Linear Solvation Energy Relationship (LSER) descriptors) and, on the other side, of the experimental conditions. This global model was established by means of partial least squares regression for the selected compounds, in an experimental domain defined by the Design of Experiment (DoE) methodology. Assessment of the model's predictive capabilities revealed satisfactory agreement between predicted and actual retention (i.e. R(2)=0.942, slope=1.004) of the assessed compounds, which is unprecedented in the field.