Constrained Version of the Dynamic Response Surface Methodology for Modeling Pharmaceutical Reactions

The Dynamic Response Surface Methodology (DRSM; Klebanov, N.; Georgakis, C. Ind. Eng. Chem. Res 2016, 55, 4022 ) is a data-driven modeling methodology for time-resolved measurements from Design of Experiments data sets. To extend its use to semi-infinite domains, a second version was proposed (Wang, Z. Y.; Georgakis, C. Ind. Eng. Chem. Res 2017, 56, 10770 ), which uses an exponential transformation of time as the independent variable. Here, we further improve upon this later version by imposing regression constraints, motivated by our qualitative understanding of the physical nature of the reaction system. We apply it to the modeling of several pharmaceutical case studies provided by our industrial collaborators. This constrained DRSM approach is able to model these compositional data more parsimoniously and with greater accuracy than the initial DRSM, eliminating the existence of oscillations near the end of some experiments from the model predictions.