Iterative model-based optimal experimental design for mixture-process variable models to predict solubility

Abstract

Crystallization process design relies heavily on predictive solubility models. However, their calibration is resource- and labour-intensive, especially for multicomponent solvent mixtures at different process temperatures. Additionally, solubility data collection often occurs in a constrained design space due to e.g., polymorphism and solvent miscibility limitations. Optimal experimental design techniques enable the efficient use of resources by specifying a (minimum) number of maximally informative experiments focused on improving a statistical criterion for a given model structure in a constrained design space. This work generates D-, A- and I-optimal experimental designs for the commonly applied Van’t-Hoff Jouyban-Acree (VH-JA) solubility regression model, in which it is demonstrated that I-optimal designs reduce the experimental burden for model calibration by approximately 25 % as compared to a typical screening dataset. Alternatively, existing datasets can be augmented to significantly improve model prediction power. The suggested workflow is applied to two case studies: itraconazole in tetrahydrofuran-water and mesalazine in ethanol-polyethylene glycol-water. The screening datasets of 72 and 212 runs were augmented with 16 additional experiments, resulting in a 33 % and 67 % reduction in the corresponding model prediction variance, respectively, which translates to improved model reliability at unprobed conditions.