Dynamic Modeling and Optimal Design Space Determination of Pharmaceutical Crystallization Processes: Realizing the Synergy between Off-the-Shelf Laboratory and Industrial Scale Data

Well-designed and operated pharmaceutical crystallization can enhance the key features of the active pharmaceutical ingredients, which can be taken to the next level by a model-based design. Model development not only requires computer implementation, kinetic identification, and advanced programming skills but also a suitable number of information-rich experiments. Numerous products have been crystallized for a long time, with many related laboratory-scale experiments and plant-scale manufacturing data accumulated from past developments and productions. The question arises: can these historical data be utilized to build process models, which can be used subsequently to optimize processes? We aim to demonstrate in this study that this approach can be feasible. To illustrate this, we used the data of two commercial crystallization production campaigns, totaling 16 industrial crystallizations, and six laboratory experiments, four of which were formerly performed for different purposes. Our tailored PBM involves primary and secondary nucleation, crystal growth, and dissolution and can simultaneously reproduce laboratory- and plant-scale dynamics. Despite relying on nontargeted experiments and measuring/sampling strategy, the estimated parameters were accurate, with an average deviation between the nominal values and 95% confidence interval bonds of 16.1%. The model was employed to construct an optimal design space (DS) for a temperature cycling operation involving, as a constraint, 2, 3, and 4 cycles: the goal was to define a temperature domain with minimal batch time and heating/cooling energy demand that respects the constraints on the product PSD and heating/cooling rates. The problem was solved as a constrained robust optimization, where discrete temperature stamps and corresponding time stamps were optimized. The optimal operation halved the current batch time. The optimized temperature profile was validated on a laboratory scale for two particle size specifications. More expansive DS (1 vs 0.5 h random temperature variation allowed around the nominal temperature profile) was observed to translate to longer batch times (30 vs 25 h) and deeper temperature cycles of 40 vs 20 °C, reflecting a trade-off between nominal performance and robustness. The optimal laboratory-scale operation was validated successfully by repeated experiments.