Digital Design of the Crystallization of an Active Pharmaceutical Ingredient Using a Population Balance Model with a Novel Size Dependent Growth Rate Expression. From Development of a Digital Twin to In Silico Optimization and Experimental Validation

Prediction and control of the product properties in crystallization processes are practical challenges in the pharmaceutical industry. Effective crystallization process design and operation techniques are needed to meet the critical quality attributes (CQAs) and minimize batch-to-batch variation. Mathematical modeling can enhance process understanding and save a considerable amount of time, effort and raw material when used in process development following the guidelines of the Quality-by-Design (QbD) framework. When the mathematical model of the process is fitted and validated with experimental data, it provides a digital twin of the process that enables execution of in silico design of experiments (DoEs), which is particularly beneficial when the number of factors increases or if the material is expensive or sparingly available, e.g., during early stage development. This work presents the benefits of crystallization process modeling by studying an active pharmaceutical ingredient (API) from Takeda Pharmaceuticals International Co., referred hereafter as Compound A. A framework for crystallization model construction, parameter estimation and validation are demonstrated through the case study of Compound A by using the population balance modeling (PBM) approach. Secondary nucleation, size dependent growth (SDG), and size dependent dissolution mechanisms are considered. Size dependency is introduced with a new formulation capturing the considerably slower growth of small crystals (D-90 < 10 mu m) while having size dependency for the larger crystal size domain (D-90 > 200 mu m) similar to the models from the literature. To make the model parameter estimation more industrially relevant, a novel method developed recently by the authors is applied to use the focused beam reflectance measurement (FBRM) data directly in the parameter estimation without further transformations. The kinetic parameters are estimated by minimizing the difference between measured and simulated concentrations, crystal size distributions (CSDs) and maximizing the correlation between the simulated crystal number density and measured FBRM counts. The paper also illustrates that the novel SDG rate expression can capture the CSD dynamics considerably better than the standard SDG rate models. The digital twin is used for in silico DoE and process optimization, and the simulation results are validated experimentally, demonstrating the benefits of model-based digital design for crystallization process development.