Application of Model-Free and Model-Based Quality-by-Control (QbC) for the Efficient Design of Pharmaceutical Crystallization Processes

摘要

The design of pharmaceutical crystallization processes is a challenging engineering problem because of the specific and versatile quality requirements of the end-product, amplified by the tight regulatory standards. The current industrial standard for crystallization process design is based on the use of the quality-by-design (QbD) framework, which relies on factorial design of experiments (DoE). Hence, QbD inherently generates a large number of resource-consuming open loop crystallization experiments. This is especially true when more complex operating conditions need to be designed, such as temperature cycles, which require a large number of decision variables in the DoE. In contrast, the recently proposed quality-by-control (QbC) approach relies on feedback control algorithms to directly achieve the desired product properties by manipulating the appropriate process conditions. The first aim of this work is to demonstrate the effectiveness of a model-free feedback control strategy, referred to as model-free (mf) QbC. Direct nucleation control (DNC) and supersaturation control (SSC) are applied as a part of the mfQbC approach, which, ideally, requires only two feedback control experiments to obtain a temperature profile that results in obtaining the desired product quality. Although mfQbC provides a rapid process design, it is often suboptimal. In addition, it is shown that the experimental data generated by mfQbC can be used for process model development and kinetic parameter estimation. The validated model enables optimization-based design using the model-based (mb) QbC framework. For this case study, a population balance (PB) based process model is developed, which involves primary and secondary nucleation, growth, and dissolution, as well as a novel formulation of agglomeration, and deagglomeration of crystals. In addition to taking into account the agglomeration, the number of agglomerates is also tracked as a balance between the agglomeration and deagglomeration events. The kinetic parameters are estimated using a novel objective function formulation relying on the minimization of the difference between the measured and simulated concentrations and crystal size distributions (CSDs) and the maximization of the correlation between the simulated crystal number density and measured crystal count data obtained from focused beam reflectance measurement (FBRM). The kinetic parameters are identified based on the experimental data generated from the mfQbC, which inherently reduced the experimental effort required for the model development. The temperature profile is optimized for the fine index and agglomeration degree minimization. The repeated open-loop implementation of mfQbC- and mbQbC-designed processes showed that the batch-to-batch variation is low and the product quality is high in both cases. The proposed general framework is illustrated for the systematic quick and optimal design of crystallization processes that require temperature cycles with a low number of experiments.