(173d) Automated Model-Based Experimental Design Procedure for Robust Digital Twin Development for Continuous Crystallization Systems

Systematic model-based design and control strategies are known to be highly effective in handling the nonlinearity of crystallization processes and in producing crystals with target crystal properties.¹ However, successful experimental implementation of these strategies requires an accurate system-specific population balance model with reliable kinetic models and appropriately estimated kinetic parameters, which can serve as digital twins of a particular process. The two major challenges in achieving this are a) the determination of relevant empirical kinetic mechanistic equations describing the crystallization kinetics of the system and b) the precise estimation of unknown kinetic parameters.² The quality of the parameter estimates depends on the experiments conducted to estimate them and the quality of the experimental data; thus, a large number of experiments are required for high accuracy making the entire process highly resource intensive.

The goal of the iterative model-based experimental design framework (IMED or MBDoE) is to use the current imprecise mathematical model to guide future experimental design to improve parameter estimates by maximizing the information gain from each experiment. With increasing attention toward continuous crystallization processes, the need for frameworks for continuous crystallization model development is increasing. The traditional route of developing models for continuous crystallization follows a batch-to-continuous route, where initial estimates of kinetic parameters are obtained in batch setups, followed by re-estimation in continuous setups.³ Although this represents a feasible approach, the overall framework could be time- and resource-intensive, and in cases where the end target is a continuous crystallization process model, directly estimating the kinetic parameters in continuous setups using an automated and systematic framework could be more efficient. This study addresses this gap by proposing a systematic iterative model-based experimental design framework for continuous crystallization systems (CIMED) to develop an accurate high-fidelity model for modeling these processes.

The first step of the computational framework focuses on employing statistical model discrimination exercises in conjunction with parameter estimation procedures to choose a reliable kinetic model for the system in consideration from a mechanistic model library generated using logical combinations of different commonly used expressions for modeling crystallization mechanisms. Once the appropriate model structure has been finalized, the iterative model-based design of experiments (MBDoE) framework is implemented using D-optimal criteria to minimize the total number of experiments necessary to obtain accurate parameter estimates with tighter confidence intervals. To experimentally validate the developed framework, a robust automated platform for conducting continuous crystallization experiments in a closed-loop manner was developed using a single-stage MSMPR setup. Communication between the experimental and high-performance computing setups was established for the online implementation of the optimized experimental conditions provided by the optimizer in a sequential manner. The developed platform and framework successfully estimated the kinetic parameters for the continuous crystallization of a model compound, diphenhydramine hydrochloride, in isopropanol, using both steady-state and dynamic measurements. To the best of our knowledge, this is the first demonstration of an automated continuous crystallization platform with an online iterative model-based experimental design framework for the development of population balance-based models for continuous systems.

Acknowledgements

This work is supported by the US Food and Drug Administration (FDA) under contract number 75F40121C00106.

References:

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