(422g) Development of Robust Design Space for Integrated Pharmaceutical Processes through Uncertainty Analysis

A hybrid modeling strategy, integrating both a mechanistic and a data-driven model, has been acknowledged as a potent tool, particularly in the context of Industry 4.0 [1]. By combining the strengths of both mechanistic and data-driven models, hybrid models effectively mitigate the limitations inherent in each approach. The approach is beneficial, especially for modeling pharmaceutical processes, which involve a lot of complicated phenomena and a large variety of materials and process settings. There have been numerous applications of hybrid models to pharmaceutical unit operations, e.g., dry granulation [2] and wet granulation [3]. While understanding model uncertainty is critical to the development and calibration of a model [4,5] limited studies have been performed on uncertainty analysis of hybrid models. The structure of model parameters is complex in hybrid models, which makes it difficult to identify improvement opportunities.

This study presents a methodology of uncertainty analysis of hybrid modeling in integrated pharmaceutical unit operations. We consider both drug substance and drug product manufacturing processes, and investigate the robust design spaces for the individual unit operations and the integrated manufacturing systems. For drug substances, a reactor-crystallizer process will be considered whereas for drug products a dry granulation system consisting of a roller compaction unit and a mill will be investigated. Hybrid models are developed for the model systems using the open-source simulation platform PharmaPy [6] and uncertainty analysis is performed based on a two-step approach, as presented by Matsunami et al. [7]. Firstly, probability density functions of mechanistic model parameters were computed based on Markov-chain Monte Carlo (MCMC) simulation. Secondly, a Monte Carlo simulation was performed for a data-driven ribbon milling model considering the uncertainty bounds obtained in the first step. As candidates of the data-driven modeling approach, the multi-linear regression (MLR) and Neural Network (NN) models were tested, whereas NN showed higher prediction accuracy in the previous study [2]. By comparing the uncertainty bounds generated in the first and the second steps, the uncertainty contributions of mechanistic and data-driven models could be quantified.

The results of the uncertainty analysis clarified the propagation of model and parameter uncertainties in the hybrid modeling framework. A deeper analysis was possible by checking the results of each step. The first MCMC simulation visualized uncertainty caused during the model calibration procedure as well as the dependencies of the model parameters. Based on the results in the second step, the suitability of data-driven model approaches was able to be judged based on uncertainty ranges as well as prediction accuracy. The contributions of mechanistic and data-driven models on the uncertainty were simulated, which could suggest which part of the hybrid model should be improved first. The results were compared with the case study performed for the hybrid model of twin-screw wet granulation [7].

In conclusion, uncertainty analysis could provide vital information to improve the performance of hybrid modeling. The validity of the presented approach was confirmed by comparing the results of the dry granulation model and the wet granulation model. Further studies would be expected to increase the applicability and robustness of the approach.

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[2] Y. Huang, R. B Lagare, P. Bailey, D. Sixon, M. Gonzalez, Z. K. Nagy, G. V Reklaitis. Hybrid model development and nonlinear model predictive control implementation for continuous dry granulation process, Computers & Chemical Engineering, 183, 108586 (2024).

[3] A. A. Barrera Jiménez, K. Matsunami, D. Van Hauwermeiren, M. Peeters, F. Stauffer, E. dos Santos Schultz, A. Kumar, T. De Beer, I. Nopens. Linking material properties to 1D-PBM parameters towards a generic model for twin-screw wet granulation, Chemical Engineering Research and Design, 193, 713–724 (2023).

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[5] Y. Barhate, H. Kilari, W.L. Wu, Z.K. Nagy, Population balance model enabled digital design and uncertainty analysis framework for continuous crystallization of pharmaceuticals using an automated platform with full recycle and minimal material use, Chem. Eng. Sci, 287, 119688, 2024.

[6] D. Casas-Orozco, D. Laky, V. Wang, M. Abdi, X. Feng, E. Wood, G.V. Reklaitis, Z.K. Nagy, Techno-economic analysis of dynamic, end-to-end optimal pharmaceutical campaign manufacturing using PharmaPy, AICHE J., 69 (9), e18142, 2023.

[7] K. Matsunami, A. A. Barrera Jiménez, T. De Beer, I. Nopens. Uncertainty analysis of hybrid modeling: A case study of partial least squares and population balance model in continuous twin-screw wet granulation, 2023 AIChE Annual Meeting, 327e (2023).