(340am) Optimization Techniques for Pharmaceutical Manufacturing Processes through Design Space Analysis

Research Interests: Optimization under uncertainty, Pharmaceutical Manufacturing, Mathematical Modeling and Simulation, Large-Scale optimization

Over the past two decades, research efforts have increased on methods for the identification of operating regions that promote manufacturing efficacy while assuring product quality. Quality-by-Design (QbD) and Quality-by-Control (QbC) have become mainstream methodological frameworks for identification of such operating regions, often referred to as the design space. The design space has been eloquently characterized as “the multidimensional combination and interaction of input variables (e.g., material attributes) and process parameters that have been demonstrated to provide assurance of quality” [1]. Given the uncertain nature of both model parameters and operating conditions, the extension considering assurance under uncertainty results in a probabilistic design space, or a design space that provides assurance of quality to an acceptable degree of certainty.

A major requirement for any method that utilizes digital modeling, such as design space identification, is the accuracy of the process digital twin. Some commercial software exists for such modeling, for instance Aspen or gPROMS FormulatedProducts, however such frameworks lack flexibility to allow for complex, custom analysis techniques with external solving algorithms and simulation/optimization of discrete processes. Therefore, throughout this body of work, the use of custom Python frameworks as well as a new open-source framework for hybrid pharmaceutical flowsheet simulation, PharmaPy [2], have been used to simulate and/or optimize pharmaceutical processes.

As an introduction to this newer framework, an example flowsheet optimization using PharmaPy is shown. Here a synthesis-purification process is shown for a representative flowsheet of an active pharmaceutical ingredient (API). Since PharmaPy is written in Python and retains the object-oriented style of software design, almost any algorithm that allows function callbacks for optimization may be employed to optimize a PharmaPy process simulation. The synthesis-purification process will be optimized using derivative-free approaches. A few process alternatives will be optimized and compared to show the utility of the simulator and the utility of derivative-free optimization approaches in such an open framework.

Although derivative-free approaches provide a computational advantage over an enumerative/combinatorial procedure, using derivative-based, simultaneous equation-oriented optimization has the benefit of guaranteeing local, or in some cases global, optima. For instance, design space identification may be set up as a flexibility analysis problem by exploiting a large-scale mixed-integer programming formulation. Utilizing a pythonic framework, it has been shown that in open-loop pharmaceutical manufacturing problems, flexibility analysis style formulations may be written and solved with a one to two order of magnitude decrease in computational time when compared with more traditional sample-based approaches for design space identification [3].

In this presentation, an overview of pharmaceutical modeling and optimization techniques in Python will be shown. A case study utilizing the new simulation package, PharmaPy, will be used to highlight the utility of the framework and the capabilities to use external packages for callback-based simulation-optimization. Then, a separate case study will be analyzed to demonstrate the advantage of simultaneous equation-oriented optimization when such models are available. The probabilistic design space of a reactor for API synthesis will be identified under model uncertainty. With these case studies, it is clear that open-source, Pythonic frameworks present an enormous opportunity for collaboration while retaining a high level of computational robustness by utilizing well-developed existing computational solvers and packages. The push for digital modeling and digital support for manufacturing robustness through QbD and QbC can be addressed through Pythonic tools and provides an excellent opportunity for companies to exploit the largest bank of readily available, open-source, scientific analysis tools. The researcher holds a unique set of skills that brings together the nexus of software development, mathematical modeling, and numerical algorithms. With knowledge of large-scale mathematical programming and the appropriate solution techniques, as demonstrated in these case studies, pharmaceutical manufacturing problems can be formulated and solved to produce efficacious consumer goods more easily while simultaneously considering economically optimal operations.

Sources:

1. Food and Drug Administration. Guidance for Industry Q8 Pharmaceutical Development; Technical Report August; U.S. Department of Health and Human Services, Food and Drug Administration, Center for Drug Evaluation and Research (CDER): Rockville, MD, USA, 2009.
2. D. Casas-Orozco, D.J. Laky, V. Wang, M. Abdi, X. Feng, E. Wood, C.D. Laird, G.V. Reklaitis, and Z.K. Nagy, PharmaPy: An Object-Oriented tool for the development of hybrid pharmaceutical flowsheets, Comput. Chem. Eng., 2021. https://doi.org/10.1016/j.compchemeng.2021.107408
3. Laky, D.; Xu, S.; Rodriguez, J.S.; Vaidyaraman, S.; García Muñoz, S.; Laird, C. An Optimization-Based Framework to Define the Probabilistic Design Space of Pharmaceutical Processes with Model Uncertainty. Processes 2019, 7, 96. https://doi.org/10.3390/pr7020096