QbD is a systematic approach to pharmaceutical development based on scientific knowledge and risk management . Continuous manufacturing is a promising alternative and important for the implementation of QbD because it reduces the need of scale-up studies ; it requires smaller equipment size and thus minimizes the plant footprint ; and it decreases human factor using automated operation and thus decreases labor cost . To facilitate the development of continuous pharmaceutical manufacturing, each unit operation must be well understood in terms of the effect of different material properties and operational conditions on the final product quality attributes. This goal can be facilitated by the utilization of computer-aided process systems engineering (PSE) approaches. Flowsheet modeling is an efficient way to understand manufacturing process dynamics. An integrated flowsheet model can be used in the design, analysis, and optimization of a chemical process . Simulation results can help identify the possible process integration requirements, study multiple designs and test control strategies. In pharmaceutical process modeling, a computationally efficient equation-oriented process simulator (gPROMS) has been used to develop models for unit operations and build flowsheet models  .
Among different modeling methods, residence time distribution (RTD) theory has been commonly used in developing pharmaceutical unit operation models. RTD is defined as the probability distribution of the time that the particles stay inside one or more unit operations in a continuous flow system . With RTD, process changes (e.g., material changes, process disturbances) can be traced throughout the system. This helps determine disturbance dissipation along the process and thus help decide when to collect final products with desired quality. Consequently mathematical models based on RTD theory are very useful for modeling the continuous pharmaceutical manufacturing process.
We focus on building validated integrated flowsheet model with RTD-based unit operation models for direct compression and granulation lines. Major unit operations such as feeders, comil, blenders, transfer pipes, feed frames, tablet presses, and granulation equipment were modeled and properly integrated. These flowsheet models are used to simulate and predict the dynamics of entire continuous direct compression processes given input such as material properties and operational conditions. Moreover, the behavior of different processes in response to disturbances can also be simulated. Flowsheet models can also be easily customized. Users can drag and drop necessary unit models and connect them based on their process design or to test different designs and different processing strategies. Graphic user interfaces (GUIs) have been implemented in our flowsheet simulations to provide users with an icon-based interface (i.e., no exposure to model code) and set parameters for each unit. Multiple process configurations can be easily set with GUIs, which makes it convenient to run different simulations.
The objective of this presentation is to highlight the use of flowsheet modeling tools in the pharmaceutical tablet manufacturing process and to demonstrate their applications for process design. Because the process models can have thousands of differential and algebraic equations (DAEs) and integral expressions, they can be difficult to solve with deterministic solvers. In these cases, surrogate modeling methodologies are adopted to address the challenges. However with the high-dimension problems, the application of surrogate modeling is limited. For example, Kriging method is computationally expensive for high dimensional problems because it needs to numerically solve a maximum likelihood estimation problem to fit the model . In contrast, Radial Basis Functions (RBF) is a promising alternative because it can provide simple and efficient model to approximate the original model . We focus on solving high-dimensional design problems by using RBF-based surrogate modeling strategies. We introduce flexibility analysis for the design problem to quantify the ability of a process to maintain feasible operation in the presence of inherent variability or external disturbances . The final goal is to achieve a more robust design for the continuous pharmaceutical manufacturing process.
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