Quality by design: optimization of a freeze-drying cycle via design space in case of heterogeneous drying behavior and influence of the freezing protocol

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Abstract
Purpose: This paper shows how to optimize the primary drying phase, for both product quality and drying time, of a parenteral formulation via design space. Methods: A non-steady state model, parameterized with experimentally determined heat and mass transfer coefficients, is used to define the design space when the heat transfer coefficient varies with the position of the vial in the array. The calculations recognize both equipment and product constraints, and also take into account model parameter uncertainty. Results: Examples are given of cycles designed for the same formulation, but varying the freezing conditions and the freeze-dryer scale. These are then compared in terms of drying time. Furthermore, the impact of inter-vial variability on design space, and therefore on the optimized cycle, is addressed. With this regard, a simplified method is presented for the cycle design, which reduces the experimental effort required for the system qualification. Conclusions: The use of mathematical modeling is demonstrated to be very effective not only for cycle development, but also for solving problem of process transfer. This study showed that inter-vial variability remains significant when vials are loaded on plastic trays, and how inter-vial variability can be taken into account during process design.

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