Development of a robust optimization strategy for primary drying in lyophilization, considering intra- and...

Conventional models for primary drying in freeze-drying, whether deterministic or stochastic, fail to adequately account for inherent process variability, including vial-to-vial heterogeneity and batch-to-batch variation, limiting their applicability for robust process design under Quality by Design (QbD) principles. This work presents a multi-batch stochastic-spatial simulation framework (MBS₃F) that explicitly incorporates spatial and stochastic variability into mechanistic modeling of primary drying. The approach links the vial heat transfer coefficient (K_v) to shelf position, enabling the representation of intra-batch heterogeneity and batch-to-batch variability through multi-batch simulation. A three-stage optimization strategy, combining deterministic design space definition, probabilistic robustness evaluation, and predictive statistical process control, is implemented in alignment with ICH Q8-Q10 guidelines. The model was validated against independent experimental data from a placebo freeze-drying run (5% w/v NaCl), achieving a coefficient of determination (R²) of 0.97 for product temperature predictions and a relative error of 4.4% for primary drying time. The proposed framework enables the robust identification of operating conditions that simultaneously ensure product quality and equipment performance, while accounting for spatial heterogeneity and process variability. These results show that integrating stochastic variability with spatially resolved mechanistic modeling enable a more realistic and reliable definition of the freeze-drying design space.