Primary Drying Optimization in Pharmaceutical Freeze-Drying: A Multivial Stochastic Modeling Framework

Primary drying is the most time-consuming and energy-intensive step in pharmaceutical freeze-drying. Minimizing the duration of this stage is of paramount importance to speed up process development and product manufacturing. In this study, we propose a stochastic modeling framework that can help to reach this target. The framework is composed of five sequential steps: model development, sensitivity analysis, model calibration, model validation, and dynamic optimization. Three critical issues are addressed and accounted for in the model structure, namely, (i) the effect of time-varying operating conditions on the process key performance indicators (KPIs); (ii) the dynamic evolution of the water vapor partial pressure inside the drying chamber; and (iii) the impact of drying heterogeneity on the primary drying duration. We cope with the first two issues by introducing macroscopic energy and mass balances within the model formulation. The third issue is addressed by allocating intralot variability as a parametric uncertainty in the model parameter with the strongest sensitivity toward the process KPIs. The proposed stochastic model is calibrated and validated with data generated from industrial experiments. Nonlinear dynamic optimization is then exploited to minimize the duration of primary drying while simultaneously guaranteeing the fulfillment of tight constraints on the product temperature and sublimation rate. Experimental results show a reduction of ∼20% of the primary drying duration with the optimized protocol when compared to standard (i.e., at constant shelf temperature and chamber pressure) protocols, while ensuring the same product quality.