Establishing a Multi-Vial Design Space for the Freeze-Drying Process by Means of Mathematical Modeling of the Primary Drying Stage

Abstract

Primary drying is the most critical stage of the freeze-drying process. This work aimed to establish a design space for this process by means of mathematical modeling of the primary drying stage, capable of addressing the thermal characteristics of distinct vial suppliers. Modeling of primary drying was implemented on Microsoft Excel using steady-state heat and mass transfer equations at two extreme conditions as assessed by risk analysis, to predict product temperature and primary-drying time. The heat transfer coefficients (K_v) of four different vial suppliers were experimentally determined, both, at the center and edge of the freeze-dryer's shelf. Statistically significant differences (ANOVA p<0.05) were observed between suppliers throughout the assessed pressure range. Overall, the average K_ve/K_vc (edge/center) ratio was higher than 1.6 for all suppliers due to the radiation effect. A design space for the drying process was established using mathematical modeling taking into account the K_v of the worst-case supplier, in the shelf edge. A primary drying cycle was carried out at a shelf temperature of -25 °C and a chamber pressure of 45 mTorr for 8 % sucrose and at -10 °C and 75 mTorr for 5 % NaCl. Freeze-dried products with good cosmetic appearance were obtained for the four vial suppliers both, in the shelf center and edge. The results show that it is possible to predict and establish the critical parameters for the primary drying stage, under a design space concept, considering the differences in the K_v of vial suppliers without adverse consequences on the quality of the finished freeze-dried product.

Keywords: Freeze-drying; Lyophilization; Mathematical model; Processing; Quality by design; Simulation; Sucrose; Thermodynamic.