Combining Mathematical Modeling and Thermal Infrared Data in the Freezing of Pharmaceutical Liquid Formulations

Infrared-based (IR) thermal imaging data was combined here with mathematical modeling to describe the freezing process of a pharmaceutical formulation being lyophilized using two different loading configurations; (i) vials in direct contact with the shelf and (ii) vials suspended over it. In all the experiments, the nucleation event was trigged at a specific time instant using the vacuum induced surface freezing (VISF) method. The IR thermal data was given as input to three different mathematical models for freezing and used to estimate the resulting cake's pore size (dp) distribution. The resulting dpvalues were then compared to experimental data obtained through SEM images coupled with an image segmentation tool. The supersaturation model showed the best agreement between the estimated dpand experimental values, while minor discrepancies were shown by the other two models. Nonetheless, the outcomes of these last two models, given as inputs to a mathematical model for the primary drying phase, resulted in satisfactory predictions of the product temperature at the moving front, the product resistance to vapor flow, and the primary drying end point. It follows that the combination of the IR thermocamera and freezing modeling is a promising tool for the in-line monitoring and optimization of a freeze-drying cycle.