Mathematical modelling of thermal interactions during freezing: Effects on product morphology and drying behaviour

Freeze-drying of biopharmaceuticals is a crucial operation to increase their stability and shelf-life. Parenteral drug products are generally frozen in vials placed in contact with a temperature-controlled shelf. Uncontrolled nucleation is a source of batch heterogeneity, as nucleation occurs at different temperatures in vials frozen at different times. Heat released from a vial undergoing solidification may be transferred to neighbouring vials, impacting their thermal profiles and altering the distribution of the nucleation temperature and the freezing rate within the batch. This study characterised thermal coupling in interacting and non-interacting loading configurations. These estimations were used as input in a simple 1D mathematical model to assess the effect of thermal interactions on the freeze-dried product morphology. Thermal interactions strongly impacted the predicted nucleation temperature, especially for late-nucleating vials, and the freezing rate. The combined effect of thermal coupling on nucleation temperature and freezing rate resulted in different frozen product morphology. Heterogeneity within a batch of interacting vials was higher compared to non-interacting vials, leading to broader pore size and drying time distributions, in agreement with experimental data. The presented model provides insight into the thermal history of each vial of the batch during freezing, supporting the rational design of freezing processes.