Advanced approach to build the design space for the primary drying of a pharmaceutical freeze-drying process

This paper deals with the design space of a pharmaceutical freeze-drying process. Mathematical modeling is used to investigate the effect of the operating conditions [shelf temperature (T(shelf)) and chamber pressure (P(c))] on product temperature (that has to remain below a limit value) and sublimation flux (that has to be lower than a level that would cause choked flow). The algorithm takes into account the variation of the design space with time due to the increase in the dried layer thickness. Besides T(shelf) and P(c), the dried layer thickness is used as the third coordinate of the diagram, thus resulting in just one graph that can be used to build recipes with variable operating conditions, as well as to analyze the effect of process failures. Such results are compared with those obtained when the variation of the design space with time is not accounted for; in this case, the design space comprises those operating conditions that fulfill the operation constraints throughout primary drying, thus giving a much more conservative recipe when designing the process or potentially misleading results when analyzing process failures. Finally, the proposed method has been used to design, and experimentally validate, a recipe for a pharmaceutical formulation.