Experimental and stochastic analysis of lyophilisation

The development of the freeze-drying processes through the use of a combination of targeted experiments and the application of multidimensional computational models is applied increasingly in pharmaceutical practice, especially for scale-up purposes. This study deals with the analysis of uncertainties in the data on material properties and model parameters, and their influence on the results delivered by advanced computational models of lyophilisation. As a means of uncertainty analysis, the Stochastic Collocation Method is applied, allowing the use of existing reliable deterministic models as black boxes in the stochastic computations. As a deterministic model, the lyophilisation model is used, based on the axisymmetric approximation of a vial, and the Boundary Element Method as a solver. Five parameters, covering material properties, process conditions and model constants, are selected for the sensitivity analysis simulation of the lyophilisation of an aqueous mannitol solution. The results show that during the initial stage of the primary drying heat transfer from the shelf is crucial, and that the uncertainties in the contact surface area and material properties of the vial play a more important role than the thermal properties of the drying material. When the temperature of the material reaches its distinct primary drying stage level the mass transfer through the porous cake becomes the most important, with great sensitivity to the Knudsen diffusivity in the porous cake. We observed uncertainties in the results for the primary drying time in the order of ±6%, and uncertainties in the results for temperatures of ±0.6°C in the frozen material and ±3°C in the porous cake. The uncertainty analysis proved to be a great help in determining the critical parameters in the heat and mass transfer during the important primary drying step, which led to a better definition of the numerical model for use in the context of design space determination.