Development of a mathematical model for the water distribution in freeze-dried solids

Purpose. Development of a mathematical model to provide information about the amount of water associated with a protein and an excipient in a lyophilized product. Methods. The moisture content of the product and the mass fraction of each component were used to derive a model for the calculation of the mass of water associating with each component. The model was applied to lyophilized formulations of rhDNase containing various amounts of mannitol or lactose. The total water content was investigated by thermogravimetry, crystalline properties by X-ray powder diffraction and water uptake behaviour using a moisture microbalance system. Results. Calculations based on the model suggest that in a lyophilized rhDNase-mannitol formulation where the sugar is crystalline, most of the water is taken up by the protein. However, in the lyophilized rhDNase-lactose formulation where the sugar is amorphous, water is taken up by both the sugar and protein to a comparative extent. At high relative humidities when the amorphous sugar undergoes crystallization, the model can accommodate such a change by allowing for the formation of an additional crystalline phase. Conclusions. The rhDNase-sugar formulations show excellent conformity to the model which provides quantitative information about the distribution of water in the lyophilized binary protein-excipient products.