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

Purpose. Development of a mathematical model to provide information about t he amount of water associated with a protein and an excipient in a lyophili zed 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 wa ter associating with each component. The model was applied to lyophilized f ormulations of rhDNase containing various amounts of mannitol or lactose. T he total water content was investigated by thermogravimetry, crystalline pr operties by X-ray powder diffraction and water uptake behaviour using a moi sture microbalance system. Results. Calculations based on the model suggest that in a lyophilized rhDN ase-mannitol formulation where the sugar is crystalline, most of the water is taken up by the protein. However, in the lyophilized rhDNase-lactose for mulation 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 a morphous 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 th e model which provides quantitative information about the distribution of w ater in the lyophilized binary protein-excipient products.