Modeling of freezing step during freeze‐drying of drugs in vials

Abstract

in Wiley InterScience (www.interscience.wiley.com).A mathematical model that simulates temperature profiles during freezing process of standard pharmaceutical formulations (mannitol and BSA based) was set up in twodimensional axsymmetric space, and the ice crystal mean sizes were semi empirically estimated from the resulting temperature profiles. Water vapor mass transfer permeability values during sublimation step were also estimated from ice phase morphological parameters. All these numerical data were compared with experimental data, and a quite good agreement was observed that confirmed the adequacy of the present model calculations. It was confirmed that, for a given formulation, the mass transfer parameters during freeze-drying were strongly dependent on morphological textural parameters, and consequently, on the nucleation temperatures that fix the ice phase morphology. The influence of freezing rate was also predicted from the simulations, proving that an increase of cooling rates led to slower primary drying rates. 2007

Ice Morphology: Fundamentals and Technological Applications in Foods

“…Sadikoglu et al 87 pointed out that the ice crystals formed during the freezing stage determined the size and shape of pores, the pore size distribution, and the pore connectivity of the porous matrix, thus affecting heat and mass transfer during the primary and secondary drying stages. Recently, Nakagawa et al, 88 using a mathematical model for the freezing process of a standard pharmaceutical formulation (mannitol and bovine serum albumin-based), confirmed that the mass transfer parameters in freeze drying were strongly dependant on the morphological parameters of the frozen phase and, consequently, on the nucleation temperatures. Nevertheless, large dendritic ice crystals (formed at lower freezing rates) that result in a higher mass transfer rate are not always appropriate for all products undergoing freeze drying.…”

Modeling of freezing step during vial freeze‐drying of pharmaceuticals—influence of nucleation temperature on primary drying rate

“…This agreement was also observed with Bovin Serum Albumin formulations. [11] Permeability during freeze-drying Dried zone permeability, noted K , could be estimated from mean ice crystals diameters values by assuming that the dried cake texture is represented by a bundle of capillary tubes (diameter d p ). In our case, we could estimate the value of Knudsen number around K n = 4 and, consequently, from the molecular diffusion theory in Knudsen regime, the dried layer permeability, K , by the following equations:…”

Application of Mechanistic Models for Process Design and Development of Biologic Drug Products

“…Several different models have been employed for identifying freezing parameters, primary drying parameters, primary drying duration, and moisture content of the cake and/or scaling up from the lab-scale to commercial-scale lyophilization parameters [69,[71][72][73][74]. Nakagawa et al, [71] have used a mathematical model that simulates temperature profiles during freezing process in two-dimensional axisymmetric space, and the ice crystal mean sizes were semi-empirically estimated from the resulting temperature profiles.…”