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

Abstract

To optimize the primary drying step of freeze-drying processes, it is very important to control morphological parameters of the frozen matrix. A mathematical model that simulates temperature profiles during freezing process of standard pharmaceutical formulations was set up and the ice crystal mean sizes were semi-empirically estimated from the simulated thermal profiles. Then, water vapor mass transfer kinetics during sublimation step was estimated from ice phase morphological parameters. All these numerical data were compared with experimental data and a quite good agreement was observed, which 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 rates was also predicted from the simulations, proving that an increase of cooling rates led to slower primary drying rates. 

Preserving enhancement in freeze-dried contrast agent ST68: Examination of excipients

“…The degree of crystallization not only affects the overall sublimation time but also the amount of stresses experienced by the sample. These stresses are caused by the rate of sublimation, “water vapor mass transfer kinetics” (Nakagawa et al 2010), determined by crystal size, and the rate of the water crystal growth (Abdelwahed et al 2006b), both minimized by the excipient’s ability to form a glassy matrix. Mannitol-protected ST68, which was shown to crystallize (Fig.…”

Mathematical modeling of the stage of freezing in technology of lyophilized drugs

“…Конечно, невозможно предсказать температуру начала кристаллизации, и поэтому она не рассматривается как фиксированный параметр в модели. Однако в некоторых исследованиях данная проблема решается использованием ультразвукового устройства, фиксирующего температуру начала кристаллизации кристалла льда [6]. Модель представляет собой сочетание 2 основных исследований: модели роста кристаллов льда в однородно переохлажденной жидкости [7] и модели равномерного роста кристалла льда, независимого от переохлаждения [8].…”

Development and Application of a Mechanistic Cooling and Freezing Model of the Spin Freezing Step within the Framework of Continuous Freeze-Drying

“…Taking the above into account, it is evident that a good understanding and control of the freezing step and its different phases (i.e., liquid cooling, nucleation, ice crystallization, and subsequent solid cooling) during freeze-drying is of importance. In practice, modelbased approaches are often utilized to gain process knowledge and to develop control mechanisms [3,[15][16][17][18][19]. Several approaches have been proposed to model the freezing step in batch freeze-drying, such as the one developed by Nakagawa et al [3,15].…”

“…In practice, modelbased approaches are often utilized to gain process knowledge and to develop control mechanisms [3,[15][16][17][18][19]. Several approaches have been proposed to model the freezing step in batch freeze-drying, such as the one developed by Nakagawa et al [3,15]. They proposed a two-dimensional axisymmetric cooling and freezing model based on the conductive heat equation (i.e., Fourier's law of heat conduction).…”

“…The cooling step was simulated using the conductive heat equation expressed in Equation (1) [3,15]. This equation describes the conductive heat flux in relation to the physical properties of the product (i.e., the mass density, the specific heat capacity, and the thermal conductivity), as well as the temperature distribution of the product under study.…”