Stochastic ice nucleation governs the freezing process of biopharmaceuticals in vials.

Biopharmaceuticals commonly require freezing to ensure the stability of the active pharmaceutical ingredients (APIs). At commercial scale, freezing is typically carried out over the course of days in pallets comprising tens of thousands of vials. The selected process conditions have to ensure both complete freezing in all vials and a satisfactory manufacturing throughput. Current process design, however, is mainly experimental, since no mechanistic understanding of pallet freezing and its underlying phenomena has been achieved so far. Within this work, we derive a mechanistic modeling framework and compare the model predictions with engineering run data from the Janssen COVID-19 vaccine. The model qualitatively reproduced all observed trends and reveals that stochastic ice nucleation governs both process duration and batch heterogeneity. Knowledge on the ice nucleation kinetics of the formulation to be frozen thus is required to identify suitable freezing process conditions. The findings of this work pave the way towards a more rational design of pallet freezing, from which a plethora of frozen drug products may benefit. For this reason, we provide open source access to the model in the form of a python package (Deck et al., 2021).

Stochastic shelf-scale modeling framework for the freezing stage in freeze-drying processes.

Freezing and freeze-drying processes are commonly used to improve the stability and thus shelf life of pharmaceutical formulations. Despite strict product quality requirements, batch heterogeneity is widely observed in frozen products, thus potentially causing process failure. Such heterogeneity is the result of the stochasticity of ice nucleation and the variability in heat transfer among vials, which lead to unique freezing histories of individual vials. We present for the first time a modeling framework for large-scale freezing processes of vials on a shelf and publish an open source implementation in the form of a python package on pypi. The model is based on first principles and couples heat transfer with ice nucleation kinetics, thus enabling studies on batch heterogeneity. Ice nucleation is assumed to be an inhomogeneous Poisson process and it is simulated using a Monte Carlo approach. We applied the model to understand the individual pathways leading to batch heterogeneity. Our simulations revealed a novel mechanism how ice nucleation leads to heterogeneity based on thermal interaction among vials. We investigated the effect of various cooling protocols, namely shelf-ramped cooling, holding steps and controlled nucleation, on the nucleation and solidification behavior across the shelf. We found that under rather general conditions holding schemes lead to similar solidification times, as in the case of controlled nucleation, thus identifying a potential pathway for freezing process optimization.

Industrial application of heat- and mass balance model for fluid-bed granulation for technology transfer and design space exploration.

This work demonstrates the application of state-of-the-art modeling techniques in pharmaceutical manufacturing for fluid bed granulation at varying scales to successfully predict process conditions and ultimately replace experiments during a technology transfer of five products. We describe a mathematical model able to simulate the time-dependent moisture profile in a fluid bed granulation process. The applicability of this model is then demonstrated by calibrating and validating it over a range of operating conditions, manufacturing scales, and formulations. The inherent capability of the moisture profile to serve as a simple, scale-independent surrogate is shown by the large number of successful scale-ups and transfers. A methodology to use this 'digital twin' to systematically explore the effects of uncertainty inherent in the process input and model parameter spaces and their impact on the process outputs is described. Two case studies exemplifying the utilization of the model in industrial practice to assess process robustness are provided. Lastly, a pathway to leverage model results to establish proven acceptable ranges for individual parameters is outlined.

Ripening of Semiconductor Nanoplatelets.

Ostwald ripening describes how the size distribution of colloidal particles evolves with time due to thermodynamic driving forces. Typically, small particles shrink and provide material to larger particles, which leads to size defocusing. Semiconductor nanoplatelets, thin quasi-two-dimensional (2D) particles with thicknesses of only a few atomic layers but larger lateral dimensions, offer a unique system to investigate this phenomenon. Experiments show that the distribution of nanoplatelet thicknesses does not defocus during ripening, but instead jumps sequentially from m to (m + 1) monolayers, allowing precise thickness control. We investigate how this counterintuitive process occurs in CdSe nanoplatelets. We develop a microscopic model that treats the kinetics and thermodynamics of attachment and detachment of monomers as a function of their concentration. We then simulate the growth process from nucleation through ripening. For a given thickness, we observe Ostwald ripening in the lateral direction, but none perpendicular. Thicker populations arise instead from nuclei that capture material from thinner nanoplatelets as they dissolve laterally. Optical experiments that attempt to track the thickness and lateral extent of nanoplatelets during ripening appear consistent with these conclusions. Understanding such effects can lead to better synthetic control, enabling further exploration of quasi-2D nanomaterials.