A Stochastic Shelf-Scale Modeling Framework for the Freezing Stage in Freeze-Drying Processes

Insights into Thermal Interactions in Frozen Pharmaceutical Vials: Effects on Ice Nucleation Times and Inhibition

PURPOSE

This study investigates the thermal interactions between adjacent vials during freezing and assesses their impact on nucleation times.

METHODS

Various loading configurations were analyzed to understand their impact on nucleation times. Configurations involving direct contact between vials and freeze-dryer shelves were studied, along with setups using empty vials between filled ones. Additionally, non-conventional loading configurations and glycol-filled vials were tested. The analysis includes 2R and 20R vials, which are commonly utilized in the freezing and lyophilization of drug products, along with two different fill depths, 1 and 1.4 cm.

RESULTS

The investigation revealed that configurations with direct contact between vials and freeze-dryer shelves led to substantial thermal interactions, resulting in delayed nucleation in adjacent vials and affecting the temperature at which nucleation takes place in a complex way. In another setup, empty vials were placed between filled vials, significantly reducing thermal interactions. Further tests with non-conventional configurations and glycol-filled vials confirmed the presence of thermal interactions with a minimal inhibitory effect.

CONCLUSIONS

These findings carry significant implications for the pharmaceutical industry, highlighting the role of thermal interactions among vials during freezing and their impact on the temperature at which ice nucleation occurs.

A Non-Isothermal Pore Network Model of Primary Freeze Drying

In this work, a non-isothermal pore network (PN) model with quasi-steady vapor transport and transient heat transfer is presented for the first time for the application of primary freeze drying. The pore-scale resolved model is physically based and allows for the investigation of correlations between spatially distributed structure and transport conditions. The studied examples were regular PN lattices with a significantly different structure, namely a spatially homogeneous PN, also denoted as monomodal PN, and a PN with significant structure variation, referred to as bimodal PN because of its bimodal pore size distribution. The material properties selected for the solid skeleton in this study are equivalent to those of maltodextrin. The temperature ranges applied here were -28 °C to -18 °C in the PN and -42 °C in the surrounding environment. The environmental vapor pressure was 10 Pa. The PNs were dried with constant temperature boundary conditions, and heat was transferred at the top side by the vapor leaving the PN. It is shown how the structural peculiarities affect the local heat and mass transfer conditions and result in a significant widening of the sublimation front in the case of the bimodal PN. The possibility of spatially and temporally resolved front structures is a unique feature of the PN model and allows the study of situations that are not yet described by classical continuum approaches, namely heterogeneous frozen porous materials. As demonstrated by the thin layers studied here, the pore-scale simulations are of particular interest for such situations, such as in lyomicroscopes or collagen scaffolds, where a length-scale separation between dry and ice-saturated regions is not possible.

Freeze-Drying of Pharmaceuticals in Vials Nested in a Rack System-Part I: Freezing Behaviour

The distribution of biopharmaceuticals often requires either ultra-cold conditions or lyophilisation. In both cases, the drug product is frozen and, thus, exposed to similar stress conditions, which can be detrimental to its quality. However, these stresses can be inhibited or mitigated by a suitable formulation and/or an appropriate freezing design. This paper addresses how the key freezing parameters, i.e., ice nucleation temperature and cooling rate, impact the freezing behaviour of a sucrose-based formulation. The analysis included two loading configurations, vials directly resting on the shelf and nested in a rack system. The loading configuration affected the product freezing rate and the ice nucleation temperature distribution, resulting in larger ice crystals in the case of vials nested in a rack system. SEM micrographs and specific surface area measurements confirmed the different product morphology. Eventually, the different product morphology impacted the bioactivity recovery of lactate dehydrogenase.

Conceptual Validation of Stochastic and Deterministic Methods To Estimate Crystal Nucleation Rates

This work presents a generalized framework to assess the accuracy of methods to estimate primary and secondary nucleation rates from experimental data. The crystallization process of a well-studied model compound was simulated by means of a novel stochastic modeling methodology. Nucleation rates were estimated from the simulated data through multiple methods and were compared with the true values. For primary nucleation, no method considered in this work was able to estimate the rates accurately under general conditions. Two deterministic methods that are widely used in the literature were shown to overpredict rates in the presence of secondary nucleation. This behavior is shared by all methods that extract rates from deterministic process attributes, as they are insensitive to primary nucleation if secondary nucleation is sufficiently fast. Two stochastic methods were found to be accurate independent of whether secondary nucleation is present, but they underestimated rates in the case where a large number of primary nuclei are formed. We hence proposed a criterion to probe the accuracy of stochastic methods for arbitrary data sets, thus providing the theoretical foundations required for their rational use. Finally, we showed how both primary and secondary nucleation rates can be inferred from the same set of detection time data by combining deterministic and stochastic considerations.

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).