(423a) State Estimation for Manufacturing of mRNA-Based Vaccines and Therapeutics: A Lyophilization Case Study

Lyophilization (aka freeze drying) is a process used to increase the stability of biotherapeutics, e.g., mRNA vaccines, in biopharmaceutical manufacturing [1], allowing for their storage at higher temperature while preserving their functionality [2, 3]. This advance could play an important role in future mRNA-based therapeutics, including the enabling of vaccine distribution in regions where a cold supply chain is lacking.

Lyophilization consists of three main stages, namely (1) freezing, (2) primary drying, and (3) secondary drying, respectively. The final stage, secondary drying, entails bound water removal, in which the accurate prediction and monitoring of bound water concentration are the key to ensuring the quality of the lyophilized product [4, 5]. Various measurement and monitoring techniques have been proposed and studied [6]. One of the most common techniques is the Karl Fischer titration, which requires sampling of the vial for offline measurements [6–8]. To avoid process interruption, some online or non-invasive techniques such as near-infrared (NIR) spectroscopy [9] and tunable diode laser absorption spectroscopy (TDLAS) [10] have been proposed. Detailed discussion of tools for the monitoring of secondary drying can be found in Ref. [6].

Instead of direct measurement, a state observer (aka state estimator, observer, estimator) can be used to estimate states that are not measured [11]; the process is known as state estimation. A state observer combines the available measurements and mechanistic understanding of a system (mechanistic model) to optimally estimate the unmeasured states. A well-designed observer can replace expensive and complicated sensors in the system, reducing the total cost and complexity of operation. In the context of lyophilization, state observers have been studied and applied to the primary drying step, which aims at estimating the temperature, interface position (amount of ice), and relevant parameters such as the heat transfer coefficient [12–19]. Observer design for primary drying is straightforward as it mainly concerns heat transfer associated with sublimation and, in many cases, an observer is not even needed as heat transfer-related quantities, e.g., temperature, can be measured easily. In secondary during, heat transfer and desorption dynamics are coupled, making the observer design more challenging and valuable. Currently, applications of state estimation to secondary drying are very limited. To our knowledge, the only literature that proposed a state estimation-like strategy for secondary drying is Ref. [8]; the technique is referred to as a soft sensor which requires the measurement of the desorption flux for estimating the residual moisture. The procedure in Ref. [8] does not exploit the mathematical structure of a state observer; the key idea is to iteratively solve the optimization to find the moisture content that matches the measured desorption flux. This technique also requires additional equipment specifically for measuring the desorption flux.

In this work, a novel technique is introduced for real-time estimation of bound water concentration during desorption, which is applied to secondary drying in lyophilization. A state observer is mathematically formulated to estimate the concentration of bound water given the mechanistic model and temperature measurement. A practical observer design strategy is described and demonstrated in detail. Our observer can accurately estimate the concentration for various desorption dynamics, noisy data, and real experiments. Nearly all the case studies presented in this work are achieved by a single observer design, indicating high robustness of the observer.

In terms of practicality and implementation, our observer is designed such that it can be simulated in real time, with the computation time of less than a second on a normal laptop. Besides, no concentration measurement is required; the only measurement data required is temperature. Temperature measurement is straightforward and very common in every step of lyophilization [6, 20], whereas accurate bound water measurement is not trivial and involves complex equipment and procedures [21]. Therefore, our technique allows for the simplest setup and operation compared to any other methods, eliminating any additional sensor and complexity. The framework can also be easily and systematically extended to other desorption-based processes.

Acknowledgements:

This research was supported by the U.S. Food and Drug Administration under the FDA BAA-22-00123 program, Award Number 75F40122C00200.

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