Real-time Estimation of Bound Water Concentration during Lyophilization with Temperature-based State Observers

Abstract

Lyophilization (aka freeze drying) has been shown to provide long-term stability for many crucial biotherapeutics, e.g., mRNA vaccines for COVID-19, allowing for higher storage temperature. The final stage of lyophilization, namely secondary drying, entails bound water removal via desorption, in which accurate prediction of bound water concentration is vital to ensuring the quality of the lyophilized product. This article proposes a novel technique for real-time estimation of the residual moisture during secondary drying in lyophilization. A state observer is employed, which combines temperature measurement and mechanistic understanding of heat transfer and desorption kinetics, without requiring any online concentration measurement. Results from both simulations and experimental data show that the observer can accurately estimate the concentration of bound water in real time for all possible concentration levels, operating conditions, and measurement noise. This framework can also be applied for monitoring and control of the residual moisture in other desorption-related processes.

Figures (13)

• Figure 1: Schematic diagram showing a mechanistic model for the secondary drying step in lyophilization.
• Figure 2: (A) Schematic diagram of the typical lyophilization process. In secondary drying, a glass vial that contains the dried product is heated such that the bound water is desorbed and removed from the product at the top. The mechanistic model is used to describe the heat transfer and desorption dynamics during secondary drying.(B) Structure of the proposed state observer. The observer receives the measured temperature and the control input (i.e., the shelf temperature and microwave power) at time step $t$, and estimates the temperature and concentration at the next time step. To initialize the observer at $t=0$, the estimated temperature can be set to the measured value. The initial concentration is completely unknown due to no measurement, so it can be set to some realistic values obtained from the literature or previous experiment.
• Figure 3: (A) Comparison between the concentration of bound water predicted by our model and the experimental data obtained from Sadikoglu_1997_Modeling. The original data reported as the total mass of water are normalized by the total mass of solid. (B) Comparison between the concentration of bound water predicted by our model and the high-fidelity model by Sheehan_1998_Modeling. The original data reported as the total mass of water are normalized by the total mass of solid. (C) Comparison between our model prediction and the experimental data from Fissore_2015_Review for both temperature and concentration.
• Figure 4: Design space showing the times required for the estimated concentration to converge to the true value at different pairs of the observer gains $L_T$ and $L_c$. Values of $L_T$ and $L_c$ outside this design space could lead to severe oscillation or divergence.
• Figure 5: Convergence of the estimated product temperature for the selected observer gains $L_T = -1$$\times$$10^{-6}$ and $L_c = 5$$\times$$10^{-7}$. Panel A shows the evolution of the estimated average temperature compared to the true value. Panel B shows the spatiotemporal evolution of the estimation error. The initial estimated temperature is set to be higher than the actual value by about 10% to demonstrate convergence.