Quantitative risk assessment via uncertainty analysis in combination with error propagation for the determination of the dynamic Design Space of the primary drying step during freeze-drying

Abstract

Traditional pharmaceutical freeze-drying is an inefficient batch process often applied to improve the stability of biopharmaceutical drug products. The freeze-drying process is regulated by the (dynamic) settings of the adaptable process parameters shelf temperature T and chamber pressure P. Mechanistic modelling of the primary drying step allows the computation of the optimal combination of T and P in function of the primary drying time. In this study, an uncertainty analysis was performed on the mechanistic primary drying model to construct the dynamic Design Space for the primary drying step of a freeze-drying process, allowing to quantitatively estimate and control the risk of cake collapse (i.e., the Risk of Failure (RoF)). The propagation of the error on the estimation of the thickness of the dried layer L as function of primary drying time was included in the uncertainty analysis. The constructed dynamic Design Space and the predicted primary drying endpoint were experimentally verified for different RoF acceptance levels (1%, 25%, 50% and 99% RoF), defined as the chance of macroscopic cake collapse in one or more vials. An acceptable cake structure was only obtained for the verification runs with a preset RoF of 1% and 25%. The run with the nominal values for the input variables (RoF of 50%) led to collapse in a significant number of vials. For each RoF acceptance level, the experimentally determined primary drying endpoint was situated below the computed endpoint, with a certainty of 99%, ensuring sublimation was finished before secondary drying was started. The uncertainty on the model input parameters demonstrates the need of the uncertainty analysis for the determination of the dynamic Design Space to quantitatively estimate the risk of batch rejection due to cake collapse.

An Experimental-Based Approach to Construct the Process Design Space of a Freeze-Drying Process: An Effective Tool to Design an Optimum and Robust Freeze-Drying Process for Pharmaceuticals

“…In an attempt to minimize the trial and error experiments, researchers have developed mathematical models for the determination of the optimum processing conditions based on the governing heat and mass transfer equations. 4,[12][13][14][15][16][17][18][19][20][21][22][23][24][25][26][27][28] In these mathematical models, 2 input parameters, namely the overall vial heat transfer coefficient and the resistance to mass transfer of the dried product, are experimentally determined. The overall vial heat transfer coefficient is typically determined from a water sublimation test, whereas the resistance to mass transfer of the dried product is determined using the drug formulation.…”

Product development resilience through set‐based design

“…Furthermore this concept of dynamically expanding the design space away from a point solution through uncertainty is extended to quantitative risk assessment. A pharmaceutical industry example is highlighted . These approaches expand point‐based design, but do not create true set designs.…”

“…A pharmaceutical industry example is highlighted. 13 These approaches expand pointbased design, but do not create true set designs.…”

Global Sensitivity Analysis as Good Modelling Practices tool for the identification of the most influential process parameters of the primary drying step during freeze-drying

“…Because of these reasons, the computational model output can be correlated with a degree of uncertainty, which could lead to a deviation from the actual (experimental) primary drying behaviour. This parameter uncertainty can be included in the model leading to the quantitative estimation of the Risk of Failure (RoF), i.e., the risk of cake collapse, for each combination of the adaptable process parameters, T s and P c [13][14][15][16][17]. This quantitative risk assessment is essential for the construction of the Design Space, defined as the multidimensional combination and interaction of input variables and process parameters leading to the expected product specifications with a controlled probability [18].…”

“…This quantitative risk assessment is essential for the construction of the Design Space, defined as the multidimensional combination and interaction of input variables and process parameters leading to the expected product specifications with a controlled probability [18]. In this way, the optimal combination of T s and P c can be determined to maximize the process efficiency for a specific RoF acceptance level, which is defined as the chance of batch rejection due to macroscopic cake collapse in one or more vials [17]. The progression of primary drying and the corresponding increase in dried layer thickness leads to a continuous change of dependent process parameters (e.g., R p ).…”