A Data-Driven Modeling Approach Using the Design of Dynamic Experiments Methodology In Calculating the Design Space of Batch Pharmaceutical Processes

The development of fundamental models for fed-batch pharmaceutical processes range from very challenging to almost impossible as not all the inner workings of the process are quantitatively known. Thus, the accurate calculation of the Design Space in which the process will be operated is a substantial challenge. One approach that has been recently proposed [1] is to use the Design of Experiments (DoE) methodology to develop data-driven models of the process. A major limitation of this approach is its inability to account for time varying operations that are often more optimal than those that are constant with time. Such time-varying operation include but are not limited to the varying the reaction temperature, the crystallizer cooling, the feeding rate of a sugar source to a fermentation. This dynamic character is even more important if the process will operate under feedback control. In such a case the operating conditions are changed by the controller to ensure the product quality at the end of the batch.

We present here an approach that utilizes the recently postulated Design of Dynamic Experiments (DoDE) methodology [2] that generalizes the classical DoE approach [3, 4]. This is achieved by systematically designing a set of experiments with respect to the time-varying decision variables. Using the collected data, a response surface model (RSM) is estimated that quantifies the impact that uncontrolled and controlled inputs (disturbances and manipulated variables, respectively) have on the quality of the product at the end of the batch. Process disturbances include the variability in feedstock properties as well as the variability in the operating conditions. The manipulated variables include those that can be changed with time such as the reactor temperature or the crystallizer cooling rate, or the substrate feed rate in fermentation, as well as others. A feedback controller aims to change the manipulated variables so that the variability in the final product is minimized.

The data-driven models derived from the DoDE data are used to quantify the design and control spaces of the process. Several simulated processes and an experimental asymmetric hydrogenation process of an API are examined to illustrate the general methodological concept that can be used in many batch pharmaceutical processes that avail the possibility of time varying conditions.

References:

1. A-Mab: a Case Study in Bioprocess Development CMC Biotech Working Group, Ver. 2.1 October 30, 2009, Internet Source: http://www.casss.org/associations/9165/files/A-Mab_Case_Study_Version_2-...
2. Georgakis, C. (2009); “A Model‐Free Methodology for the Optimization of Batch Processes: Design of Dynamic Experiments” Proceedings of the 8th IFAC International Symposium on Dynamics and Control of Process Systems (DYCOPS) Istanbul, Turkey, July 2011
3. Box, G. E., & Draper, N. R. (2007); Response Surfaces, Mixtures, and Ridge Analyses (2^nd Edition) Wiley‐Interscience.
4. Montgomery, D. C. (2005); Design and Analysis of Experiments (6th Edition ed.) John Wiley & Sons, Inc.