An Optimization-Based Framework to Define the Probabilistic Design Space of Pharmaceutical Process with Model Inherent Uncertainty

An optimization-based framework to define the probabilistic design space of pharmaceutical process with model inherent uncertainty

Shu Xu, Carl Laird, Purdue University

Shankar Vaidyaraman, Salvador Garc’a-Mu–oz, Eli Lily & Company

To guarantee product quality, while at the same time to increase manufacturing flexibility and enhance process robustness, FDA launched quality by design (QbD) initiative to replace the conventional quality by testing (QbT) approach [1]. A distinguishing feature of QbD is to promote the concept of design space (DS) which is defined by process parameters and within which product quality is assured.

Traditionally, a data-driven approach based on design of experiment (DOE) and response surface analysis can be applied in DS determination [2]. However, such an approach might require expensive experimental runs and cannot handle complicated interactions within process parameters.  To overcome such a problem, we can take advantage of mechanistic models built based on mass or energy balance which intrinsically accounts for parameter interactions. Yet a new challenge is posed which lies in model inherent uncertainty caused by parameter estimation.  Such model uncertainty will propagate to the quality prediction and give rise to a probabilistic design space, to determine which computationally expensive Monte Carlo simulations are commonly used [3].

The design space proposed in the pharmaceutical industries and the concept of flexibility index studied in petrochemical processes [4] coincide in quantifying operating flexibility for manufactures. As a result, to obtain a probabilistic design space, instead of running Monte Carlo simulations, we propose a novel optimization-based framework based on the flexibility index formulation, and it consists of four steps: creating process parameter grid, calculating the flexibility index for each grid point, performing statistical test and generating a probability map. Furthermore, such a framework gives birth to a rigorous model to obtain the flexibility region which corresponds to the largest hypercube within the design space bracketed by feasibility constraints. A series of simulated and industrial case studies are conducted, and the results not only demonstrate the negative impact of model uncertainties on the feasible region, but also demonstrate a superior performance of the new framework regarding efficacy and efficiency in comparison with Monte Carlo simulations.

Bibliography

[1]  Food and Drug Administration. (Aug. 2009). Guidance for Industry Q8 Pharmaceutical Development. Technical Report, U.S. Department of Health and Human Services, FDA(CDER), Rockville, MD.

[2] Huang, J., Kaul, G., Cai, C., Chatlapalli, R., Hernandez-Abad, P., Ghosh, K., & Nagi, A. (2009). Quality by design case study: An integrated multivariate approach to drug product and process development. International Journal of Pharmaceutics, 382(1), 23Ð32.

[3]  Garc’a-Mu–oz, S., Luciani, C. V, Vaidyaraman, S., & Seibert, K. D. (2015). Definition of Design Spaces Using Mechanistic Models and Geometric Projections of Probability Maps. Organic Process Research & Development, 19(8), 1012Ð1023.

[4] Grossmann, I. E., Calfa, B. A., & Garcia-Herreros, P. (2014). Evolution of concepts and models for quantifying resiliency and flexibility of chemical processes. Computers & Chemical Engineering, 70, 22Ð34.