(664g) An Optimization-Based Framework to Define the Probabilistic Design Space of Pharmaceutical Process with Model Inherent Uncertainty

Authors: 
Xu, S., The University of Texas at Austin
Laird, C., Purdue University
Vaidyaraman, S., Eli Lilly and Company

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.

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