Mathematical tools for the quantitative definition of a design space

Amanda Rogers, Marianthi G. Ierapetritou

Research output: Chapter in Book/Report/Conference proceedingChapter

1 Scopus citations


This chapter focuses on the application of process modeling to determination of design space for pharmaceutical manufacturing processes. The first two sections define design space and related terms from a regulatory perspective and discuss how these apply in practice during pharmaceutical process development. In Sect. 3, a variety of mathematical techniques that can be used to guide design space development are introduced. An emphasis is placed on the use of feasibility analysis and the relationship between process feasibility and design space. Statistical techniques, including latent variable and Bayesian methods, are also discussed in detail. For methods that have been reported in the literature for pharmaceutical manufacturing applications, an overview of the relevant case studies is provided. If methods have not yet been applied to pharmaceutical processes, potential applications for these techniques are indicated. To illustrate the applicability of these concepts to pharmaceutical manufacturing processes, a brief case study is presented in Sect. 4. A discussion of design space verification and issues related to scale-up is provided in Sect. 5. Finally a brief summary of the concepts presented and their potential role in design space development for pharmaceutical processes is given in Sect. 6. This chapter is intended to provide readers with an understanding of mathematical techniques that can be used during process development to assist in the determination of process design space. An overview of the problem formulation and solution approaches for each method are presented. More detailed mathematical developments for each technique are available in the references provided. Table 1 provides a list of symbols that are used throughout this chapter, while Table 2 describes acronyms used within this chapter.

Original languageEnglish (US)
Title of host publicationMethods in Pharmacology and Toxicology
PublisherHumana Press Inc.
Number of pages55
StatePublished - Jan 1 2016

Publication series

NameMethods in Pharmacology and Toxicology
ISSN (Print)1557-2153
ISSN (Electronic)1940-6053

All Science Journal Classification (ASJC) codes

  • Molecular Medicine
  • Pharmacology, Toxicology and Pharmaceutics(all)
  • Pharmacology (medical)


  • Bayesian reliability
  • Black-box feasibility
  • Derivative-free optimization
  • Design space
  • Feasibility analysis
  • Flexibility analysis
  • Partial least squares (PLS)
  • Pharmaceutical process development
  • Principal component analysis (PCA)
  • Process modeling

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