Similarity transformation approach to identifiability analysis of nonlinear compartmental models

Sandor Vajda, Keith R. Godfrey, Herschel Albert Rabitz

Research output: Contribution to journalArticle

150 Scopus citations

Abstract

Through use of the local state isomorphism theorem instead of the algebraic equivalence theorem of linear systems theory, the similarity transformation approach is extended to nonlinear models, resulting in finitely verifiable sufficient and necessary conditions for global and local identifiability. The approach requires testing of certain controllability and observability conditions, but in many practical examples these conditions prove very easy to verify. In principle the method also involves nonlinear state variable transformations, but in all of the examples presented in the paper the transformations turn out to be linear. The method is applied to an unidentifiable nonlinear model and a locally identifiable nonlinear model, and these are the first nonlinear models other than bilinear models where the reason for lack of global identifiability is nontrivial. The method is also applied to two models with Michaelis-Menten elimination kinetics, both of considerable importance in pharmacokinetics, and for both of which the complicated nature of the algebraic equations arising from the Taylor series approach has hitherto defeated attempts to establish identifiability results for specific input functions.

Original languageEnglish (US)
Pages (from-to)217-248
Number of pages32
JournalMathematical Biosciences
Volume93
Issue number2
DOIs
StatePublished - Jan 1 1989

All Science Journal Classification (ASJC) codes

  • Statistics and Probability
  • Medicine(all)
  • Modeling and Simulation
  • Immunology and Microbiology(all)
  • Biochemistry, Genetics and Molecular Biology(all)
  • Agricultural and Biological Sciences(all)
  • Applied Mathematics

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