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Identifiability and indistinguishability of nonlinear pharmacokinetic models

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Three nonlinear model structures of interest in pharmacokinetics are analyzed to determine whether the unknown, independent, model parameters can be deduced if perfect input-output data were available. This is the problem of identifiability. The method used is based on the local state isomorphism theorem. In certain circumstances, the modeler may be undecided between several model structures and it is then of interest to determine whether different model structures can be distinguished from perfect input-output data. This is the problem of model indistinguishability. The technique used, again based on the local state isomorphism theorem, parallels the similarity transformation approach for linear systems described previously in this journal. The analysis is performed on three two-compartment examples having one linear and one nonlinear (Michaelis-Menten) elimination pathway. In each model there is, on physiological and other grounds, some uncertainty over the precise location (central compartment or peripheral compartment) of one of the elimination pathways.

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The work described in this paper has been supported by Grant GR/F 6381.7 “Identifiability and Other Properties of Physically Based System Models,” from the UK Science and Engineering Research Council and by NATO Collaborative Grant 900662 “Identification and Parameter Estimation of Pharmacokinetic Systems.”

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Godfrey, K.R., Chapman, M.J. & Vajda, S. Identifiability and indistinguishability of nonlinear pharmacokinetic models. Journal of Pharmacokinetics and Biopharmaceutics 22, 229–251 (1994).

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