Structural identifiability of parallel pharmacokinetic experiments as constrained systems
S.Y. Amy Cheung (1), James W. T. Yates (2), Leon Aarons (3), Amin Rostami-Hodjegan (3)
(1) Clinical Pharmacometrics, Clinical Pharmacology Science, AstraZeneca R&D Alderley Park, UK, (2) Oncology innovative medicines DMPK, AstraZeneca R&D Alderley Park, UK, (3) School of Pharmacy and Pharmaceutical Sciences, The University of Manchester, Oxford Road, Manchester, M13 9PT, United Kingdom
Objectives: Pharmacokinetic analysis using compartmental models can be restricted with respect to the estimation of parameter values. This is because the experimenter is only able to apply inputs and observations in a very small number of compartments in the system. This has implications for the structural identifiability  of such systems and consequently limits the complexity and mechanistic relevance of the models that may be applied to such experiments. A number of strategies are presented whereby models are rendered globally identifiable by considering a series of experiments in parallel .
Methods: Structural identifiability is the property of whether an experiment can uniquely identify the unconstrained model parameters. The ‘same' experiment may sometimes be carried out several times on a system, in which it can be assumed a priori that some, but not all, of its rate constants change between experiments. The models representing each experimental observation thus share some common rate constant values depend on the dosing method and physiological nature of the model. This forms a much more constrained structure, encapsulates more information of the system and still can be readily analysed.
Results: The methodology is applied to a number of examples, including classic compartmental models and a series of mechanistic compartmental models such as parent-metabolite models . It is shown that by considering parallel experimental strategies, individually unidentifiable or locally identifiable models, in many cases are rendered uniquely identifiable.
Conclusions: A formulation has been presented that places the concept of parallel experiments in the context of a single constrained model structure. Incorporation of prior knowledge into parallel experiment model structures with constrained parameterization allows sufficient information to be present in the input-output behaviour to give unique parameter estimates. The results show that the parallel experiment strategy can be very powerful in providing a globally uniquely identifiable model.
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Cheung, S. Y. A., Yates, J. W. T., Aarons, L., (2006) Strucutural identifiability of parallel pharmacokinetic experiments as constrained systems: Proceedings of the 6th IFAC Symposium on Modeling and Control in Biomedical Systems held at Reims Congress Center, France.
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