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Parameter space boundaries for unidentifiable compartmental models.

S Vajda, J J Distefano, K R Godfrey

    Mathematical Biosciences
    |November 1, 1989
    PubMed
    Summary
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    This study presents new methods for unidentifiable compartmental models, generating all possible parameter solutions within bounded regions. These approaches link parameter interval analysis with exhaustive modeling for robust model identification.

    Area of Science:

    • Systems Biology
    • Mathematical Modeling
    • Pharmacokinetics

    Background:

    • Unidentifiable compartmental models pose challenges in parameter estimation.
    • Existing methods like parameter interval analysis and exhaustive modeling have limitations.

    Purpose of the Study:

    • To develop general methods for identifying parameters in unidentifiable compartmental models.
    • To generate the complete set of all non-negative parameter solutions.
    • To extend existing parameter bounding strategies.

    Main Methods:

    • Review of parameter interval analysis and exhaustive modeling.
    • Development of methods to generate bounded regions of parameter solutions.
    • Analysis of boundary points yielding equivalent submodels.

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    Main Results:

    • A comprehensive set of all non-negative parameter solutions is generated.
    • Parameters are localized within bounded regions in parameter space.
    • Boundary solutions correspond to equivalent submodels, linking different identification approaches.

    Conclusions:

    • The presented methods provide a unified framework for parameter identification in unidentifiable models.
    • The relationship between exhaustive modeling and parameter interval analysis is elucidated.
    • These techniques enhance the robustness and interpretability of compartmental model parameters.