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Indistinguishability and identifiability analysis of linear compartmental models
L Q Zhang1, J C Collins, P H King
1Department of Biomedical Engineering, Vanderbilt University, Nashville, Tennessee 37235.
Mathematical Biosciences
|February 1, 1991
Summary
This study presents an algorithm to identify indistinguishable compartmental model structures with identical input-output properties. The developed software systematically generates and tests these models, ensuring accurate system analysis and parameter identifiability.
Area of Science:
- Pharmacokinetics and Pharmacodynamics
- Systems Biology
- Mathematical Modeling
Background:
- Compartmental models are crucial for understanding biological systems.
- Indistinguishable models with identical input-output properties pose challenges in unique structure determination.
- A priori information may be insufficient to specify a single, correct model structure.
Purpose of the Study:
- To develop an algorithm for generating and analyzing indistinguishable compartmental model structures.
- To systematically investigate models with the same number of compartments and input-output structure.
- To ensure accurate identifiability and relevance of generated model structures.
Main Methods:
- An algorithm was developed to investigate the complete set of models with identical input-output structures.
- Geometrical rules were applied to filter candidate models based on necessary criteria for indistinguishability.
- Three programs were utilized: one for local identifiability, one for geometrical rule application, and one for transfer function equality checks.
- Jacobian matrix ranks, moment invariants, structural controllability, and structural observability were employed for rigorous testing.
Main Results:
- The algorithm successfully generates and tests sets of indistinguishable compartmental models.
- Geometrical rules effectively eliminate a majority of candidate models.
- Transfer function equality and identifiability are confirmed for relevant models.
- The approach corroborated existing findings in compartmental modeling.
Conclusions:
- The developed algorithm and software provide a robust method for handling indistinguishable compartmental models.
- This approach enhances the reliability of system analysis by ensuring accurate model selection and identifiability.
- The methodology is applicable to various fields requiring complex system modeling and analysis.