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Structural identifiability for a class of non-linear compartmental systems using linear/non-linear splitting and
Michael J Chapman1, Keith R Godfrey, Michael J Chappell
1School of MIS-Maths, Coventry University, CV1 5FB, Coventry, UK. m.chapman@coventry.ac.uk
Mathematical Biosciences
|February 27, 2003
Summary
Two parameterizations of non-linear compartmental models exhibit identical input-output behavior only if they differ by a state space transformation. Linear analysis simplifies non-linear identifiability, especially for complex models, aided by symbolic computation.
Area of Science:
- Systems Biology
- Control Theory
- Mathematical Modeling
Background:
- Non-linear compartmental models are widely used in systems biology.
- Model parameterization and identifiability are crucial for biological insight.
- Understanding the relationship between different parameterizations is essential.
Purpose of the Study:
- To investigate the conditions under which different parameterizations of non-linear compartmental models yield the same input-output behavior.
- To explore the utility of linear analysis in simplifying non-linear identifiability problems.
- To demonstrate the application of symbolic computation in analyzing complex models.
Main Methods:
- Analysis of controllability and observability restrictions.
- Application of local diffeomorphic changes of basis for state space transformation.
- Utilizing linear analysis for identifiability assessment.
- Employing symbolic computation for complex model analysis.
Main Results:
- Identical input-output behavior in non-linear compartmental models requires a locally diffeomorphic state space change of basis between parameterizations.
- Linear analysis provides valuable insights into identifiability under specific restrictions.
- Non-linear identifiability analysis can be significantly simplified by initial linear analysis.
- Symbolic computation aids in performing linear analysis for models with four or more compartments.
Conclusions:
- The choice of parameterization for non-linear compartmental models is not arbitrary; distinct parameterizations must be related by specific state space transformations to maintain identical input-output dynamics.
- Linear analysis serves as a powerful, simplifying tool for assessing the identifiability of non-linear compartmental models, particularly when controllability and observability are constrained.
- For intricate biological systems modeled with numerous compartments, computational approaches like symbolic computation are indispensable for efficient and accurate identifiability analysis.
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