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Mechanistic models, a category encompassing both physiological and compartmental modeling, differ from empirical models' approaches to incorporating known factors about the systems being modeled. Empirical models describe data with minimal assumptions, while mechanistic models aim to provide a robust description of available data by specifying assumptions and integrating known factors about the system. Compartmental analysis is a key example of a mechanistic model in pharmacokinetics and...
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Robust global identifiability theory using potentials--Application to compartmental models.

N Wongvanich1, C E Hann1, H R Sirisena1

  • 1Department of Electrical and Computer Engineering, University of Canterbury, Private Bag 4800, Christchurch, New Zealand.

Mathematical Biosciences
|February 10, 2015
PubMed
Summary
This summary is machine-generated.

This study introduces a new global practical identifiability theory for compartmental models. This potential jet space approach robustly identifies parameters without simulations, outperforming differential jet space methods.

Keywords:
Compartmental modelIdentifiabilityParameter identificationPotential jet space

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Area of Science:

  • Mathematical Modeling
  • Systems Biology
  • Parameter Estimation

Background:

  • Compartmental models are crucial for understanding biological systems.
  • Parameter identifiability is essential for reliable model analysis.
  • Existing methods often require complex simulations and can be sensitive to noise.

Purpose of the Study:

  • To develop a novel global practical identifiability theory for linear and nonlinear compartmental models.
  • To enable robust parameter identification without differential equation simulations.
  • To extend the theory for accurate initial condition identification.

Main Methods:

  • Prolonging compartmental systems onto the potential jet space.
  • Formulating input-output equations as integrals of measured data.
  • Applying the theory to nitrous oxide (N2O) uptake and a nonlinear immunological mastitis model.
  • Incorporating an iterative method for initial condition identification.

Main Results:

  • The potential jet space approach provided accurate parameter identification for N2O uptake models, even with 3% noise.
  • Differential jet space methods proved unstable and unsuitable for parameter identification.
  • The theory accurately predicted infected pathogen concentrations in a nonlinear immunological model within 9% error, with up to 10% noise.

Conclusions:

  • The proposed potential jet space theory offers a robust and efficient method for identifying parameters in compartmental models.
  • This approach overcomes limitations of simulation-based methods and is resilient to noise.
  • The theory has broad applicability in systems biology and other fields requiring model analysis.