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Mechanistic models play a crucial role in algorithms for numerical problem-solving, particularly in nonlinear mixed effects modeling (NMEM). These models aim to minimize specific objective functions by evaluating various parameter estimates, leading to the development of systematic algorithms. In some cases, linearization techniques approximate the model using linear equations.
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Calculating all multiple parameter solutions of ODE models to avoid biological misinterpretations.

Maria Pia Saccomani1, Karl Thomaseth2

  • 1Department of Information Engineering, University of Padova, Padova, 35131 Italy.

Mathematical Biosciences and Engineering : MBE
|November 9, 2019
PubMed
Summary
This summary is machine-generated.

Structural identifiability analysis helps determine if biological model parameters can be uniquely estimated from data. This study presents an algorithmic approach to find all parameter solutions for locally identifiable ordinary differential equation (ODE) models.

Keywords:
HIV modelbiological systemsdifferential equationlocal identifiabilitymultiple parameter solutionsparameter estimation

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Area of Science:

  • Systems biology
  • Mathematical modeling
  • Computational biology

Background:

  • Biological system dynamics are often modeled using nonlinear ordinary differential equations (ODEs).
  • Parameter estimation from experimental data is crucial for understanding these models.
  • Structural identifiability analysis assesses if model parameters can be uniquely determined from data.

Purpose of the Study:

  • To address the critical issue of local identifiability in biological modeling.
  • To present theoretical background and applications for locally identifiable ODE models with rational functions.
  • To propose an algorithmic approach for calculating all numerical parameter solutions and predicting unmeasured variable behavior.

Main Methods:

  • Focus on local identifiability analysis for ODE models.
  • Integration of structural identifiability analysis with practical identifiability.
  • Development of an algorithmic approach implemented in the DAISY software.
  • Calculation of all numerical parameter solutions and prediction of unmeasured variable dynamics.

Main Results:

  • Structural identifiability analysis complements practical identifiability results.
  • The DAISY software can identify all numerical parameter solutions for locally identifiable models.
  • Multiple parameter solutions can lead to different predictions for unmeasured variables.
  • A case study on an HIV model highlights the importance of considering multiple parameter solutions.

Conclusions:

  • Local identifiability is a critical consideration in biological modeling.
  • Awareness of multiple parameter solutions is essential for comprehensive system description.
  • Ignoring multiple solutions can lead to biological misinterpretation.
  • The proposed algorithmic approach aids in uncovering hidden parameter behaviors.