Structural identifiability and sensitivity

Area of Science:

• Mathematical modeling
• Systems biology
• Control theory

Background:

• Ordinary differential equation (ODE) models are widely used in science and engineering.
• Accurate parameter estimation from experimental data is essential for these models.
• Model structural identifiability, ensuring unique parameter values, is a prerequisite for successful estimation.

Purpose of the Study:

• To investigate the local identifiability of linear and nonlinear ODE models.
• To develop and validate a method for assessing model identifiability using the sensitivity matrix.
• To explore strategies for enhancing model identifiability.

Main Methods:

• Analysis of the rank of the sensitivity matrix of model output with respect to parameters.
• Numerical implementation for calculating the sensitivity matrix without approximation.
• Extension of the identifiability analysis to multi-output systems.
• Systematic evaluation using elementary examples and random parameter sampling.

Main Results:

• Demonstrated that adding nonlinear elements can transform an unidentifiable model into an identifiable one.
• Showed that structural and parametric identifiability are linked in models with nonlinear elements.
• Confirmed that increasing the number of outputs or inputs improves identifiability.

Conclusions:

• Model identifiability must be systematically evaluated before parameter estimation.
• The sensitivity matrix approach provides a robust method for assessing local identifiability.
• Strategies like incorporating nonlinearity and optimizing input/output configurations enhance model identifiability.