Design optimality for models defined by a system of ordinary differential equations

Area of Science:

• Pharmacokinetics and Pharmacodynamics
• Mathematical Modeling
• Experimental Design

Background:

• Many scientific processes, particularly in pharmacokinetics (PK) and pharmacodynamics (PD), are modeled using systems of ordinary differential equations (ODEs).
• Estimating unknown parameters in ODE models often relies on optimal experimental design.
• Standard optimal design methods require linearization of ODE solutions, which is not feasible for models lacking analytical solutions.

Purpose of the Study:

• To develop and discuss methods for computing optimal experimental designs when analytical solutions to ODEs do not exist.
• To apply these methods to well-known models (Iodine, Michaelis-Menten) and a specific PK model (biokinetic model of ciprofloxacin and ofloxacin).
• To evaluate the efficiency and parameter estimation quality of the computed designs.

Main Methods:

• Development of novel methods for optimal design computation without relying on analytical ODE solutions.
• Application of proposed methods to Iodine, Michaelis-Menten, and a two-parameter biokinetic PK model.
• Comparison of designs based on efficiency and parameter estimation accuracy across different optimality criteria and data points.

Main Results:

• Successful computation of optimal designs for example ODE models, including a specific biokinetic PK model.
• Demonstration of the proposed methods' applicability where traditional linearization techniques fail.
• Evaluation of design efficiency and parameter estimation quality for ciprofloxacin and ofloxacin biokinetic model.

Conclusions:

• The proposed methods provide a viable approach for optimal experimental design in ODE systems lacking analytical solutions.
• The methodology is effective for improving parameter estimation in PK/PD studies.
• The developed techniques can also be applied to sensitivity analysis of ODE systems.