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Exploring Inductive Linearization for simulation and estimation with an application to the Michaelis-Menten model.

Sepideh Sharif1, Chihiro Hasegawa2, Stephen B Duffull2

  • 1Otago Pharmacometrics Group, School of Pharmacy, University of Otago, Dunedin, New Zealand. sepi.sharif@postgrad.otago.ac.nz.

Journal of Pharmacokinetics and Pharmacodynamics
|July 5, 2022
PubMed
Summary
This summary is machine-generated.

Inductive Linearization coupled with eigenvalue decomposition offers faster and accurate solutions for nonlinear ordinary differential equations (ODEs) in pharmacokinetic-pharmacodynamic systems. Improvements enhance efficiency for simulation and estimation tasks.

Keywords:
(PKPD) model developmentAdaptive step size algorithmInductive LinearizationNonlinear ordinary differential equationsNumerical methodsOptimization

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Area of Science:

  • Pharmacometrics
  • Computational Biology
  • Mathematical Modeling

Background:

  • Nonlinear ordinary differential equations (ODEs) are prevalent in pharmacokinetic-pharmacodynamic (PK/PD) modeling.
  • Exact analytical solutions for these ODEs are often unattainable, necessitating robust numerical methods.
  • Inductive Linearization (IL) provides an iterative approach to approximate nonlinear ODEs with linear time-varying (LTV) ODEs.

Purpose of the Study:

  • To explore and enhance the efficiency of Inductive Linearization when integrated with eigenvalue decomposition (EVD) for solving nonlinear ODEs.
  • To investigate specific improvements for IL-EVD, focusing on simulation and parameter estimation in PK/PD models.
  • To evaluate the performance of the enhanced IL-EVD method against a standard numerical solver.

Main Methods:

  • Coupling Inductive Linearization with eigenvalue decomposition (EVD) for solving the resulting linear time-varying ODEs.
  • Implementing three key improvements: convergence criteria, optimized step sizes for EVD, and initial condition updates for estimation.
  • Evaluating performance using single-subject stochastic simulation-estimation on a pharmacokinetic model with Michaelis-Menten elimination.
  • Comparing results against MATLAB's ode45, a variable-step Runge-Kutta method.

Main Results:

  • All implemented improvements enhanced the computational speed of the Inductive Linearization technique.
  • Accuracy was maintained, with comparable parameter estimates to the ode45 reference method.
  • The enhanced IL-EVD approach demonstrated faster execution times than ode45 for the tested PK model.
  • The methods are readily implementable in common statistical software like R and MATLAB.

Conclusions:

  • The enhanced Inductive Linearization coupled with eigenvalue decomposition offers a computationally efficient and accurate alternative for solving nonlinear ODEs in PK/PD.
  • The proposed improvements significantly boost the performance of IL-EVD for both simulation and estimation.
  • Further research is warranted to extend this technique to population pharmacokinetic modeling.