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Related Experiment Video

Updated: Oct 27, 2025

A Modeling and Simulation Method for Preliminary Design of an Electro-Variable Displacement Pump
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A Modeling and Simulation Method for Preliminary Design of an Electro-Variable Displacement Pump

Published on: June 1, 2022

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Delay differential equations based models in NONMEM.

Xiaoyu Yan1, Robert Bauer2, Gilbert Koch3

  • 1School of Pharmacy, Faculty of Medicine, The Chinese University of Hong Kong, Shatin, Hong Kong.

Journal of Pharmacokinetics and Pharmacodynamics
|July 24, 2021
PubMed
Summary
This summary is machine-generated.

NONMEM 7.5 now includes delay differential equation (DDE) solvers for pharmacometric models. The expectation-maximization (EM) method offers more stable parameter estimation than first-order conditional estimation (FOCE) with these new DDE solvers.

Keywords:
DDE solverDelay differential equationsNONMEMStiff differential equations

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Last Updated: Oct 27, 2025

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Area of Science:

  • Pharmacometrics
  • Computational Biology
  • Mathematical Modeling

Background:

  • Delay differential equations (DDEs) are crucial for modeling time delays in pharmacokinetic and pharmacodynamic (PK/PD) data.
  • Previous versions of NONMEM lacked dedicated DDE solvers, limiting complex PK/PD analyses.

Purpose of the Study:

  • To introduce the fundamental concepts of DDE-based models.
  • To demonstrate the application of newly implemented DDE solvers in NONMEM 7.5.
  • To provide practical examples and guidance for developing DDE models.

Main Methods:

  • Implementation of novel DDE solvers within NONMEM 7.5.
  • Evaluation of solver accuracy, stiffness handling, and parameter estimation performance.
  • Comparison of first-order conditional estimation (FOCE) and expectation-maximization (EM) methods for parameter estimation.

Main Results:

  • NONMEM 7.5's DDE solvers deliver accurate and precise solutions, with precision tunable via error tolerance parameters.
  • The expectation-maximization (EM) method demonstrates superior stability over FOCE for population parameter estimation with DDE models.
  • All implemented DDE solvers effectively handle stiff problems.

Conclusions:

  • The integration of DDE solvers in NONMEM 7.5 significantly enhances its capability for analyzing complex PK/PD data with time delays.
  • The EM method is recommended for population parameter estimation when using DDE models in NONMEM due to its enhanced stability.
  • This work provides essential resources, including control streams and datasets, for researchers to implement DDE models effectively.