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Mathematical Sciences
Applied Mathematics
Dynamical systems in applications
Tutorial for Modeling Delays in Biological Systems in the NONMEM Software

Tutorial for Modeling Delays in Biological Systems in the NONMEM Software

Robert J Bauer ¹, Wojciech Krzyzanski ²

Robert J Bauer ¹, Wojciech Krzyzanski ²

¹ICON Clinical Research, LLC, Blue Bell, Pennsylvania, USA.
²Department of Pharmaceutical Sciences, University at Buffalo, Buffalo, New York, USA.

⁰ICON Clinical Research, LLC, Blue Bell, Pennsylvania, USA.

Cpt: Pharmacometrics & Systems Pharmacology +

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June 17, 2025

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June 17, 2025

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View abstract on PubMed

Summary

This summary is machine-generated.

This tutorial introduces pharmacokinetic/pharmacodynamic (PKPD) models with delays, using specialized techniques like delay differential equations (DDEs) and distributed DDEs (DDDEs) in NONMEM software for biological system analysis.

Area Of Science

Pharmacometrics
Pharmacokinetics and Pharmacodynamics (PKPD)
Mathematical Biology

Background

Biological systems commonly exhibit delays, necessitating advanced modeling techniques.
Traditional methods like transit compartments, delay differential equations (DDEs), and distributed DDEs (DDDEs) are mathematically complex and infrequently used.
Recent NONMEM implementation of DDDEs enhances their applicability in PKPD modeling.

Purpose Of The Study

To provide a tutorial on implementing PKPD models with delays in NONMEM.
To demonstrate the application of DDEs and DDDEs for modeling biological delays.
To offer guidance on selecting appropriate delay modeling techniques.

Main Methods

Implementation of PKPD models incorporating delays using DDEs and DDDEs.
Utilizing the NONMEM software for pharmacokinetic and pharmacodynamic data analysis.
Detailed explanation of model coding within the NONMEM control stream.

Main Results

Successful application of DDEs and DDDEs in NONMEM for PKPD models with delays.
Analysis of biological and pharmacological principles underlying the model equations.
Discussion of data analysis results from implemented models.

Conclusions

NONMEM's enhanced capabilities facilitate the use of complex delay modeling techniques (DDEs, DDDEs).
The tutorial provides practical examples and coding for PKPD models with delays.
Guidelines are offered for choosing delay modeling strategies based on data and study objectives.

Keywords:

NONMEM biostatistics delay differential equations distributed delay systems nonlinear models pharmacometrics software therapeutics

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