PhD Courses in Denmark

Dynamic Modelling of Toxic Effects

PhD School at the Faculty of SCIENCE at University of Copenhagen


The toxicity of a chemical not only depends on chemical properties and the exposed species, but also on exposure time, the endpoint measured, and the exposure conditions. Mathematical modelling is a powerful tool to interpret the results of laboratory toxicity tests and to make educated extrapolations. In this course, you will learn the basics of toxicokinetic and toxicodynamic modelling, and how they can be linked. This foundation allows you to analyse and interpret body residue and toxicity data on a mechanistic basis.

A detailed schedule for the content of the specific talks and exercises will be provided in spring.

The overall content is given in this summary:
The toxicity of a chemical depends on properties of the compound and of the species that is exposed, but also on the exposure time, the endpoint (e.g. growth, reproduction or survival), and the exposure conditions (temperature, food level, etc.). In ecotoxicology, the interdependencies of these factors are generally ignored by rigid standardisation of the tests and descriptive summary statistics such as EC50 and NOEC. However, we need a more mechanistic interpretation of toxicity to make an unbiased comparison of toxicity between species and chemicals, and to extrapolate the effects to untested exposure conditions. Because it is impossible to test all chemicals on all species under all possible exposure scenarios, extrapolation is of key importance for ecotoxicologists and environmental risk assessors.

Mathematical modelling is a powerful tool to interpret the results of laboratory toxicity tests and to make educated extrapolations. The process of mechanistically modelling toxicity can be divided into two steps: toxicokinetics (TK) and toxicodynamics (TD). TK deals with the uptake, biotransformation and distribution of a chemical into the body of an organism, whereas TD deals with the next step: from internal concentration of the active compound to effects on the organism over time.

In this course, you will learn the basics of TK and TD modelling, and how they can be linked. Furthermore, you will learn to analyze and interpret toxicity data on a mechanistic basis.


For TK modelling, we will focus on 1- and 2-compartment models; TD modelling will focus on a simple Dynamic Energy Budget model (DEBkiss), although we will also treat survival modelling with GUTS in the on-line part of the course. The course comprises a combination of lectures, computer exercises and discussions.

In the computer exercises you will learn to build and use basic TKTD models yourself in Matlab, guided by a series of general exercises.
The course will be divided into two parts: An at-home and on-line part taking place from October 14th till November 11th, with an on-line meeting each Monday afternoon from 13.30-17.00.

At these meetings, there will be lectures introducing theory and discussions on the reading materials and exercises.
In between meetings, we ask you to study reading materials and make computer exercises to get acquainted with the software and with the topics. The on-line part focusses on TK and TD principles, and more specifically on TK and survival models (GUTS).

The second part takes place on site at Danhostel Roskilde Vandrehjem, meeting Sunday November 17th for dinner and a short introduction, and finishing Friday November 22nd after lunch. During the on-site part of the course, we will focus more specifically on sub-lethal effects (with a DEB-based model).

Each course day will consist of a mixture of lectures, exercises and group projects, that will help you to master the modeling and interpret your data output

Learning outcome

In this course, students will:

• Understand the concepts of TK and TD (online)
• Understand the basics of mechanistic effect modelling (online)
• Learning to work with the BYOM platform in Matlab (online)
• Build simple TK models, and TD models for survival (online)
• Build TKTD models for sub-lethal effects (on-site)
• Use them to analyze and interpret toxicity data (on-site)
• Analyze a case study, and discuss and interpret the results (on-site)
• Learn to use advanced analysis options with the BYOM platform under Matlab (on-site)


Jager T, Heugens EHW, Kooijman SALM. 2006. Making sense of ecotoxicological test results: Towards application of process-based models. Ecotoxicology 15:305-314.
Ashauer R, Escher BI. 2010. Advantages of toxicokinetic and toxicodynamic modelling in aquatic ecotoxicology and risk assessment. Journal of Environmental Monitoring 12:2056-2061.
Jager, T.; Martin, B. T.; Zimmer, E. I., DEBkiss or the quest for the simplest generic model of animal life history. Journal of Theoretical Biology 2013, 328, 9-18.
Jager T. (2020). Revisiting simplified DEBtox models for analyzing ecotoxicity data. Ecological Modelling 416:108904.

More information including references can be found on: and 

Teaching and learning methods

Teaching will be a combination of lectures, computer exercises, group projects, and discussions. After both the on-line and on-site parts, we ask the students to perform a specific data analysis at home, individually, and report that to the teachers.


Nina Cedergreen (University of Copenhagen)
Andreas Focks (University of Osnabrück)
Andre Gergs (Bayer)
Simon Hansul (University of Osnabrück)


Course fee:
5000 DKK academia (MSc, PhD, Post doc students)
18500 DKK participants employed in industry

NB. Course fee regarding QTOX PhD students will be covered by the QTOX-funding.

The price for academia and participants employed in industry covers a full course including breakfast and lunch buffet at the course centre Danhostel Roskilde, Vindeboder 7, 4000 Roskilde

Please note that overnight accommodation are on the participants own expense.

To sign up and make your payment for the course (via credit card or Mobilepay):
please register on this website
and state your choice of accommodation:

1) no accommodation - NB. dinner at your own expense!
2) accommodation in shared room with 3-6 participants (including dinner) DKK 1500
3) accommodation in single room (including dinner) DKK 3000

Final deadline for application is 30. June 2024, or when the maximum number of participants has been reached.

The registration is binding, and the course fee and expense of accommodation is non-refundable in case of participant cancellation after deadline 30. June 2024.
All participants must bring their own lap-top with Matlab (version 2016b or newer) installed.

UCPH discloses non-sensitive personal data to course leader/speakers, if any. In addition, we will disclose non-sensitive personal data to the other participants in the course. Non-sensitive personal data includes names, job positions, institution names & addresses, telephone numbers and e-mail addresses