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Courses / TKTD summerschool

TKTD summerschool 'DynModTox'

After skipping the course in 2018, we unfortunately had to cancel the course again in 2020 due to the Covid-19 situation. We decided to organise the summer school again in 2021, changing the format and turning it into an autumn school. This year, we'll break up the course into an on-line pre-course (with homework), and an intensive 5-day on-site part in Denmark. We will, however, monitor the COVID-situation closely, and may decide at some point to make the whole course on-line only. It is also possible to join in for the pre-course only, for a reduced fee.

Download 2021 flyer.

Practical essentials

Language: English.
Credits: 5 ECTS, for entire course, 2 ECTS for pre-course only.
Level: PhD students, but master students and post-PhD participants are very welcome.
Location: on-line pre-course, and on-site in Roskilde, Denmark. However, we might still have to decide to turn this into a fully on-line event.
Duration: Pre-course: on-line, 5 Wednesday afternoon sessions (13 Sept.-13 Oct. 2021, lectures+discussion), with homework (reading+exercises) in between. Main course: on-site (or on-line if forced by travel/meeting restrictions), 5 full days (17-22 Oct. 2021).
Capacity: minimum 10, maximum 30 participants.
Course fee:
5000 DKK academia (MSc and PhD students), 15000 DKK industry, 1000 DKK for on-line part only. Note that, if the main course is on-site as planned, there are additional costs for travel and stay in Denmark.
PC/software: Participants need a PC with Matlab installed. For the on-site part, participants must bring their own laptop, with Matlab installed (with travel adapter if needed!).

Teachers: the teaching team consists of Tjalling Jager, Nina Cedergreen, Roman Ashauer, Andreas Focks, André Gergs and Neil Sherborne. Other guest lecturers/assistants may make an appearance.
Use this link for more administrative information and registration: Registration and administration will be handled by the University of Copenhagen. If have questions about the practical issues (registration, payment, etc.), please contact Nina Cedergreen (ncf(at) Deadline for application is 31 May 2021 or when the maximum number of participants has been reached.

About the course

Mathematical modelling is a powerful tool to interpret the results of laboratory toxicity tests and to make educated extrapolations. The process of mechanistically modelling of 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 steps, from internal concentration of the active compound to effects on the organism over time.

This course will teach the basics of TK and TD modelling, how they can be linked, and how to analyse and interpret toxicity data on a mechanistic basis. For TK modelling, we will focus on 1- and 2-compartment models. TD modelling will be based on a simple Dynamic Energy Budget model (DEBkiss), although we will treat survival modelling with GUTS in the pre-course (since GUTS is the simplest, non-trivial, TKTD model around).

Note that the course format in 2021 will be slightly different from the format used in previous years.

Previous courses

In 2012, the first summer course "Dynamic modelling of toxic effects" was held from 11-18th of August in the Søminestationen, Holbæk, Denmark with 25 participants. The course focussed on TKTD modelling in general, and on GUTS and DEBtox in particular. Overall, the course was a success, but some changes were needed because we tried to put too much into the course (too much time was used in coding and dealing with error messages). Impressions from the 2012 course.

Learning from this experience, we decided to focus on basic TK and sub-lethal effects modelling. Furthermore, we decided to offer two platforms (OpenModel next to Matlab), and provide templates and worked out examples for the exercises to facilitate the coding. In this way, the course would be useful both for the novice and the experienced coder.

In 2014, we offered this summer course again (5-13 August) with 15 participants. Not in the same location but in the hostel Vandrerhjem in Roskilde, Denmark. This time, we focussed on (basic) toxicokinetics and sub-lethal effects using DEB theory (in the form of the simplified DEBkiss model). Thereby, we skipped most of GUTS. The use of OpenModel next to Matlab, and the templates for the exercises was a great success in our opinion, so we will keep this for future courses. Impressions from the 2014 course.

In 2016, the third round of the course was held, again at the Søminestationen, Holbæk (9-16 August). We had a full house with 27 participants. The course basically followed the same format as in 2014, but with more freedom in the group projects (for example, some groups focussed on GUTS, and one on rats and one on duckweed). This turned out very well, so we'll build on this for the next course. Impressions from the 2016 course.

We skipped the course in 2018 for personal reasons, and in 2020 we had to cancel due to the corona crisis.

We will offer this course again in 2021, in a slightly different format. Due to problems with openModel, we will use Matlab only. However, templates will be provided to make the course accessible for novice Matlab users. We will split the course into an on-line pre-course and an intensive 1-week on-site course.

The 2012 group

The 2014 group (minus one person)

The 2016 group

Course format

Starting with the 2021 course, we'll organise the course in two parts:

On-line, we'll meet on 5 consecutive Wednesday afternoons. Each session will contain lectures by the teachers, time for questions/discussions, and explanation/feedback on homework exercises and reading materials. In between these meetings, we'll ask you to do homework: reading provided texts, exercises in Matlab, and preparation of questions for the next session. This pre-course focusses on the basic skills needed for modelling, simple toxicokinetic (TK) modelling, and TKTD modelling for the endpoint survival (GUTS). It will be possible to only follow the on-line course (but not to skip the on-line course and only join the main course).

Lecture topics covered in the pre-course (preliminary):
  • Modelling basics (ODEs, systems, building blocks), Matlab/BYOM basics, TK and TKTD basics and background.
  • Basic statistics for model fitting (error models, SSQ, likelihood).
  • Numerical methods for ODE solving and model optimisation.
  • TK in more detail, linking TK to effects.
  • GUTS-SD basics (TKTD for survival), somewhat more advanced statistics for model fitting (profiling, Bayes).
  • GUTS in environmental risk assessment (e.g., EFSA opinion, simulation of FOCUS profiles).

We will likely provide an assignment after the pre-course, and ask you to hand in a (short) report, to decide if you can receive the ECTS credits. Details will follow, but we'll likely ask you to (individually) analyse a data set for body residues and/or survival effects.

Main course:
On-site in Denmark (on on-line if forced), we'll have 5 full days of intensive training. In this part, the focus lies on TKTD modelling for sub-lethal endpoints (i.e., growth and reproduction) using DEB-based models. We will use the simplified DEBkiss model here. The Matlab exercises will guide you step wise through the analysis of a rather complex life-cycle data set.

Lecture topics covered in the main course (preliminary):
  • Energy-budget modelling, structure and background.
  • Detailed structure of DEBkiss.
  • Statistics for fitting growth and reproduction data
  • Modelling stress effects on growth and reproduction.
  • Using DEB-TKTD in environmental risk assessment.
  • Organisms that require model adaptations.
  • Introduction to standard 'full' DEB (differences with DEBkiss).
Apart from the pre-cooked exercises that we ask you to do, we'll also include time for more adventurous group projects. We still have to decide how to organise this part of the course, but we are leaning towards providing each group with a data set (as in the 2014 course), rather than asking participants to work on their own data (as in the 2016 course).

We will likely provide an assignment after the main course, and ask you to hand in a (short) report, to decide if you can receive the ECTS credits. Details will follow, but we'll likely ask you to (individually) analyse a data set for growth and reproduction effects.

Note that we focus in this course on applications in ecotoxicology (mainly invertebrates and fish). Even though the same modelling principles are used in modelling toxicity for other organisms, we will not go into detail about how to deal with them.

Software platforms, required Matlab skills

For this course, we currently use Matlab only. Previous courses also offered the possibility to work in OpenModel, but that is not as stable, flexible and powerful as Matlab. We tried to make the process of using Matlab as painless as possible by working with BYOM and providing templates that take away almost all of the coding complexities. Therefore, you do not need to be skilled in Matlab programming/coding. However, you do need to know the basics of the Matlab language and how to modify and run code. Experience with previous courses shows that novel Matlab users will quickly have the skills required to do the exercises.

If you're new to Matlab, the tutorial from Udemy is a good place to start. Further, the Mathworks offers many free resources to get started. Finally, the book "Essential MATLAB for Engineers and Scientists" (if you can find/lend/buy it). You only need to know the basics of Matlab to be able to do the exercises, so don't overdo it. Installing and getting to know Matlab is something you need to do before the start of the pre-course.

If your institute does not have access to a Matlab license, you can try to work with the 30-day trial version, or buy the student version (if you qualify as a student according to Matlab) for just 35 Euro from the Mathworks.

Math skils

This is not a math or stats course, but it will make use of mathematics and statistics. More specifically, (systems of) ordinary differential equations (ODEs) and basic likelihood functions. It helps to have a basic working knowledge of ODEs and likelihood statistics, though we will also spend some time on these topics in the pre-course.

During the pre-course, we will offer you lectures and reading material on the basics of (working with) differential equations and likelihood functions, focussing on the application to TK/TKTD modelling. We assume that you have a working knowledge of mathematical functions, powers and logarithms, derivatives and integration, and basic statistical distributions such as the binomial and the normal (e.g., bachelor-level biology). If you're math skills are rusty, this part of the course may take somewhat more time. Practice with the previous course learns that math skills are hardly ever a bottleneck for following this course. However, students with a stronger math/modelling background will, by the end of the course, be more advanced in TKTD modelling than those with a less of a quantitative background.

Managing expectations

This course deals with many aspects associated with TKTD modelling: biology, (eco)toxicology, mathematics, statistics, coding, numerical methods, etc. If you are a novice in one or more of these fields, you will not be a full-fledged TKTD modeller after this course. Furthermore, it is unlikely that you will leave this course with a finalised model for your specific species-of-interest and your data sets. However, you will leave this course with a good overview of the TKTD modelling field, hands-on experience, and improved skills on all the disciplines listed above, preparing you for more specialist courses on these topics (such as coding or math courses, or the DEB course).


The course is coordinated by Nina Cedergreen. Course contents and lectures will mainly be the responsibility Tjalling Jager, with contributions from Nina Cedergreen, Roman Ashauer, Andreas Focks, André Gergs and Neil Sherborne. Guest lectures may be provided by other experts.

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