Go to content oder Go to navigation


Johannes Tillil
MSc Mathematics in Medicine and Life Sciences / University of Lübeck

PharMetrX Research+ Program
PhD student year: 2023

University of PhD: University of Potsdam
Supervisor: Wilhelm Huisinga
Co-Supervisor: Charlotte Kloft

PhD Project

Model reduction of non-linear reaction kinetic models in the context of time-scale separation, coarse-graining and graph-theoretical approaches

Quantitative systems pharmacology (QSP) models incorporate effects and reactions of a large number of molecular species to mechanistically model reaction pathways in tissues and the body. QSP models are an important tool in drug development and drug target identification. However, the large number of states and parameters limit their use in a clinical setting due to their computational complexity and difficulty to accurately model pathways in individual patients. It is often possible to reduce the order of QSP models while retaining the input-output dynamics of interest. This makes QSP models easier to work with from a numerical stand point and may enable previously impossible population modeling of the QSP parameters.


My PhD project builds upon previous work of Jane Knöchel and Undine Falkenhagen from the Potsdam group of PharMetrX:

   - To gain insight into QSP model dynamics Jane Knöchel previously developed the novel input-response indices and state classification indices.

In addition, she developed an iterative model order reduction algorithm that classifies dynamic states as environmental, partially neglected, completely neglected or in quasi steady state. It uses the input-response indices to obtain a sensible search path through the space of reduced models. One goal of my PhD project is to leverage insights into model dynamics gained via the state classification indices for guiding our model reduction algorithm.

   - Undine Falkenhagen developed a statistical framework that enables us to reduce QSP models with respect to a virtual population of patients.

Furthermore, she reduced a QSP model of blood coagulation into a mechanistically derived pharmacodynamic (PD) model of Warfarin effect on the international normalised ratio that is fit for use in model-informed precision dosing.


The first step in my PhD project focuses on improving our previously developed model order reduction algorithm by introducing a more extensive search path through the space of reduced models and novel methods of reducing dynamic states, potentially extended to heuristically guided simultaneous reduction of multiple states. Developing a more effective model order reduction algorithm enables us to reduce more and more complex QSP models into mechanistically derived PD models than was previously possible.

Ultimately, the goal of my PhD work is to develop and improve methods for gaining an intimate understanding of QSP model dynamics and to leverage this knowledge for building better reduced QSP models and mechanistically derived PD models.


Please see the list of all publications and PhD theses.


  • 03/2023: Entering PharMetrX
  • 02/2022-06/2022: Erasmus semester at Syddansk Universitet, Odense, Denmark
  • 10/2020-02/2023: M.Sc. Mathematics in Medicine and Life Sciences at University of Lübeck, Germany
  • 10/2017-09/2020: B.Sc. Mathematics at University of Potsdam, Germany