OSTMCM

OSTMCM – Optimal and Suboptimal Treatment in Mathematical Cancer Modells

Project Leader: Prof. Dr. Kurt Chudej
Contact: Prof. Dr. Kurt Chudej

Project start: 2016 Project end: 2018/10/30

Project team: External partners:

Prof. Dr. Helmut Maurer, Universität Münster

Prof. Dr. Alfio Borzi, Lehrstuhl für Wissenschaftliches Rechnen, Universität Würzburg

Tim Breitenbach, M.Sc., Lehrstuhl für Wissenschaftliches Rechnen, Universität Würzburg

Melina-Lorén Kienle Garrido, M.Sc., Lehrstuhl für Wissenschaftliches Rechnen, Universität Würzburg

Dominik Huebner M.Sc., früher Lehrstuhl für Ingenieurmathematik, Universität Bayreuth

Lisa Wagner M.Sc., Numerische Mathematik und Wissenschaftliches Rechnen, Universität Darmstadt




Project description:

Application Background

We solve numerically certain mathematical optimal control models for the treatment of cancer.

Contribution to the Mission of MODUS

There exist a large number of mathematical cancer models published in medical papers. We focus on certain mathematical cancer models. We are interested in the numerical computation of challenging models concerned with the combined therapy via antiangiogenic treatment and radiotherapy. These mathematical optimal control problemes are challenging both from the theoretical as well as from the numerical point of view since these models include differential-algebraic behaviour. After the computation of optimal controls we have to compute suboptimal controls restricted to step functions on a coarse grid, which have the potential to be applied in reality.

Results

Numerical results for a combined therapy via antiangiogenic treatment and radiotherapy for a specific mathematical cancer model have been computed and published. Currently we investigate alternative formulations of the mathematical optimal control problem.

References

  • Kienle Garrido, Melina-Lorén; Breitenbach, Tim; Chudej, Kurt; Borzì, Alfio: Modeling and Numerical Solution of a Cancer Therapy Optimal Control Problem. In: Applied Mathematics. Bd. 9 (2018) Heft 8 . - S. 985-1004.
  • Chudej, Kurt; Huebner, Dominik; Pesch, Hans Josef: Numerische Lösung eines mathematischen Modells für eine optimale Krebskombinationstherapie aus Anti-Angiogenese und Strahlentherapie. In: Wiedemann, Thomas (Hrsg.): Tagungsband ASIM 2016 - 23. Symposium Simulationstechnik: am 7.-9.10. 2016 an der HTW Dresden. - Wien, Österreich, 2016. - S. 169-176. - (ARGESIM Report; 52)


University of Bayreuth -