Trainee Project
A mathematical approach of the brain tumor treatment problem
2023/05/02 - 2023/09/29
The therapeutic methods conventionally used for the treatment of malignant tumors are radiotherapy, chemotherapy or a combination of the two. The central problem for treating the patient as well as possible is the choice of the therapeutic dose (the intensity of the treatment) and the periods/frequencies of administration of these doses. Therapy can therefore be seen as a scheduling problem. Doctors are regularly confronted with the same problem: if the therapeutic dose is too high, too many healthy cells can be killed and we observe the selection of tumor stem cells resistant to treatments causing recurrences; if the treatment is not effective enough, the tumor continues to grow or spread.

From a decision-making point of view, currently the action of the therapist (e.g., the choice of doctor) is defined empirically or by applying standardized protocols that are poorly adapted to the individual characteristics of tumours. The purpose of the internship is to build a theoretical framework for the therapist's decision-making and to study what mathematics can potentially bring in terms of decision-making. For this, we will model the therapist and the cell populations as players of a game whose functions must be inferred and validated by a theoretical model which will be tested by simulations. Knowledge in game theory, dynamical systems, and biological modeling will have to be acquired to tackle this problem. The trainee will first make a complete state of the art on the use of game theory in oncology. Secondly, a focus on the case of glioma will be made. Thirdly, a theoretical game model will be proposed and tested in simulations and compared to the experimental results available in the literature.
Starting date: April 15. Duration; 5 months. 620E/month
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