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BCAMSevero Ochoa Award

basque center for applied mathematics

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Kroos, Julia Maria

Thesis

  • An SDE Approach to Cancer Therapy Including Stem Cells

    Date:
    27-08-2014
    University:
    Westfälische Wilhelms-Universität Münster
    Country:
    Germany
    File:
    Deskargatu PDF
    Comments:
    Discrete mathematical models for cancer propagation only describe the behavior of cancer cells to a certain extend. In this thesis we present a stochastic model for cancer cells that incorporates intrinsic and extrinsic uncertainties as well as the rather new concept of cancer stem cells. Here, we derive a model for differentiated cancer cells, cancer stem cells and normal tissue cells, prove the existence of solutions and analyze the behavior of the different populations with regards to their persistence times. Subsequently different treatment strategies including chemotherapy and radiation therapy and combinations of these therapies are introduced and incorporated in the SDE-model. In order to quantify the treatment strategies we introduced two quality measures: the tumor control probability (TCP) and the normal tissue complication probability (NTCP). For both measures discrete formulas as well as stochastic approaches were derived and compared.
Eusko Jaurlaritza - Gobierno Vasco ikerbasque - Basque Foundation for Science Bizkaia xede. Bizkaiko Foru Aldundia innobasque - Agencia vasca de la innovación Universidad del PaÌs Vasco (UPV/EHU)