A mathematical model to simulate glioma growth and radiotherapy at the microscopic level

In the present work, a new mathematical approach for modelling the influence of radiotherapy on the progression of malignant primary brain tumours is proposed. A hybrid approach is used to model the cellular tumour progression, the development of the local nutrient concentration and the density of the extracellular matrix (ECM). The description of radiotherapy is based on the linear-quadratic model. The effects of irradiation are influenced by the administrated dose and two parameters, which represent the radiosensitivity of the tissue. Due to the discrete approach, the impact of the therapy can be described for every single tumour cell. The implementation of the cell cycle allows, alongside the more precise description of the biological processes, for mapping the variability of the radiosensitivity of cells in the different cell phases. Furthermore, the choice of different fractionation schemes allows a variable adaption of the radiotherapy to the tumour. The main contribution is the novel combination of the microscopic tumour growth model including the microenviron-ment with the influences of the radiotherapy model. Furthermore we can provide a comparison of the growth model re-sults to histological data of glioblastoma.