Solving the PIHNA model while accounting for radiotherapy

Glioblastoma is the most aggressive type of glioma. During the last decades, several models have been proposed for simulating the growth procedure of glioma. One of the latest proposed models builds upon the proliferation - diffusion model by incorporating the angiogenic net rates and different concentration of cell populations (normoxic, hypoxic and necrotic). This proliferation- invasion- hypoxia- necrosis-angiogenesis model (PIHNA) does not take into account radiotherapy. This work presents the mathematical foundation for solving PIHNA model in two dimensions with incorporated radiotherapy effect using the Linear Quadratic Model, which uses radiobiology parameters.