Delay effects in the response of low grade gliomas to radiotherapy: a mathematical model and its therapeutical implications

Low grade gliomas (LGGs) are a group of primary brain tumors, which are highly infiltrative and generally incurable but have median survival time of more than 5 years because of low proliferation. Management of LGGs has historically been controversial because these patients are typically young, with few, if any, neurological symptoms. Recently Pallud et al. studied patients with LGGs treated with first-line radiation therapy and found the counter-intuitive result that tumors with a fast response to the therapy had a worse prognosis than those responding late. We construct a mathematical model describing the basic facts of glioma progression. Radiation therapy included in our mathematical model captures the essentials of the dynamics and explains the relationship between proliferation, response to the therapy and prognosis. It can also provide an explanation to the observations of Pallud et al. and it can be used to explore different radiation regimes. Using the model we propose radiation fractionation schemes that might be therapeutically useful by helping to evaluate the tumor malignancy. It could help the oncologists in making the best possible decision on when and how act on the tumor.