  Low grade gliomas (LGGs) are a group of primary brain tumors usually
encountered in young patient populations. These tumors represent a difficult
challenge because many patients survive a decade or more and may be at a higher
risk for treatment-related complications. Specifically, radiation therapy is
known to have a relevant effect on survival but in many cases it can be
deferred to avoid side effects while maintaining its beneficial effect.
However, a subset of low-grade gliomas manifests more aggressive clinical
behavior and requires earlier intervention. Moreover, the effectiveness of
radiotherapy depends on the tumor characteristics. Recently Pallud et al.,
[Neuro-oncology, 14(4):1-10, 2012], studied patients with LGGs treated with
radiation therapy as a first line therapy. and found the counterintuitive
result that tumors with a fast response to the therapy had a worse prognosis
than those responding late. In this paper we construct a mathematical model
describing the basic facts of glioma progression and response to radiotherapy.
The model provides also an explanation to the observations of Pallud et al.
Using the model we propose radiation fractionation schemes that might be
therapeutically useful by helping to evaluate the tumor malignancy while at the
same time reducing the toxicity associated to the treatment.
