Pérez García, Victor M.. 

We study optimal radiotherapy fractionations for low-grade glioma using mathematical models. Both space-independent and space-dependent models are studied. Two different optimization criteria have been developed, the first one accounting for the global effect of the tumor mass on the disease sympthoms and the second one related to the delay of the malignant transformation of the tumor. The models are studied theoretically and numerically using the method of feasible directions. We have searched for optimal distributions of the daily doses $d_j$ in the standard protocol of 30 fractions using both models and the two different optimization criteria. The optimal results found in all cases are minor deviations from the standard protocol and provide only marginal potential gains. Thus, our results support the optimality of current radiation fractionations over the standard 6 week treatment period. This is also in agreement with the observation that minor variations of the fractionation have failed to provide measurable gains in survival or progression free survival, pointing out to a certain optimality of the current approach.