J. Math. Biol. DOI 10.1007/s00285-015-0908-x Mathematical Biology Optimization of radiation dosing schedules for proneural glioblastoma

Abstract Glioblastomas are the most aggressive primary brain tumor. Despite treat-ment with surgery, radiation and chemotherapy, these tumors remain uncurable and few significant increases in survival have been observed over the last half-century. We recently employed a combined theoretical and experimental approach to predict the effectiveness of radiation administration schedules, identifying two schedules that led to superior survival in a mouse model of the disease (Leder et al., Cell 156(3):603– 616, 2014). Here we extended this approach to consider fractionated schedules to best minimize toxicity arising in early- and late-responding tissues. To this end, we decom-posed the problem into two separate solvable optimization tasks: (i) optimization of the amount of radiation per dose, and (ii) optimization of the amount of time tha