Purpose A previously developed ordinary differential equation (ODE) that models the dynamic interaction and distinct radiosensitivity between cancer stem cells (CSC) and differentiated cancer cells (DCC) was used to explain the definitive treatment failure in Glioblastoma Multiforme (GBM) for conventionally and hypo-fractionated treatments. In this study, optimization of temporal dose modulation based on the ODE equation is performed to explore the feasibility of improving GBM treatment outcome. Methods A non-convex optimization problem with the objective of minimizing the total cancer cell number while maintaining the normal tissue biological effective dose (BEDnormal) at 100 Gy, equivalent to the conventional 2 Gy x 30 dosing scheme was formulated. With specified total number of dose fractions and treatment duration, the optimization was performed using a paired simulated annealing algorithm with fractional doses delivered to the CSC and DCC compartments and time intervals between fractions as variables. The recurrence time, defined as the time point at which the total tumor cell number regrows to 2.8x10(9) cells, was used to evaluate optimization outcome. Optimization was performed for conventional treatment time frames equivalent to currently and historically utilized fractionation schemes, in which limited improvement in recurrence time delay was observed. The efficacy of a super hyperfractionated approach with a prolonged treatment duration of one year was therefore tested, with both fixed regular and optimized variable time intervals between dose fractions corresponding to total number of fractions equivalent to weekly, bi-weekly, and monthly deliveries (n = 53, 27, 13). Optimization corresponding to BEDnormal of 150 Gy was also obtained to evaluate the possibility in further recurrence delay with dose escalation. Results For the super hyperfractionated schedules with dose fraction number equivalent to weekly, bi-weekly, and monthly deliveries, the recurrence time points were found to be 430.5, 423.9, and 413.3 days, respectively, significantly delayed compared with the recurrence time of 250.3 days from conventional fractionation. Results show that optimal outcome was achieved by first delivering infrequent fractions followed by dense once per day fractions in the middle and end of the treatment course, with sparse and low dose treatments in the between. The dose to the CSC compartment was held relatively constant throughout while larger dose fractions to the DCC compartment were observed in the beginning and final fractions that preceded large time intervals. Dose escalation to BEDnormal of 150 Gy was shown capable of further delaying recurrence time to 452 days. Conclusion The development and utilization of a temporal dose fractionation optimization framework in the context of CSC dynamics have demonstrated that substantial delay in GBM local tumor recurrence could be achieved with a super hyperfractionated treatment approach. Preclinical and clinical studies are needed to validate the efficacy of this novel treatment delivery method.
