(A) Representative MRIs showing human and mouse gliomas that are resolved by radiation treatment but then recur.
(B) Representative images and quantification of a radiation dose response assayed in E2f1-Luc glioma-bearing 24 hr after a given radiation dose. Error bars are SD.
(C) Schematic of the mathematical model used to describe the radiation response. The tumor is modeled as two separate cellular components: the stem-like resistant cells (SLRCs) and the differentiated sensitive cells (DSCs). SLRCs can repopulate the tumor, and some DSCs cells, represented by γ, are able to revert to SLRCs in response to radiation.
(D) Flow-chart summarizing the workflow described in the paper.
See also .

(A) Original model-predicted tumor response and growth following standard, single-dose, optimum-1, and scramble control radiation treatment schedules. Model parameters are listed under “Original Parameters” in .
(B) Kaplan-Meier survival plot of various radiation schedules. IR, ionizing radiation.
(C) Schematic depicting the various schedules tested. The arrow position represents the time of dose during the 8am–5pm treatment window. The size of the arrow correlates with the size of the dose.
(D) Table summarizing number of mice treated, the performance relative to standard therapy, and the original model-predicted performance of each group. ns, not significant.
(E) Hazard ratios of the various radiation schedules, compared to the standard radiation schedule. Error bars represent the 95% confidence interval (CI) of the hazard ratio (HR).
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(A) Predicted tumor growth in response to standard, hypofractionated, hyperfractionated, and optimum-1 radiation treatment schedules. These curves are based on the original model; parameters are listed under Original Parameters in .
(B) Kaplan-Meier survival plot of hypo- and hyperfractionated radiation schedules. Standard and optimum-1 survival are the same curves as and are shown for comparison.
(C) Schematic depicting the hyper- and hypofractionated schedules tested. The arrow position represents the time of dose during the 8am–5pm treatment window. The size of the arrow correlates with the size of the dose.
(D) Hazard ratios of the hypo- and hyperfractionated radiation schedules, compared to the standard radiation schedule. Error bars represent the 95% CI of the HR.
(E) Reparameterization of the time-dependent model based on volumetric MRI studies of mouse gliomas treated with 2 weeks of the standard schedule.
(F) Time-dependent model-predicted tumor growth in response to the various treatment schedules. Model parameters are listed under “Second Iteration” in .
(G) Table summarizing number of mice treated, the performance relative to standard therapy, and the predicted performance of the original and time-dependent model for each treatment group.
See also .

(A and B) Graph showing predicted size of the stem-like resistant cell population for hyperfractionated, optimimum-1, and optimum-2 schedules, using the original model (A) or the time-dependent model (B). All values are normalized to predictions for standard therapy. Parameters in (A) and (B) are, respectively, from the Original Parameters and Second Iteration in .
(C) Representative gating strategy for eGFP+ tumor cell side-population (SP) analysis. The upper panel depicts the gate used to identify GFP-positive cells, based on a GFP-negative sample shown in the insert. The lower panel depicts the gate used to identify the SP, based on a Fumitremorgin C-verapamil-treated control shown in the insert.
(D) Representative images and quantification of SP analysis 24 hr after the conclusion of the standard, hyperfractionated, optimum-1, and optimum-2 schedules. For quantification, all values are normalized to the average SP of the standard schedule. Error bars represent the SD.
(E) Kaplan-Meier analysis comparing standard, optimum-1, and optimum-2 schedules. These mice represent an entirely independent cohort from mice in and .
(F) Hazard ratios of the optimum-1 and optimum-2, compared to standard radiation.
(G) Schematic briefly describing the optimum-1 and optimum-2 schedules. The arrow position represents the time of dose during the 8am–5pm treatment window. The size of the arrow correlates with the size of the dose. Error bars represent the 95% CI of the HR.

(A) Survival-fit, model-predicted tumor growth in response to various radiation treatment schedules. These predictions are from the time-dependent model reparameterized to fit the mouse survival data with the parameters under “Final Iteration” in .
(B) Table summarizing the number of mice treated, the performance relative to standard therapy, and the predicted performance survival data reparameterized time-dependent model for each treatment group.
(C) Sensitivity analysis of the model's parameters, ranked from most to least sensitive, as determined by the sensitivity analysis ().
(D) Predictions of the SLRC/DSC ratio while varying the fraction of cells capable of reversion (γ_o).
(E) Sensitivity plot showing the relative efficacy of several schedules while varying the fraction of cells capable of reversion (γ_o). An explanation of how we found the parameters for (E) can be found in Section 5 of the .
See also .