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Figure 1: Treatment plan visualization. This graph highlights the impact of traversing the biological dose function. α/β =10, minimum equivalent dose in 2 Gy fractions = 85 Gy, nE = 25, DE = 45 Gy, and nB = 5. The constraint is given in equivalent dose in 2 Gy fractions and represented by the top horizontal dotted line. The lower dotted line represents the equivalent dose in 2 Gy fractions at which the first treatment method stops and the second method begins. The blue solid line represents the dose trajectory of external beam radiation therapy. The dotted red line shows what the equivalent brachytherapy trajectory would be. This is a phantom trajectory in that it is just used in this graphic to track where brachytherapy starts. Once the external beam radiation therapy treatment is done, the organ is left at the equivalent dose in 2 Gy fractions marked by the first dotted line. Brachytherapy picks up along the solid red line. The difference between the x-values of the endpoints of this solid red line gives the brachytherapy dose constraints we plug into inverse planning simulated annealing

Figure 1: Treatment plan visualization. This graph highlights the impact of traversing the biological dose function. α/β =10, minimum equivalent dose in 2 Gy fractions = 85 Gy, n<sub>E</sub> = 25, D<sub>E</sub> = 45 Gy, and n<sub>B</sub> = 5. The constraint is given in equivalent dose in 2 Gy fractions and represented by the top horizontal dotted line. The lower dotted line represents the equivalent dose in 2 Gy fractions at which the first treatment method stops and the second method begins. The blue solid line represents the dose trajectory of external beam radiation therapy. The dotted red line shows what the equivalent brachytherapy trajectory would be. This is a phantom trajectory in that it is just used in this graphic to track where brachytherapy starts. Once the external beam radiation therapy treatment is done, the organ is left at the equivalent dose in 2 Gy fractions marked by the first dotted line. Brachytherapy picks up along the solid red line. The difference between the x-values of the endpoints of this solid red line gives the brachytherapy dose constraints we plug into inverse planning simulated annealing