Spatial Agreement of Brainstem Dose Distributions Depending on Biological Model in Proton Therapy for Pediatric Brain Tumors

Abstract

Purpose: During radiation therapy for pediatric brain tumors, the brainstem is a critical organ at risk, possibly with different radio-sensitivity across its substructures. In proton therapy, treatment planning is currently performed using a constant relative biological effectiveness (RBE) of 1.1 (RBE_1.1), whereas preclinical studies point toward spatial variability of this factor. To shed light on this biological uncertainty, we investigated the spatial agreement between isodose maps produced by different RBE models, with emphasis on (smaller) substructures of the brainstem.

Methods and materials: Proton plans were recalculated using Monte Carlo simulations in 3 anonymized pediatric patients with brain tumors (a craniopharyngioma, a low-grade glioma, and a posterior fossa ependymoma) to obtain dose and linear energy transfer distributions. Doses and volume metrics for the brainstem and its substructures were calculated using a constant RBE_1.1, 4 phenomenological RBE models with varying (α/β)_x parameters, and with a simpler linear energy transfer-dependent model. The spatial agreement between the dose distributions of constant RBE_1.1 versus the variable RBE models was compared using the Dice similarity coefficient.

Results: The spatial agreement between the variable RBE dose distributions and RBE_1.1 decreased with increasing isodose levels in all patient cases. The patient with ependymoma showed the greatest variation in dose and dose volumes, where V_50Gy(RBE) in the brainstem increased from 32% (RBE_1.1) to 35% to 49% depending on the applied model, corresponding to a spatial agreement (Dice similarity coefficient) between 0.79 and 0.95. The remaining patients showed similar trends, however, with lower absolute values due to lower brainstem doses.

Conclusions: All phenomenological RBE models fully enclosed the isodose volumes of the constant RBE_1.1, and the volumes based on variable RBE spatially agreed. The spatial agreement was dependent on the isodose level, where higher isodose levels showed larger expansions and less agreement between the variable RBE models and RBE_1.1.

Figure 1

50 Gy(RBE) isodose curves ([α/β]_x = 2.1 Gy) and LET_d distributions for the 3 patients. Delineated structures are midbrain (green), pons (blue), and medulla oblongata (yellow). The LET_d in voxels receiving doses below 0.1 Gy(RBE) according to the RBE_1.1 dose is set transparent. Abbreviations: CAR = Carabe; LET_d = dose-averaged linear energy transfer; LWD = LET-weighted dose; MCN = McNamara; RBE = relative biological effectiveness; ROR = Rørvik; WED = Wedenberg. (A color version of this figure is available at https://doi.org/10.1016/j.adro.2020.08.008.)

Figure 2

V_50Gy(RBE) metrics and corresponding Dice similarity coefficients within the brainstem and substructures for the 3 patients. (α/β)_x = 2.1 Gy was used for the phenomenological RBE models. Abbreviations: CAR = Carabe; DSC = dice similarity coefficient; LWD = LET-weighted dose; MCN = McNamara; RBE = relative biological effectiveness; ROR = Rørvik; WED = Wedenberg.

Figure 3

Dice similarity coefficients relative to RBE_1.1 for every 5 Gy(RBE) isodose step in the brainstem for the 3 patients. (α/β)_x = 2.1 Gy was used for the phenomenological RBE models. Abbreviations: CAR = Carabe; DSC = dice similarity coefficient; LWD = LET-weighted dose; MCN = McNamara; RBE = relative biological effectiveness; ROR = Rørvik; WED = Wedenberg.

Figure 4

Median dose (D_50%) in the brainstem and substructures for the 3 patients. (α/β)_x = 2.1 Gy was used for the phenomenological RBE models. The medulla oblongata for the patient with glioma is not shown due to doses of 0 Gy(RBE). Abbreviations: CAR = Carabe; LWD = LET-weighted dose; MCN = McNamara; RBE = relative biological effectiveness; ROR = Rørvik; WED = Wedenberg.

Figure 5

V_50Gy(RBE) and corresponding Dice similarity coefficients in the brainstem for the 3 patients using (α/β)_x = 2.1, 2.5, and 3.3 Gy. Abbreviations: CAR = Carabe; DSC = dice similarity coefficient; MCN = McNamara; RBE = relative biological effectiveness; ROR = Rørvik; WED = Wedenberg.

Figure 6

RBE volume histograms comparing differences between (α/β)_x = 2.1, 2.5, and 3.3 Gy for the brainstem. For reference, the median LET_d and dose from RBE_1.1 in the brainstem for each patient are shown in the boxes in the bottom left corner. Abbreviations: CAR = Carabe; LET_d = dose-averaged linear energy transfer; MCN = McNamara; RBE = relative biological effectiveness; ROR = Rørvik; WED = Wedenberg.