Impact of respiratory motion on variable relative biological effectiveness in 4D-dose distributions of proton therapy

Organ motion during radiation therapy with scanned protons leads to deviations between the planned and the delivered physical dose. Using a constant relative biological effectiveness (RBE) of 1.1 linearly maps these deviations into RBE-weighted dose. However, a constant value cannot account for potential nonlinear variations in RBE suggested by variable RBE models. Here, we study the impact of motion on recalculations of RBE-weighted dose distributions using a phenomenological variable RBE model.

4D-dose calculation including variable RBE was implemented in the open source treatment planning toolkit matRad. Four scenarios were compared for one field and two field proton treatments for a liver cancer patient assuming (α∕β)_x = 2 Gy and (α∕β)_x = 10 Gy: (A) the optimized static dose distribution with constant RBE, (B) a static recalculation with variable RBE, (C) a 4D-dose recalculation with constant RBE and (D) a 4D-dose recalculation with variable RBE. For (B) and (D), the variable RBE was calculated by the model proposed by McNamara. For (C), the physical dose was accumulated with direct dose mapping; for (D), dose-weighted radio-sensitivity parameters of the linear quadratic model were accumulated to model synergistic irradiation effects on RBE.

Dose recalculation with variable RBE led to an elevated biological dose at the end of the proton field, while 4D-dose recalculation exhibited random deviations everywhere in the radiation field depending on the interplay of beam delivery and organ motion. For a single beam treatment assuming (α∕β)_x = 2 Gy, D_95% was 1.98 Gy (RBE) (A), 2.15 Gy (RBE) (B), 1.81 Gy (RBE) (C) and 1.98 Gy (RBE) (D). The homogeneity index was 1.04 (A), 1.08 (B), 1.23 (C) and 1.25 (D).

For the studied liver case, intrafractional motion did not reduce the modulation of the RBE-weighted dose postulated by variable RBE models for proton treatments.