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

<b>Background:</b> 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. <b>Material and methods:</b> 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 (<i>α</i>∕<i>β</i>)<i>_x</i> = 2 Gy and (<i>α</i>∕<i>β</i>)<i>_x</i> = 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. <b>Results:</b> 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 (<i>α</i>∕<i>β</i>)<i>_x</i> = 2 Gy, D₉₅<i>_%</i> 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). <b>Conclusion:</b> 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.

<b>背景：</b> 采用扫描质子进行放射治疗时，器官运动会导致计划物理剂量与实际递送物理剂量之间出现偏差。当使用固定值1.1的相对生物效应（relative biological effectiveness, RBE）时，会将这些偏差线性映射为相对生物效应加权剂量。然而，可变RBE模型所提示的RBE潜在非线性变化，无法通过固定RBE值进行解释。本研究采用现象学可变RBE模型，探究运动对RBE加权剂量分布重计算的影响。
<b>材料与方法：</b> 本研究在开源治疗计划工具包matRad中实现了包含可变RBE的四维剂量计算。针对1野和2野质子治疗的肝癌患者，设定(α/β)_x=2 Gy及(α/β)_x=10 Gy两种情况，对比以下4种场景：(A) 采用固定RBE的优化静态剂量分布；(B) 采用可变RBE的静态重计算；(C) 采用固定RBE的四维剂量重计算；(D) 采用可变RBE的四维剂量重计算。其中场景B与D的可变RBE通过McNamara提出的模型计算得到。场景C采用直接剂量映射法累积物理剂量；场景D则通过累积线性二次模型的剂量加权放射敏感性参数，以建模RBE的协同辐射效应。
<b>结果：</b> 采用可变RBE的剂量重计算会导致质子射野末端的生物剂量升高；而四维剂量重计算则因射束递送与器官运动的相互作用，在辐射野内各处出现随机偏差。针对(α/β)_x=2 Gy的单射束治疗场景，D95%分别为：(A)1.98 Gy(RBE)、(B)2.15 Gy(RBE)、(C)1.81 Gy(RBE)、(D)1.98 Gy(RBE)；均匀性指数分别为：(A)1.04、(B)1.08、(C)1.23、(D)1.25。
<b>结论：</b> 针对本研究中的肝癌病例，分次内运动并未降低质子治疗中可变RBE模型所预测的RBE加权剂量调制效应。