碳离子治疗计划中的RBE加权剂量鲁棒优化方法

提出基于混合束模型的相对生物学效应(RBE)加权剂量鲁棒优化方法，用于减少碳离子束射程和摆位偏差对生物剂量分布的影响。建立概率组合鲁棒优化模型，利用二次型目标函数表达式，分别制定针对物理吸收剂量和RBE加权剂量的碳离子束治疗计划，并基于共轭梯度优化算法求解出各自最优的权重解，使得靶区和危及器官(OAR)实际剂量分布在射程和摆位偏差组合情况下尽量满足剂量要求。采用C型靶模型测试鲁棒优化方法的有效性。与基于计划靶区(PTV)的常规优化方法相比，针对物理吸收剂量的鲁棒优化计划临床靶区(CTV)的$ \Delta {D}_{95{\text{%}} } $减少10.00 cGy，OAR的$ \Delta {D}_{5{\text{%}} } $和$ \Delta {D}_{\mathrm{m}\mathrm{a}\mathrm{x}} $分别减少21.50和35.97 cGy，计划的鲁棒性得到了很好的提升。针对RBE加权剂量的鲁棒优化计划CTV的$ \Delta {D}_{95{\text{%}} } $降低14.00 cGy(RBE)，OAR的$ \Delta {D}_{5{\text{%}} } $和$ \Delta {D}_{\mathrm{m}\mathrm{a}\mathrm{x}} $分别减少19.00和26.28 cGy(RBE)，说明该方法不仅减少了CTV的生物剂量变化，也减少了OAR的生物剂量热点。该结果证明了基于混合束模型的RBE加权剂量鲁棒优化方法在有效提高碳离子放疗计划鲁棒性的同时使OAR也得到了很好的保护。

Robust Optimization Method for RBE-weighted Dose in Carbon-ion Treatment Planning

A robust optimization method for computing RBE-weighted dose based on the mixed beam model is proposed to reduce the influence of range and setup uncertainties on dose distribution in carbon-ion radiotherapy. Firstly, a probabilistic robust model was established and the objective function was expressed using the quadratic function. Then two treatment plans were designed regarding to physical absorbed dose and RBE-weighted dose. Finally, the conjugate gradient method was adopted to find the respective optimal solutions so as to make the actual dose distribution across the target volume and organ at risk(OAR) meet the dose requirements as much as possible. The C-shaped model was utilized to evaluate the effectiveness of this method. Compared with the conventional dose optimization method based on the planning target volume(PTV), the robust treatment planning based on physical absorbed dose made $ \Delta {D}_{95{\text{%}} } $ reduce 10.0 cGy in the clinical target volume(CTV), and the $\Delta {{D}}_{5\mathrm{{\text{%}} }}$ and $\Delta {{D}}_{\mathrm{m}\mathrm{a}\mathrm{x}}$ parameters of the OAR decreased by 21.50 and 35.97 cGy respectively, indicating that the robustness of the plans has been greatly improved. Besides, the robust treatment planning based on RBE-weighted dose showed that $ \Delta {D}_{95{\text{%}} } $ reduced by 14.00 cGy(RBE) in the CTV while $ \Delta {D}_{5{\text{%}} }\mathrm{a}\mathrm{n}\mathrm{d}\mathrm{?}\Delta {D}_{\rm max} $ in the OAR reduced by 19.00 and 26.28 cGy(RBE), respectively. These results illustrate that the robust optimization method not only reduced the variation of biological dose in the CTV, but also reduced the hot spots of biological dose in the OAR. Collectively, the robust optimization method for RBE-weighted dose based on the mixed beam model could effectively enhance the robustness of carbon-ion radiotherapy treatment planning while sparing OAR simultaneously.