Department of Mathematics, North Carolina State University, Raleigh, NC, 27695-8205, USA.
Department of Radiation Oncology, University Hospital Zürich, Zürich, CH, 8091, Switzerland.
Med Phys. 2019 Jul;46(7):2988-3000. doi: 10.1002/mp.13593. Epub 2019 Jun 7.
Spatiotemporal fractionation schemes for photon radiotherapy have recently arisen as a promising technique for healthy tissue sparing. Because spatiotemporally fractionated treatments have a characteristic pattern of delivering high doses to different parts of the tumor in each fraction, uncertainty in patient positioning is an even more pressing concern than in conventional uniform fractionation. Until now, such concerns in patient setup uncertainty have not been addressed in the context of spatiotemporal fractionation.
A stochastic optimization model is used to incorporate patient setup uncertainty to optimize spatiotemporally fractionated plans using expected penalties for deviations from prescription values. First, a robust uniform reference plan is optimized with a stochastic optimization model. Then, a spatiotemporal plan is optimized with a constrained stochastic optimization model that minimizes a primary clinical objective and constrains the spatiotemporal plan to be at least as good as the uniform reference plan with respect to all other objectives. A discrete probability distribution is defined to characterize the random setup error occurring in each fraction. For the optimization of uniform plans, the expected penalties are computed exactly by exploiting the symmetry of the fractions, and for the spatiotemporal plans, quasi-Monte Carlo sampling is used to approximate the expectation.
Using five clinical liver cases, it is demonstrated that spatiotemporally fractionated treatment plans maintain the same robust tumor coverage as a stochastic uniform reference plan and exhibit a reduction in the expected mean BED of the uninvolved liver. This is observed for a spectrum of probability distributions of random setup errors with shifts in the patient position of up to 5 mm from the nominal position. For probability distributions with small variance in the patient position, the spatiotemporal plans exhibit an 8-30% reduction in expected mean BED in the healthy liver tissue for shifts up to 2.5 mm and reductions of 5-25% for shifts up to 5 mm.
In the presence of patient setup uncertainty, spatiotemporally fractionated treatment plans exhibit the same robust tumor coverage as their uniformly fractionated counterparts and still retain the benefit in sparing healthy tissues.
光子放射治疗的时空分割方案最近作为一种有前途的健康组织保护技术而出现。由于时空分割治疗在每一分片中都具有向肿瘤的不同部位输送高剂量的特征模式，因此患者定位的不确定性比传统的均匀分割更为紧迫。到目前为止，时空分割中尚未解决患者设置不确定性的问题。
使用随机优化模型来合并患者设置不确定性，以使用对偏离处方值的偏差的预期惩罚来优化时空分割计划。首先，使用随机优化模型优化稳健的均匀参考计划。然后，使用约束随机优化模型优化时空计划，该模型最小化主要临床目标，并限制时空计划在所有其他目标上至少与均匀参考计划一样好。定义离散概率分布来描述在每个分数中发生的随机设置误差。对于均匀计划的优化，通过利用分数的对称性，可以精确计算预期的惩罚，而对于时空计划，则使用准蒙特卡罗采样来近似期望。
使用五个临床肝脏病例，证明时空分割治疗计划保持与随机均匀参考计划相同的稳健肿瘤覆盖，并表现出未受影响的肝脏的预期平均 BED 的降低。这在患者位置从名义位置偏移高达 5mm 的随机设置误差概率分布范围内观察到。对于患者位置方差较小的概率分布，时空计划在未受影响的肝脏组织中表现出预期平均 BED 的 8-30%降低，对于高达 2.5mm 的偏移量降低 5-25%。
在存在患者设置不确定性的情况下，时空分割治疗计划与均匀分割的治疗计划具有相同的稳健肿瘤覆盖范围，并且仍然保留了保护健康组织的益处。
