Shinde Nimita, Li Wangyao, Chen Ronald C, Gao Hao
ArXiv. 2025 Sep 5:arXiv:2502.16333v2.
Spatiotemporal optimization in radiation therapy involves determining the optimal number of dose delivery fractions (temporal) and the optimal dose per fraction (spatial). Traditional approaches focus on maximizing the biologically effective dose (BED) to the target while constraining BED to organs-at-risk (OAR), which may lead to insufficient BED for complete tumor cell kill. This work proposes a formulation that ensures adequate BED delivery to the target while minimizing BED to the OAR.
A spatiotemporal optimization model is developed that incorporates an inequality constraint to guarantee sufficient BED for tumor cell kill while minimizing BED to the OAR. The model accounts for tumor proliferation dynamics, including lag time (delay before proliferation begins) and doubling time (time for tumor volume to double), to optimize dose fractionation.
The performance of our formulation is evaluated for varying lag and doubling times. The results show that mean BED to the target consistently meets the minimum requirement for tumor cell kill. Additionally, the mean BED to OAR varies based on tumor proliferation dynamics. In the prostate case with lag time of 7 days and doubling time of 2 days, it is observed that mean BED delivered to femoral head is lowest at around 20 fractions, making this an optimal choice. While in the head-and-neck case, mean BED to OAR decreases as the number of fractions increases, suggesting that a higher number of fractions is optimal.
A spatiotemporal optimization model is presented that minimizes BED to the OAR while ensuring sufficient BED for tumor cell kill. By incorporating tumor lag and doubling time, the approach identifies optimal number of fractions. This model can be extended to support hyperfractionation or accelerated fractionation strategies, offering a versatile tool for clinical treatment planning.
放射治疗中的时空优化涉及确定最佳的剂量分割次数（时间方面）和每次分割的最佳剂量（空间方面）。传统方法侧重于在将危及器官（OAR）的生物等效剂量（BED）限制在一定范围内的同时，使靶区的生物等效剂量最大化，这可能导致无法给予足够的生物等效剂量来完全杀死肿瘤细胞。本研究提出一种公式，可确保向靶区输送足够的生物等效剂量，同时将危及器官的生物等效剂量降至最低。
开发了一种时空优化模型，该模型纳入了一个不等式约束，以保证有足够的生物等效剂量来杀死肿瘤细胞，同时将危及器官的生物等效剂量降至最低。该模型考虑了肿瘤增殖动力学，包括滞后时间（增殖开始前的延迟时间）和倍增时间（肿瘤体积翻倍所需的时间），以优化剂量分割。
针对不同的滞后时间和倍增时间，对我们提出的公式的性能进行了评估。结果表明，靶区的平均生物等效剂量始终满足杀死肿瘤细胞的最低要求。此外，危及器官的平均生物等效剂量会因肿瘤增殖动力学而有所不同。在滞后时间为7天、倍增时间为2天的前列腺病例中，观察到在大约20次分割时，输送到股骨头的平均生物等效剂量最低，这使其成为最佳选择。而在头颈部病例中，危及器官的平均生物等效剂量随着分割次数的增加而降低，这表明分割次数越多越佳。
提出了一种时空优化模型，该模型在确保有足够的生物等效剂量来杀死肿瘤细胞的同时，将危及器官的生物等效剂量降至最低。通过纳入肿瘤滞后时间和倍增时间，该方法可确定最佳的分割次数。此模型可扩展以支持超分割或加速分割策略，为临床治疗计划提供了一种通用工具。
