Shinde Nimita, Li Wangyao, Chen Ronald C, Gao Hao
Department of Radiation Oncology, University of Kansas Medical Center, Kansas City, KS, United States of America.
Phys Med Biol. 2025 Jun 20;70(12). doi: 10.1088/1361-6560/ade48c.
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 proposed formulation is implemented for proton modality. The performance of our method is evaluated for varying lag times and doubling times. The results show that the mean BED to the target consistently meets the minimum requirement for tumor cell kill. Additionally, the mean BED to the OAR varies based on tumor proliferation dynamics. In the prostate case with lag time of 7 d and doubling time of 2 d, it is observed that the mean BED delivered to femoral head is lowest at approximately 20 fractions, making this an optimal choice. While in the head-and-neck case, the mean BED to the OAR decreases as the number of fractions increases, suggesting that a higher number of fractions is optimal. Thus, the proposed model effectively determines the optimal fractionation strategy under different tumor proliferation conditions.A spatiotemporal optimization model is presented that minimizes BED to the OAR while ensuring sufficient BED for tumor cell kill. By incorporating tumor lag time 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递送分次数量（时间方面）和每次分次的最佳剂量（空间方面）。传统方法侧重于在将生物等效剂量（BED）限制于危及器官（OAR）的同时，使靶区的生物等效剂量最大化，这可能导致用于完全杀死肿瘤细胞的生物等效剂量不足。这项工作提出了一种公式，可确保向靶区递送足够的生物等效剂量，同时将危及器官的生物等效剂量最小化。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用于杀死肿瘤细胞，同时将危及器官的生物等效剂量最小化。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）和倍增时间（肿瘤体积翻倍所需的时间），以优化剂量分割。所提出的公式应用于质子治疗模式。针对不同的滞后时间和倍增时间，评估了我们方法的性能。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根据肿瘤增殖动力学而变化。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次分次时，传递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次数量的增加而降低，这表明分次数量越多越佳。因此，所提出的模型有效地确定了不同肿瘤增殖条件下的最佳分割策略。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用于杀死肿瘤细胞的同时，将危及器官的生物等效剂量最小化。通过纳入肿瘤滞后时间和倍增时间，该方法确定了最佳的分次数量。该模型可以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。
