基于免疫激活动力学的放疗与免疫治疗联合的放疗时机最优控制模型与仿真分析

Optimal Control Model and Simulation Analysis of Radiotherapy Timing for the Combination of Radiotherapy and Immunotherapy Based on Immune Activation Kinetics

摘要: 放疗与免疫治疗联合应用在肿瘤控制中表现出协同效应，而放疗时机是决定疗效的关键因素。本文基于放疗与免疫治疗协同作用的肿瘤动力学模型，构建以肿瘤总体积最小化和生存时间最大化为目标的两个最优控制模型，定量分析了首次放疗时间与分次放疗间隔对治疗效果的影响。数值结果表明，尽早启动首次放疗并最大限度缩短分割间隔可显著提升联合治疗的整体疗效；此外，敏感性分析结果表明，首次放疗时间对肿瘤控制的影响显著高于分割时间间隔。

Abstract: The combined application of radiotherapy and immunotherapy shows a synergistic effect in tumor control, and the timing of radiotherapy is a key factor determining the therapeutic efficacy. Based on the tumor dynamics model of the synergistic effect of radiotherapy and immunotherapy, this paper constructs two optimal control models with the goals of minimizing the total tumor volume and maximizing the survival time. We quantitatively analyze the influence of the start time of the first fraction and the interval between fractions on the treatment effect. The numerical results show that initiating the first fraction as early as possible and minimizing the interfraction interval can significantly improve the overall efficacy of the combined treatment. Moreover, the sensitivity analysis results indicate that the impact of the start time of the first fraction on tumor control is significantly higher than that of the interfraction interval.