在癌症治疗中，放射治疗（RT）会因DNA损伤而导致肿瘤细胞直接死亡，但它也会增加放射敏感性免疫细胞的死亡，随后导致局部复发和免疫检查点配体PD-L1的上调。由于PD-1和PD-L1之间的结合会削弱抗肿瘤免疫，因此将RT与PD-L1抑制剂（抗PD-L1）相结合是提高RT治疗效果的潜在方法。一些实验表明，与 IR 或抗 PD-L1 单一疗法相比，电离辐射 (IR) 和抗 PD-L1 联合治疗可改善肿瘤减少，从而支持了这一假设。在这项工作中，我们创建了一个简化的 ODE 模型来研究 IR 和抗 PD-L1 治疗下肿瘤生长的顺序。我们的协同分析表明，当同时给予 IR 和抗 PD-L1 时，IR 和抗 PD-L1 均可促进彼此的肿瘤缩小。单独给予IR和抗PD-L1时，应先给予高剂量的IR，以有效降低肿瘤负荷，然后再给予效力较强的抗PD-L1，以维持肿瘤缩小并减缓复发。增加抗PD-L1的持续时间可以改善肿瘤的缩小，但不能延长肿瘤复发至对照病例水平的持续时间。在一些简化下，我们还证明该模型具有不稳定的无肿瘤平衡和局部渐近稳定的肿瘤持续平衡。我们的分叉图揭示了随着肿瘤生长速率的增加，从肿瘤消除到肿瘤持续存在的转变。在肿瘤持续存在的情况下，抗PD-L1和IR都可以长期减少肿瘤数量。版权所有©2024 Elsevier Inc.保留所有权利。

In cancer treatment, radiation therapy (RT) induces direct tumor cell death due to DNA damage, but it also enhances the deaths of radiosensitive immune cells and is followed by local relapse and up-regulation of immune checkpoint ligand PD-L1. Since the binding between PD-1 and PD-L1 curtails anti-tumor immunities, combining RT and PD-L1 inhibitor, anti-PD-L1, is a potential method to improve the treatment efficacy by RT. Some experiments support this hypothesis by showing that the combination of ionizing irradiation (IR) and anti-PD-L1 improves tumor reduction comparing to the monotherapy of IR or anti-PD-L1. In this work, we create a simplified ODE model to study the order of tumor growths under treatments of IR and anti-PD-L1. Our synergy analysis indicates that both IR and anti-PD-L1 improve the tumor reduction of each other, when IR and anti-PD-L1 are given simultaneously. When giving IR and anti-PD-L1 separately, a high dosage of IR should be given first to efficiently reduce tumor load and then followed by anti-PD-L1 with strong efficacy to maintain the tumor reduction and slow down the relapse. Increasing the duration of anti-PD-L1 improves the tumor reduction, but it cannot prolong the duration that tumor relapses to the level of the control case. Under some simplification, we also prove that the model has an unstable tumor free equilibrium and a locally asymptotically stable tumor persistent equilibrium. Our bifurcation diagram reveals a transition from tumor elimination to tumor persistence, as the tumor growth rate increases. In the tumor persistent case, both anti-PD-L1 and IR can reduce tumor amount in the long term.Copyright © 2024 Elsevier Inc. All rights reserved.