虽然放疗长期以来因其通过坏死或凋亡直接消融癌细胞的能力而被认可，但放疗引起的远隔效应表明，由于免疫反应，其影响超出了局部肿瘤破坏的范围。人们使用模拟肿瘤生长的数学模型（例如 Gompertz 定律）和辐射效应（例如线性二次模型）对细胞增殖和坏死进行了广泛的研究。然而，由于放射敏感性和其他因素的个体差异，放疗诱导的免疫反应的有效性可能因患者而异。我们提出了一种新颖的宏观方法，旨在定量分析控制免疫系统、放疗和肿瘤之间相互作用的复杂动态。进展。基于先前证明放射治疗和免疫治疗在癌症治疗中的协同效应的研究，我们提供了一个全面的数学框架来理解驱动这些相互作用的潜在机制。我们的方法利用宏观观察和数学建模来捕捉这种相互作用的总体动态，提供有价值的信息优化癌症治疗策略的见解。其中一项表明，冈珀兹定律可以用两个有效参数来描述治疗效果。这一结果允许进行定量数据分析，为疾病进展和临床决策提供有用的指示。通过对文献中的不同数据集进行验证，我们证明了我们的方法在预测疾病的时间演变和评估潜力方面的可靠性和多功能性放射治疗-免疫治疗联合治疗的疗效。这进一步支持了远隔效应的巨大潜力，表明在特定病例中，根据肿瘤大小，它可能会赋予放射治疗完全疗效。版权所有 © 2024 Castorina、Castiglione、Ferini、Forte、Martorana 和 Giuffrida。

While radiotherapy has long been recognized for its ability to directly ablate cancer cells through necrosis or apoptosis, radiotherapy-induced abscopal effect suggests that its impact extends beyond local tumor destruction thanks to immune response. Cellular proliferation and necrosis have been extensively studied using mathematical models that simulate tumor growth, such as Gompertz law, and the radiation effects, such as the linear-quadratic model. However, the effectiveness of radiotherapy-induced immune responses may vary among patients due to individual differences in radiation sensitivity and other factors.We present a novel macroscopic approach designed to quantitatively analyze the intricate dynamics governing the interactions among the immune system, radiotherapy, and tumor progression. Building upon previous research demonstrating the synergistic effects of radiotherapy and immunotherapy in cancer treatment, we provide a comprehensive mathematical framework for understanding the underlying mechanisms driving these interactions.Our method leverages macroscopic observations and mathematical modeling to capture the overarching dynamics of this interplay, offering valuable insights for optimizing cancer treatment strategies. One shows that Gompertz law can describe therapy effects with two effective parameters. This result permits quantitative data analyses, which give useful indications for the disease progression and clinical decisions.Through validation against diverse data sets from the literature, we demonstrate the reliability and versatility of our approach in predicting the time evolution of the disease and assessing the potential efficacy of radiotherapy-immunotherapy combinations. This further supports the promising potential of the abscopal effect, suggesting that in select cases, depending on tumor size, it may confer full efficacy to radiotherapy.Copyright © 2024 Castorina, Castiglione, Ferini, Forte, Martorana and Giuffrida.