Abstract Based on tumor radiobiologic mechanisms, this paper develops a new tumor growth dynamic model with radiotherapy. It investigates how the reoxygenation of hypoxic cells and the radiosensitivity of radiotherpy influence the effect of tumor radiotherapy. The existence of the positive periodic solution, the asymptotic stabilities of the tumor-free equilibrium and the hypoxic tumor cell-free periodic solution and the corresponding sufficient criteria are obtained in this paper. The theoretical results indicate that when the value of the sensitivity coefficient of radiotherapy becomes bigger and the reoxygenation rate of tumor cells becomes higher, the radiotherapy of tumor is more effective. In addition, we apply our model to simulate the volumetric imaging data from 12 available head-and-neck cancer patients treated with an integrated computed tomography/linear accelerator system and obtain a very good fitting effect. Finally, we apply patient specific parameters obtained by simulating clinical data of 12 tumor cases to investigate their individual similarities and differences, so that we can provide some guidance for medical workers to implement personalized treatment strategies for tumor patients.

中文翻译：

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放疗过程中肿瘤体积变化的数学建模与分析

摘要 基于肿瘤放射生物学机制，本文建立了一种新的肿瘤生长动态模型与放射治疗。它研究了缺氧细胞的复氧和放疗的放射敏感性如何影响肿瘤放疗的效果。本文得到了正周期解的存在性、无瘤平衡和缺氧无瘤细胞周期解的渐近稳定性以及相应的充分准则。理论结果表明，放疗敏感性系数越大，肿瘤细胞复氧率越高，肿瘤放疗效果越好。此外，我们应用我们的模型来模拟来自 12 个可用的头颈部癌症患者的体积成像数据，这些患者接受了集成的计算机断层扫描/直线加速器系统，并获得了非常好的拟合效果。最后，我们应用通过模拟12例肿瘤病例的临床数据获得的患者特异性参数来研究它们个体的异同，以便为医务工作者实施肿瘤患者的个性化治疗策略提供一些指导。