In the past few years, proton therapy has taken the centre stage in treating various tumour types. The primary contribution of this study is to investigate the tumour control probability (TCP), relapse time and the corresponding secondary cancer risks induced by proton beam radiation therapy. We incorporate tumour relapse kinetics into the TCP framework and calculate the associated second cancer risks. To calculate proton therapy-induced secondary cancer induction, we used the well-known biologically motivated mathematical model, initiation-inactivation-proliferation formalism. We used the available in vitro data for the linear energy transfer (LET) dependence of cell killing and mutation induction parameters. We evaluated the TCP and radiation-induced second cancer risks for protons in the clinical range of LETs, i.e. approximately 8 $\mathrm{keV/\mu m}$ for the tumour volume and 1-3 $\mathrm{keV/\mu m}$ for the organs at risk. This study may serve as a framework for further work in this field and elucidates proton-induced TCP and the associated secondary cancer risks, not previously reported in the literature. Although studies with a greater number of cell lines would reduce uncertainties within the model parameters, we argue that the theoretical framework presented within is a sufficient rationale to assess proton radiation TCP, relapse and carcinogenic effects in various treatment plans. We show that compared with photon therapy, proton therapy markedly reduces the risk of secondary malignancies and for equivalent dosing regimens achieves better tumour control as well as a reduced primary recurrence outcome, especially within a hypo-fractionated regimen.

中文翻译：

---

模拟质子治疗引起的复发和二次癌症风险。

在过去的几年中，质子治疗已成为治疗各种肿瘤类型的中心舞台。本研究的主要贡献是研究质子束放射治疗诱发的肿瘤控制概率（TCP）、复发时间以及相应的继发癌症风险。我们将肿瘤复发动力学纳入 TCP 框架并计算相关的第二次癌症风险。为了计算质子治疗引起的继发性癌症诱导，我们使用了著名的生物动机数学模型，即起始-失活-增殖形式主义。我们使用现有的体外数据来了解细胞杀伤和突变诱导参数的线性能量转移（LET）依赖性。我们评估了 LET 临床范围内质子的 TCP 和辐射诱发的第二次癌症风险，即肿瘤体积约为 8 $\mathrm{keV/\mu m}$ 和 1-3 $\mathrm{keV/\mu m}$ 对于处于危险中的器官。这项研究可以作为该领域进一步工作的框架，并阐明质子诱导的 TCP 和相关的继发性癌症风险，这是以前文献中未报道的。尽管使用更多细胞系的研究会减少模型参数内的不确定性，但我们认为其中提出的理论框架是评估质子辐射 TCP、各种治疗计划中的复发和致癌作用的充分理由。我们发现，与光子疗法相比，质子疗法显着降低了继发性恶性肿瘤的风险，并且在同等剂量方案下，可以实现更好的肿瘤控制并减少原发性复发结果，特别是在大分割方案中。