The tumour control probability (TCP) is the probability that a treatment regimen of radiation therapy (RT) eradicates all tumour cells in a given tissue. To decrease the toxic effects on healthy cells, RT is usually delivered over a period of weeks in a series of fractions. This allows tumour cells to repair sublethal damage (RSD) caused by radiation. In this article, we introduce a stochastic model for tumour response to radiotherapy which accounts for the effects of RSD. The tumour is subdivided into two cell types: 'affected' cells which have been damaged by RT and 'unaffected' cells which have not. The model is formulated as a birth-death process for which we can derive an explicit formula for the TCP. We apply our model to prostate cancer, and find that the radiosensitivity parameters and the probability of sublethal damage during radiation are the parameters to which the TCP predictions are most sensitive. We compare our TCP predictions to those given by Zaider and Minerbo's one-class model (Zaider & Minerbo, 2000) and Dawson and Hillen's two-class model (Dawson & Hillen, 2006) and find that for low doses of radiation, our model predicts a lower TCP. Finally, we find that when the probability of sublethal damage during radiation is large, the mean field assumption overestimates the TCP.

中文翻译：

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肿瘤控制概率的随机模型，说明了亚致死性损伤的修复。

肿瘤控制概率（TCP）是放射疗法（RT）的治疗方案根除给定组织中所有肿瘤细胞的概率。为了减少对健康细胞的毒性作用，RT通常以一系列的成分在数周的时间内递送。这允许肿瘤细胞修复由辐射引起的亚致死损伤（RSD）。在本文中，我们介绍了肿瘤对放疗反应的随机模型，该模型解释了RSD的影响。肿瘤可分为两种细胞类型：被RT损伤的“受影响”细胞和尚未受到RT损伤的“未受影响”细胞。该模型被公式化为出生-死亡过程，为此我们可以为TCP导出一个明确的公式。我们将模型应用于前列腺癌，并发现辐射敏感性参数和辐射过程中亚致死性损坏的概率是TCP预测最敏感的参数。我们将TCP预测与Zaider和Minerbo的一类模型（Zaider＆Minerbo，2000）以及Dawson和Hillen的两类模型（Dawson＆Hillen，2006）所给出的预测值进行比较，发现对于低剂量的辐射，我们的模型可以预测较低的TCP。最后，我们发现，当辐射过程中发生亚致死力的可能性很大时，平均场假设会高估TCP。（2006年），发现对于低剂量的辐射，我们的模型预测出较低的TCP。最后，我们发现，当辐射过程中发生亚致死力的可能性很大时，平均场假设会高估TCP。（2006年），发现对于低剂量的辐射，我们的模型预测出较低的TCP。最后，我们发现，当辐射过程中发生亚致死力的可能性很大时，平均场假设会高估TCP。