The tumour control probability (TCP) is a treatment planning tool that evaluates the probability of tumour eradication and helps in the assessment of the relative efficacy of different radiotherapy regimens. The response of tumours to radiation differs greatly even between patients with same types of cancers. Tumour heterogeneity or cellular diversity among cancer cells has a pronounced impact on the success of administered radiotherapy protocols. Tumour heterogeneity can be explained using the cancer stem cells (CSCs) hypothesis, which posits that CSCs are responsible for tumour initiation and propagation as well as therapeutic resistance. Moreover, the existence of plasticity or bidirectional transition between CSCs and non-CSCs indicates that, sometimes, non-CSCs appear to mimic CSC phenotypes, resulting in an increase in resistance. Here, we have developed a stochastic model to investigate the impact of plasticity on the efficacy of radiotherapy. The effect of plasticity on TCP is explored by applying the model to standard and hyper-fractionated schedules for a three week period of treatment as well as standard, hyper-fractionated, and accelerated hyper-fractionated schedules with an equal total dose of 30 Gy. Our results confirm that tumour control becomes increasingly difficult in the presence of plasticity as well as for the most resistant tumours. For the case with equal total dose, it is observed that increasing fractionation, at first enhances the probability of CSCs and tumour removal, but ultimately results in lower TCP_S+P and TCP_S. In addition, the combination of radiotherapy and targeted therapy (with increasing CSC differentiation) improves both the probability of CSC and tumour removal, in the absence of plasticity. However, in the presence of plasticity, the impact of combination therapy is not significant.

中文翻译：

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细胞可塑性对肿瘤控制概率影响的数学研究

肿瘤控制概率（TCP）是一种治疗计划工具，可评估肿瘤根除的可能性，并有助于评估不同放疗方案的相对疗效。即使在患有相同类型癌症的患者之间，肿瘤对放射线的反应也有很大差异。癌细胞之间的肿瘤异质性或细胞多样性对放射治疗方案的成功有显着影响。肿瘤异质性可以用癌症干细胞（CSCs）假说来解释，该假说认为CSCs负责肿瘤的起始和繁殖以及治疗抗性。此外，CSC和非CSC之间存在可塑性或双向过渡，这表明有时非CSC似乎模仿CSC表型，导致耐药性增加。这里，我们已经开发了一个随机模型来研究可塑性对放疗效果的影响。通过将模型应用于治疗三周的标准和超细分时间表以及总剂量等于30 Gy的标准，超细分和加速超细分时间表，探索了可塑性对TCP的影响。我们的结果证实，在存在可塑性以及对最具抵抗力的肿瘤的情况下，控制肿瘤变得越来越困难。对于总剂量相等的情况，观察到分级分离的增加首先会提高CSC和肿瘤切除的可能性，但最终会降低TCP 通过将模型应用于治疗三周的标准和超细分时间表以及总剂量等于30 Gy的标准，超细分和加速超细分时间表，探索了可塑性对TCP的影响。我们的结果证实，在存在可塑性以及对最具抵抗力的肿瘤的情况下，控制肿瘤变得越来越困难。对于总剂量相等的情况，观察到分级分离的增加首先会提高CSC和肿瘤切除的可能性，但最终会导致TCP降低 通过将模型应用于治疗三周的标准和超细分时间表以及总剂量等于30 Gy的标准，超细分和加速超细分时间表，探索了可塑性对TCP的影响。我们的结果证实，在存在可塑性以及对最具抵抗力的肿瘤的情况下，控制肿瘤变得越来越困难。对于总剂量相等的情况，观察到分级分离的增加首先会提高CSC和肿瘤切除的可能性，但最终会导致TCP降低 我们的结果证实，在存在可塑性以及对最具抵抗力的肿瘤的情况下，控制肿瘤变得越来越困难。对于总剂量相等的情况，观察到分级分离的增加首先会提高CSC和肿瘤切除的可能性，但最终会导致TCP降低 我们的结果证实，在存在可塑性以及对最具抵抗力的肿瘤的情况下，控制肿瘤变得越来越困难。对于总剂量相等的情况，观察到分级分离的增加首先会提高CSC和肿瘤切除的可能性，但最终会导致TCP降低_{S + P}和TCP_小号。另外，放射疗法和靶向疗法的结合（随着CSC分化的增加）在没有可塑性的情况下提高了CSC和肿瘤切除的可能性。但是，在存在可塑性的情况下，联合治疗的影响并不明显。