The tumor control probability (TCP) is a metric used to calculate the probability of controlling or eradicating tumors through radiotherapy. Cancer cells vary in their response to radiation, and although many factors are involved, the tumor microenvironment is a crucial one that determines radiation efficacy. The tumor microenvironment plays a significant role in cancer initiation and propagation, as well as in treatment outcome. We have developed stochastic formulations to study the impact of arbitrary microenvironmental fluctuations on TCP and extinction probability (EP), which is defined as the probability of cancer cells removal in the absence of treatment. Since the derivation of analytical solutions are not possible for complicated cases, we employ a modified Gillespie algorithm to analyze TCP and EP, considering the random variations in cellular proliferation and death rates. Our results show that increasing the standard deviation in kinetic rates initially enhances the probability of tumor eradication. However, if the EP does not reach a probability of 1, the increase in the standard deviation subsequently has a negative impact on probability of cancer cells removal, decreasing the EP over time. The greatest effect on EP has been observed when both birth and death rates are being randomly modified and are anticorrelated. In addition, similar results are observed for TCP, where radiotherapy is included, indicating that increasing the standard deviation in kinetic rates at first enhances the probability of tumor eradication. But, it has a negative impact on treatment effectiveness if the TCP does not reach a probability of 1.

肿瘤控制概率（TCP）是用于计算通过放射疗法控制或根除肿瘤的概率的度量。癌细胞对放射的反应各不相同，尽管涉及许多因素，但肿瘤微环境是决定放射功效的关键因素。肿瘤微环境在癌症的发生和扩散以及治疗结果中起着重要作用。我们已经开发了随机公式来研究任意微环境波动对TCP和灭绝概率（EP）的影响，该概率定义为在没有治疗的情况下癌细胞被清除的概率。由于在复杂情况下无法导出解析解，因此我们采用了改进的Gillespie算法来分析TCP和EP，考虑细胞增殖和死亡率的随机变化。我们的研究结果表明，增加动力学速率的标准偏差最初会增加根除肿瘤的可能性。但是，如果EP未达到1的概率，则标准偏差的增加随后会对癌细胞去除的概率产生负面影响，从而随着时间的推移而降低EP。当出生率和死亡率都被随机修改并且是反相关的时，对EP的影响最大。另外，对于包括放疗在内的TCP观察到相似的结果，表明首先增加动力学速率的标准偏差会增加根除肿瘤的可能性。但是，如果TCP未达到1的概率，则会对治疗效果产生负面影响。