肿瘤生长的平均场动力学和使用低影响化学预防的控制
Mean-field dynamics of tumor growth and control using low-impact chemoprevention
摘要：
癌症由于其不受控制的生长、抗性亚克隆的发展以及转移性扩散到重要器官而构成危险。虽然癌症发展中的主要转变越来越好地理解，我们缺乏定量理论如何预测化学预防影响生存。我们采用主方程和概率生成函数，后者在统计物理学中是众所周知的，推导出肿瘤生长的动力学平均场近似。我们还数值研究了相关的随机生灭过程。我们的研究结果预测，当癌症处于发展的早期阶段时，肿瘤会呈指数增长，此后会呈超指数增长。数值模拟结果与我们的分析方法基本一致。我们评估了恒定的低影响治疗如何影响肿瘤生长和耐药克隆的频率。我们表明，治疗结果是高度可预测的治疗开始足够早或晚的初始肿瘤大小和初始数量的化疗耐药细胞，而随机动力学占主导地位的治疗开始在中间肿瘤大小，具有高的结果敏感性，无论是在肿瘤控制和耐药亚克隆的出现。化学预防的结果可以理解为最小的生理影响，导致长期控制和防止或减缓耐药亚克隆的出现。我们认为，我们的模型和结果也可以应用于肿瘤切除后的早期临床检测癌症的管理。
英文摘要：
Cancer poses danger because of its unregulated growth, development of resistant subclones, and metastatic spread to vital organs. Although the major transitions in cancer development are increasingly well understood, we lack quantitative theory for how chemoprevention is predicted to affect survival. We employ master equations and probability generating functions, the latter well known in statistical physics, to derive the dynamics of tumor growth as a mean-field approximation. We also study numerically the associated stochastic birth-death process. Our findings predict exponential tumor growth when a cancer is in its early stages of development and hyper-exponential growth thereafter. Numerical simulations are in general agreement with our analytical approach. We evaluate how constant, low impact treatments affect both neoplastic growth and the frequency of chemoresistant clones. We show that therapeutic outcomes are highly predictable for treatments starting either sufficiently early or late in terms of initial tumor size and the initial number of chemoresistant cells, whereas stochastic dynamics dominate therapies starting at intermediate neoplasm sizes, with high outcome sensitivity both in terms of tumor control and the emergence of resistant subclones. The outcome of chemoprevention can be understood in terms of both minimal physiological impacts resulting in long-term control and either preventing or slowing the emergence of resistant subclones. We argue that our model and results can also be applied to the management of early, clinically detected cancers after tumor excision.
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