We investigate the robustness of adaptive chemotherapy schedules over repeated cycles and a wide range of tumor sizes. We introduce a non-stationary stochastic three-component fitness-dependent Moran process to quantify the variance of the response to treatment associated with multidrug adaptive schedules that are designed to mitigate chemotherapeutic resistance in an idealized (well-mixed) setting. The finite cell (N tumor cells) stochastic process consists of populations of chemosensitive cells, chemoresistant cells to drug 1, and chemoresistant cells to drug 2, and the drug interactions can be synergistic, additive, or antagonistic. First, the adaptive chemoschedule is determined by using the N → ∞ limit of the finite-cell process (i.e. the adjusted replicator equations) which is constructed by finding closed treatment response loops (which we call evolutionary cycles) in the three component phase-space. The schedules that give rise to these cycles are designed to manage chemoresistance by avoiding competitive release of the resistant cell populations. To address the question of how these cycles are likely to perform in practice over large patient populations with tumors across a range of sizes, we then consider the statistical variances associated with the approximate stochastic cycles for finite N, repeating the idealized adaptive schedule over multiple periods. For finite cell populations, the error distributions remain approximately multi-Gaussian in the principal component coordinates through the first three cycles, with variances increasing exponentially with each cycle. As the number of cycles increases, the multi-Gaussian nature of the distribution breaks down due to the fact that one of the three subpopulations typically saturates the tumor (competitive release) resulting in treatment failure. This suggests that to design an effective and repeatable adaptive chemoschedule in practice will require a highly accurate tumor model and accurate measurements of the subpopulation frequencies or the errors will quickly (exponentially) degrade its effectiveness, particularly when the drug interactions are synergistic. Possible ways to extend the efficacy of the stochastic cycles in light of the computational simulations are discussed.

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适应性化疗方案是否健全？三策略随机演化博弈模型

我们研究了重复周期和各种肿瘤大小的适应性化疗方案的鲁棒性。我们引入了一种非平稳随机三成分适应性依赖的Moran过程，以量化与多药适应性方案相关联的治疗反应的方差，这些方案旨在缓解理想化（充分混合）环境中的化疗耐药性。有限细胞（N个肿瘤细胞）随机过程由化学敏感性细胞，对药物1的化学抗性细胞和对药物2的化学抗性细胞的群体组成，并且药物相互作用可以是协同的，加性的或拮抗的。首先，通过使用有限元过程的N→∞极限来确定自适应化学调度（即 通过在三个分量相空间中找到闭合的处理响应循环（我们称为进化循环）来构建调整后的复制子方程。产生这些循环的时间表旨在通过避免耐药细胞群体的竞争性释放来管理化学耐药性。为了解决这些周期在大范围肿瘤范围内的大型患者人群中如何在实践中执行的问题，我们然后考虑与有限N的近似随机周期相关的统计方差，在多个周期内重复理想化的适应性计划。对于有限的细胞群体，在前三个周期中，误差分布在主成分坐标中保持近似高斯分布，并且每个周期的方差呈指数增长。随着周期数的增加，由于三个亚群之一通常使肿瘤饱和（竞争性释放）而导致治疗失败，因此分布的多高斯性质破裂了。这表明在实践中设计有效且可重复的适应性化学时间表将需要高度准确的肿瘤模型和亚人群频率的准确测量，否则错误将迅速（以指数方式）降低其有效性，尤其是在药物相互作用具有协同作用时。根据计算仿真，讨论了扩展随机周期功效的可能方法。由于三个亚群之一通常使肿瘤饱和（竞争性释放），导致治疗失败，因此分布的多高斯性质破裂了。这表明在实践中设计有效且可重复的适应性化学时间表将需要高度准确的肿瘤模型和亚人群频率的准确测量，否则错误将迅速（以指数方式）降低其有效性，尤其是在药物相互作用具有协同作用时。根据计算仿真，讨论了扩展随机周期功效的可能方法。由于三个亚群之一通常使肿瘤饱和（竞争性释放），导致治疗失败，因此分布的多高斯性质破裂了。这表明在实践中设计有效且可重复的适应性化学时间表将需要高度准确的肿瘤模型和亚人群频率的准确测量，否则错误将迅速（以指数方式）降低其有效性，尤其是在药物相互作用具有协同作用时。根据计算仿真，讨论了扩展随机周期功效的可能方法。这表明在实践中设计有效且可重复的适应性化学时间表将需要高度准确的肿瘤模型和亚人群频率的准确测量，否则错误将迅速（以指数方式）降低其有效性，尤其是在药物相互作用具有协同作用时。根据计算仿真，讨论了扩展随机周期功效的可能方法。这表明在实践中设计有效且可重复的适应性化学时间表将需要高度准确的肿瘤模型和亚人群频率的准确测量，否则错误将迅速（以指数方式）降低其有效性，尤其是在药物相互作用具有协同作用时。根据计算仿真，讨论了扩展随机周期功效的可能方法。