论文标题
诺顿西蒙模型的肿瘤遏制
Tumor containment for Norton-Simon models
论文作者
论文摘要
一些临床和临床前数据表明，以轻度，患者特异性剂量治疗某些肿瘤可能会延迟对治疗的抵抗力并增加生存时间。一个具有敏感和抗性肿瘤细胞的最近数学模型确定了针对肿瘤遏制而不是根除的治疗的条件确实是最佳的。然而，该模型从敏感细胞到抗性细胞忽略了突变，并假设敏感细胞的生长速率在耐药种群的大小中不侵入。后者在化学疗法的标准模型中并非如此。本文展示了如何分配此假设，并允许从敏感细胞到抗性细胞进行突变。这是通过一种新的数学分析来实现的，该数学分析比较了跨时间的肿瘤大小，而不是时间的函数，而是抗药性种群大小的函数。
Some clinical and pre-clinical data suggests that treating some tumors at a mild, patient-specific dose might delay resistance to treatment and increase survival time. A recent mathematical model with sensitive and resistant tumor cells identified conditions under which a treatment aiming at tumor containment rather than eradication is indeed optimal. This model however neglected mutations from sensitive to resistant cells, and assumed that the growth-rate of sensitive cells is non-increasing in the size of the resistant population. The latter is not true in standard models of chemotherapy. This article shows how to dispense with this assumption and allow for mutations from sensitive to resistant cells. This is achieved by a novel mathematical analysis comparing tumor sizes across treatments not as a function of time, but as a function of the resistant population size.
