BACKGROUND The mathematical design of optimal therapies to fight cancer is an important research field in today's Biomathematics and Biomedicine given its relevance to formulate patient-specific treatments. Until now, however, cancer optimal therapies have considered that malignancy exclusively depends on the drug concentration and the number of cancer cells, ignoring that the faster the cancer grows the worse the cancer is, and that early drug doses are more prejudicial. Here, we analyze how optimal therapies are affected when the time evolution of treated cancer is envisaged as an additional element determining malignancy, analyzing in detail the implications for imatinib-treated Chronic Myeloid Leukemia. METHODS Taking as reference a mathematical model describing Chronic Myeloid Leukemia dynamics, we design an optimal therapy problem by modifying the usual malignancy objective function, unaware of any temporal dimension of cancer malignance. In particular, we introduce a time valuation factor capturing the increase of malignancy associated to the quick development of the disease and the persistent negative effects of initial drug doses. After assigning values to the parameters involved, we solve and simulate the model with and without the new time valuation factor, comparing the results for the drug doses and the evolution of the disease. RESULTS Our computational simulations unequivocally show that the consideration of a time valuation factor capturing the higher malignancy associated with early growth of cancer and drug administration allows more efficient therapies to be designed. More specifically, when this time valuation factor is incorporated into the objective function, the optimal drug doses are lower, and do not involve medically relevant increases in the number of cancer cells or in the disease duration. CONCLUSIONS In the light of our simulations and as biomedical evidence strongly suggests, the existence of a time valuation factor affecting malignancy in treated cancer cannot be ignored when designing cancer optimal therapies. Indeed, the consideration of a time valuation factor modulating malignancy results in significant gains of efficiency in the optimal therapy with relevant implications from the biomedical perspective, specially when designing patient-specific treatments.

中文翻译：

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时间评估在癌症最佳疗法中的作用：慢性粒细胞白血病的研究。

背景技术鉴于抗癌的最佳疗法的数学设计与制定针对患者的特定疗法有关，因此是当今生物数学和生物医学的重要研究领域。然而，迄今为止，癌症最佳疗法一直认为恶性肿瘤仅取决于药物浓度和癌细胞数量，而忽略了癌症生长越快越不利于癌症，并且早期药物剂量更具偏见。在这里，我们分析了当治疗的癌症的时间演变被视为决定恶性肿瘤的另一个因素时，最佳疗法如何受到影响，并详细分析了对伊马替尼治疗的慢性粒细胞白血病的影响。方法以描述慢性粒细胞白血病动力学的数学模型作为参考，我们通过修改通常的恶性目标函数来设计最佳治疗问题，而无需意识到癌症恶性的任何时间尺度。特别是，我们引入了一个时间评估因子，以捕获与疾病的快速发展相关的恶性肿瘤的增加以及初始药物剂量的持续负面影响。在为相关参数分配值之后，我们在有和没有新的时间评估因子的情况下对模型进行求解和仿真，比较药物剂量和疾病演变的结果。结果我们的计算仿真明确表明，考虑到时间价值评估因素，可以捕获与癌症早期生长和药物给药相关的更高恶性肿瘤，因此可以设计出更有效的治疗方法。进一步来说，当将此时间评估因素纳入目标函数时，最佳药物剂量较低，并且不涉及癌细胞数量或疾病持续时间的医学相关增加。结论根据我们的模拟以及生物医学证据的强烈暗示，在设计癌症最佳疗法时，不能忽略影响治疗癌症恶性程度的时间评估因素。确实，考虑到时间因素调节恶性肿瘤，可以从生物医学的角度，特别是在设计针对患者的治疗方法时，在最佳治疗中显着提高治疗效率，并具有相关的意义。并且不涉及癌细胞数量或疾病持续时间的医学相关增加。结论根据我们的模拟以及生物医学证据的强烈暗示，在设计癌症最佳疗法时，不能忽略影响治疗癌症恶性程度的时间评估因素。的确，考虑到时间因素可调节恶性肿瘤，可从生物医学的角度，特别是在设计针对患者的治疗方法时，在最佳治疗中显着提高治疗效率，并具有相关的意义。并且不涉及癌细胞数量或疾病持续时间的医学相关增加。结论根据我们的模拟以及生物医学证据的强烈暗示，在设计癌症最佳疗法时，不能忽略影响治疗癌症恶性程度的时间评估因素。确实，考虑到时间因素调节恶性肿瘤，可以从生物医学的角度，特别是在设计针对患者的治疗方法时，在最佳治疗中显着提高治疗效率，并具有相关的意义。