鉴于其与制定患者特异性治疗的相关性,对抗癌症的最佳疗法的数学设计是当今生物数学和生物医学的重要研究领域。直到现在,然而,癌症最佳疗法认为恶性肿瘤完全取决于药物浓度和癌细胞的数量,忽略癌症生长得越快,癌症就越严重,早期药物剂量更有偏见。这里,我们分析了如何最佳治疗的影响时,治疗癌症的时间演变被认为是一个额外的因素决定的恶性肿瘤,详细分析伊马替尼治疗慢性髓系白血病的意义。
以描述慢性髓系白血病动力学的数学模型为参考,我们通过修改通常的恶性肿瘤目标函数来设计最佳治疗问题,不知道癌症恶性肿瘤的任何时间维度。特别是,我们引入了一个时间评估因子,该因子捕获了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.在为所涉及的参数赋值后,我们在有和没有新的时间估值因子的情况下求解和模拟模型,比较药物剂量和疾病演变的结果。
我们的计算模拟明确表明,考虑到捕获与癌症早期生长和药物管理相关的较高恶性程度的时间评估因素,可以设计出更有效的治疗方法。更具体地说,当这个时间估值因子被纳入目标函数时,最佳药物剂量较低,并且不涉及癌症细胞数量或疾病持续时间的医学相关增加。
根据我们的模拟和生物医学证据强烈表明,在设计癌症最佳治疗方案时,不能忽视在治疗癌症中存在影响恶性肿瘤的时间评估因素.的确,考虑时间评估因素调节恶性肿瘤会导致最佳治疗的效率显着提高,并从生物医学角度具有相关意义。特别是在设计针对患者的治疗方法时。
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.
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.
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.
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.