Scientific Reports ( IF 3.8 ) Pub Date : 2024-01-15 , DOI: 10.1038/s41598-023-48305-z Ophir Nave 1 , Yehuda Shor 2 , Raziel Bar 2 , Eliezer Elimelech Segal 2 , Moriah Sigron 1
In this study, we examined a mathematical model of breast cancer (BC) treatment that combines an oral oestrogen receptor inhibitor, AZD9496 with Palbociclib, a selective inhibitor of cyclin- dependent kinases CDK4 and CDK6. Treatment is described by analytical functions that enable us to control the dosage and time interval of the treatment, thus personalising the treatment for each patient. Initially, we investigated the effect of each treatment separately, and finally, we investigated the combination of both treatments. By applying numerical simulations, we confirmed that the combination of AZD9496 with palbociclib was the optimal treatment for BC. The dosage of AZD9496 increased and decreased throughout the treatment period, while the intervals were constant between treatments. Palbociclib changed almost cyclically, whereas the time intervals remained constant. To investigate the mathematical model, we applied the singularly perturbed homotopy analysis method, which is a numerical algorithm. The significant advantage of this method is that the mathematical model does not have to contain a small parameter (as is standard in perturbation theory). However, it is possible to artificially introduce a small parameter into the system of equations, making it possible to study the model using asymptotic methods.
中文翻译:
使用两种药物组合治疗乳腺癌的新疗法:AZD9496 和 palbociclib
在这项研究中,我们检查了乳腺癌 (BC) 治疗的数学模型,该模型将口服雌激素受体抑制剂 AZD9496 与 Palbociclib(细胞周期蛋白依赖性激酶 CDK4 和 CDK6 的选择性抑制剂)相结合。治疗是通过分析功能来描述的,使我们能够控制治疗的剂量和时间间隔,从而为每位患者提供个性化的治疗。最初,我们分别研究了每种治疗的效果,最后,我们研究了两种治疗的组合。通过应用数值模拟,我们证实 AZD9496 与 Palbociclib 的组合是 BC 的最佳治疗方法。 AZD9496的剂量在整个治疗期间增加和减少,而治疗之间的间隔是恒定的。 Palbociclib 几乎呈周期性变化,而时间间隔保持不变。为了研究数学模型,我们应用了奇异摄动同伦分析方法,这是一种数值算法。这种方法的显着优点是数学模型不必包含小参数(这是微扰理论中的标准)。然而,可以人为地在方程组中引入一个小参数,从而可以使用渐近方法来研究模型。