Ledzewicz Urszula, Amini Behrooz, Schättler Heinz
Dept. of Mathematics and Statistics, Southern Illinois University, Edwardsville, Il 62025, United States email:
Math Biosci Eng. 2015 Dec;12(6):1257-75. doi: 10.3934/mbe.2015.12.1257.
A 3-compartment model for metronomic chemotherapy that takes into account cancerous cells, the tumor vasculature and tumor immune-system interactions is considered as an optimal control problem. Metronomic chemo-therapy is the regular, almost continuous administration of chemotherapeutic agents at low dose, possibly with small interruptions to increase the efficacy of the drugs. There exists medical evidence that such administrations of specific cytotoxic agents (e.g., cyclophosphamide) have both antiangiogenic and immune stimulatory effects. A mathematical model for angiogenic signaling formulated by Hahnfeldt et al. is combined with the classical equations for tumor immune system interactions by Stepanova to form a minimally parameterized model to capture these effects of low dose chemotherapy. The model exhibits bistable behavior with the existence of both benign and malignant locally asymptotically stable equilibrium points. In this paper, the transfer of states from the malignant into the benign regions is used as a motivation for the construction of an objective functional that induces this process and the analysis of the corresponding optimal control problem is initiated.
一种考虑癌细胞、肿瘤脉管系统和肿瘤免疫系统相互作用的节拍式化疗三室模型被视为一个最优控制问题。节拍式化疗是指以低剂量定期、几乎持续地给予化疗药物，可能会有短暂中断以提高药物疗效。有医学证据表明，特定细胞毒性药物（如环磷酰胺）的这种给药方式具有抗血管生成和免疫刺激作用。Hahnfeldt等人建立的血管生成信号数学模型与Stepanova的肿瘤免疫系统相互作用经典方程相结合，形成一个参数最少的模型，以捕捉低剂量化疗的这些效应。该模型表现出双稳态行为，存在良性和恶性局部渐近稳定平衡点。在本文中，将状态从恶性区域转移到良性区域用作构建诱导此过程的目标泛函的动机，并开始分析相应的最优控制问题。
