Ledzewicz Urszula, Wang Shuo, Schattler Heinz, Andre Nicolas, Heng Marie Amelie, Pasquier Eddy
Institute of Mathematics, Lodz University of Technology, 90-924 Lodz, Poland. email:
Math Biosci Eng. 2017 Feb 1;14(1):217-235. doi: 10.3934/mbe.2017014.
Effects that tumor heterogeneity and drug resistance have on the structure of chemotherapy protocols are discussed from a mathematical modeling and optimal control point of view. In the case when two compartments consisting of sensitive and resistant cells are considered, optimal protocols consist of full dose chemotherapy as long as the relative proportion of sensitive cells is high. When resistant cells become more dominant, optimal controls switch to lower dose regimens defined by so-called singular controls. The role that singular controls play in the structure of optimal therapy protocols for cell populations with a large number of traits is explored in mathematical models.
从数学建模和最优控制的角度讨论了肿瘤异质性和耐药性对化疗方案结构的影响。在考虑由敏感细胞和耐药细胞组成的两个区室的情况下，只要敏感细胞的相对比例较高，最优方案就包括全剂量化疗。当耐药细胞变得更占优势时，最优控制切换到由所谓的奇异控制定义的较低剂量方案。在数学模型中探讨了奇异控制在具有大量特征的细胞群体的最优治疗方案结构中所起的作用。
