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首页> 外文期刊>Journal of Computer and Systems Sciences International >Optimal Multitherapy Strategy in Mathematical Model of Dynamics of the Number of Nonuniform Tumor Cells
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Optimal Multitherapy Strategy in Mathematical Model of Dynamics of the Number of Nonuniform Tumor Cells

机译：肿瘤细胞数目不均匀动力学模型中的最佳多药治疗策略

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摘要

Mathematical model of dynamics of the number of tumor cells is considered. A tumor is assumed to consist of two cell types, each being under the influence of a specific chemotherapeutic agent that is capable of destroying cells of this specific type. The laws of growth of the number of all types of cells are considered to be given by logistic equations. The measure of the influence of each chemotherapeutic agent on the tumor is defined by a therapy function. Two types of therapy functions are used: a monotonically increasing function and a nonmonotonic function with a threshold value. In the first case, the higher the concentration of the agent, the stronger its influence on the tumor. In the second case, there exists a certain threshold value of the chemotherapeutic agent concentration: once it is exceeded, therapy efficiency decreases. The variant, when the total amount of each agent has an integral limit, is also studied. Necessary optimality conditions are formulated using the Pontrya-gin's maximum principle. They are used as a base for making important conclusions about the character of the optimal therapy strategy. We find numerically solutions to the optimal control problems, when the control is aimed at minimizing the total number of tumor cells for the cases of monotonic and threshold therapy functions, as well as with account of the integral constraints for the amounts of chemotherapeutic agents.
机译：考虑肿瘤细胞数目动力学的数学模型。假定肿瘤由两种细胞类型组成，每种细胞都受到能够破坏该特定类型细胞的特定化学治疗剂的影响。所有类型细胞数量的增长定律被认为是由逻辑方程式给出的。每种化学治疗剂对肿瘤的影响的量度由治疗功能定义。使用两种类型的治疗功能：具有阈值的单调递增函数和非单调函数。在第一种情况下，药剂的浓度越高，其对肿瘤的影响越强。在第二种情况下，存在一定的化学治疗剂浓度阈值：一旦超过该阈值，治疗效率就会降低。当每种试剂的总量具有整数限制时，也会研究该变体。使用Pontrya-gin的最大原理来制定必要的最优条件。它们被用作得出关于最佳治疗策略特征的重要结论的基础。当控制旨在使单调和阈治疗功能情况下的肿瘤细胞总数最小化，并且考虑到化学治疗剂数量的整体约束时，我们找到了最佳控制问题的数值解决方案。

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