Global Solvability and Optimal Control to a Haptotaxis Cancer Invasion Model with Two Cancer Cell Species
Global Solvability and Optimal Control to a Haptotaxis Cancer Invasion Model with Two Cancer Cell Species
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DOI：
10.1007/s00245-020-09712-0
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发表时间：
2020-08
影响因子：
1.8
通讯作者：
Feng Dai;Bin Liu
中科院分区：
文献类型：
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作者：
Feng Dai;Bin Liu
本文讨论了两种癌细胞侵入周围健康组织的趋触模型的最优控制问题。癌细胞可以通过被认为是控制变量的治疗剂（放射疗法或化学疗法）来治疗。我们的主要目标是描述一个最佳的控制，平衡的治疗效果与其副作用。首先，利用Banach不动点定理和一种新的估计的迭代准则以及改进的估计的Moser型迭代技巧，得到了状态系统在空间维上的整体有界弱解.然后，利用极小化序列的技巧证明了最优对的存在性。利用控制-状态映射的Lipschitz连续性和凸摄动方法，得到了系统的一阶最优性必要条件。最后，我们提出了数值的时空动力学的物种，最优控制和最佳方案的治疗剂管理，以说明在这项工作中所获得的理论结果的具体实现，并验证一些临床研究结果。
This paper deals with an optimal control problem for a haptotaxis model which describes two types of cancer cell invading the surrounding healthy tissue. Cancer cells can be treated by therapeutic agents (radiotherapy or chemotherapy) considered as the control variable. Our primary goal is to characterize an optimal control which balances the therapeutic benefits with its side effects. Firstly, the global bounded weak solution of state system in spatial dimensionsare obtained by using the Banach fixed-point theorem and a new iteration criterion ofestimates as well as the adapted Moser-type iteration technique ofestimates. Subsequently, the existence of optimal pair is proved by applying the technique of minimizing sequence. Furthermore, we derive the first-order necessary optimality condition by means of the Lipschitz continuity of the control-to-state mapping and the methods of convex perturbation. Finally, we present numerically the spatio-temporal dynamics of species, optimal control and optimal regimen of therapeutic agents administrated to illustrate the concrete realization of the theoretical results obtained in this work, and to validate some clinical findings.