Mathematical Details on a Cancer Resistance Model
Mathematical Details on a Cancer Resistance Model
复制标题
抗癌模型的数学细节
DOI：
10.3389/fbioe.2020.00501
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发表时间：
2020-06-17
影响因子：
5.7
通讯作者：
Sontag, Eduardo D.
中科院分区：
文献类型：
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作者：
Greene, James M.;Sanchez-Tapia, Cynthia;Sontag, Eduardo D.
在癌症治疗中，限制化疗成功的最重要因素之一是耐药现象。我们最近引入了一个框架，用于量化诱导和非诱导对癌症化疗的耐药性的影响（Greene等人，2018a,2019）。在这项工作中，我们详细阐述了Greene等人（2018a）中概述的最优控制问题的相关细节。通过庞特里亚金极大值原理和微分李代数技术，将控制结构精确地表征为bang-bang和路径约束弧的串联。结构可识别性分析也提出了，表明可以测量患者特定的参数，从而在治疗开始前用于设计最佳疗法。为了完整起见，还包括对存在性结果的详细分析。
One of the most important factors limiting the success of chemotherapy in cancer treatment is the phenomenon of drug resistance. We have recently introduced a framework for quantifying the effects of induced and non-induced resistance to cancer chemotherapy (Greene et al.,2018a,2019). In this work, we expound on the details relating to an optimal control problem outlined in Greene et al. (2018a). The control structure is precisely characterized as a concatenation of bang-bang and path-constrained arcs via the Pontryagin Maximum Principle and differential Lie algebraic techniques. A structural identifiability analysis is also presented, demonstrating that patient-specific parameters may be measured and thus utilized in the design of optimal therapies prior to the commencement of therapy. For completeness, a detailed analysis of existence results is also included.