神经母细胞瘤及其治疗数学模型的动力学和优化控制:数学模型的启示

José García Otero, Mariusz Bodzioch, Juan Belmonte-Beitia
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摘要

Celyvir 是一种先进的治疗药物,由含有溶瘤病毒 ICOVIR 5 的间充质干细胞(MSCs)组成。 本文建立了一个动态系统,试图捕捉癌症、免疫系统和腺病毒之间的基本关系。本文研究了两种治疗方式:连续治疗和周期治疗,其中周期治疗更接近实际情况。在分析第一种模式时,除了确定临界点、临界点特性和分叉点外,还进行了大量的数值模拟。结果表明,Celyvir 可在某些双稳态状态下产生肿瘤进展平衡,甚至不受肿瘤影响。此外,还进行了敏感性分析,以确定系统中哪些参数最为重要。随后,我们提出了一个具有非线性目标函数的最优控制问题,其治疗目标不仅是使肿瘤细胞数量和治疗总成本最小化,还要防止肿瘤达到临界大小。结果表明,最优控制是 "砰砰 "控制。第二个模型确定了病毒载量的临界值,在这个临界值上可以确保治疗的成功。在这两个模型中,低病毒载量显然会导致疾病复发。最后,研究表明,应采用周期性 "撞击 "疗法来优化 Celyvir 的治疗。
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On the dynamics and optimal control of a mathematical model of neuroblastoma and its treatment: Insights from a mathematical model

Celyvir is an advanced therapy medicine, consisting of mesenchymal stem cells (MSCs) containing the oncolytic virus ICOVIR 5. This paper sets out a dynamic system which attempts to capture the fundamental relationships between cancer, the immune system and adenoviruses. Two forms of treatment were studied: continuous and periodic, the second being closer to the real situation. In the analysis of the first model, in addition to identifying the critical points, their properties and bifurcation points, a number of numerical simulations were carried out. It has thus been shown that there are bistability regimes in which Celyvir can produce an equilibrium of tumor progression, or even freedom from tumor. A sensitivity analysis was also performed to determine which parameters are most important in the system. Subsequently, an optimal control problem with nonlinear objective functional has been formulated, where the therapeutic goal is not only to minimize the size of the tumor cell population and the total cost of treatment, but also to prevent the tumor from reaching a critical size. It has been shown that the optimal control is bang–bang. With the second model, a threshold value of viral load has been identified at which the success of the treatment could be ensured. It is clear in both models that a low viral load would lead to relapse of the disease. Finally, it is shown that a periodic bang–bang regime should be used to optimize treatment with Celyvir.

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