de Los Reyes V Aurelio A, Jung Eunok, Kim Yangjin
Institute of Mathematics, C.P. Garcia Street, U.P. Campus, Diliman, 1101 Quezon City, Philippines Department of Mathematics, Konkuk University, 1 Hwayang-dong, Gwangjin-gu, Seoul 143701, Republic of Korea.
Department of Mathematics, Konkuk University, 1 Hwayang-dong, Gwangjin-gu, Seoul 143701, Republic of Korea
J R Soc Interface. 2015 May 6;12(106). doi: 10.1098/rsif.2014.1392.
Glioblastoma, the most aggressive type of brain cancer, has median survival time of 1 year after diagnosis. It is characterized by alternating modes of rapid proliferation and aggressive invasion in response to metabolic stress in the microenvironment. A particular microRNA, miR-451, and its downstream signalling molecules, AMPK complex, are known to be key determinants in switching cell fate. These components form a core control system determining a balance between cell growth and migration which is regulated by fluctuating glucose levels in the microenvironment. An important factor from the treatment point of view is that low levels of glucose affect metabolism and activate cell migration through the miR-451-AMPK control system, creating 'invisible' migratory cells and making them inaccessible by conventional surgery. In this work, we apply optimal control theory to deal with the problem of maintaining upregulated miR-451 levels that prevent cell infiltration to surrounding brain tissue and thus induce localization of these cancer cells at the surgical site. The model also considers the effect of a drug that blocks inhibitive pathways of miR-451 from AMPK complex. Glucose infusion control and drug infusion control are chosen to represent dose rates of glucose and drug intravenous administrations, respectively. The characteristics of optimal control lead us to investigate the structure of optimal intravenous infusion regimen under various circumstances and predict best clinical outcomes with minimum expense possible.
胶质母细胞瘤是最具侵袭性的脑癌类型，诊断后的中位生存时间为1年。其特征是在微环境中的代谢应激下，快速增殖和侵袭的模式交替出现。一种特定的微小RNA，即miR-451，及其下游信号分子AMPK复合物，被认为是决定细胞命运转换的关键因素。这些成分形成了一个核心控制系统，决定细胞生长和迁移之间的平衡，该平衡由微环境中波动的葡萄糖水平调节。从治疗角度来看，一个重要因素是低水平的葡萄糖会影响代谢，并通过miR-451-AMPK控制系统激活细胞迁移，产生“隐形”迁移细胞，使传统手术无法触及。在这项工作中，我们应用最优控制理论来解决维持miR-451水平上调的问题，这可以防止细胞浸润到周围脑组织，从而使这些癌细胞定位在手术部位。该模型还考虑了一种阻断miR-451从AMPK复合物抑制途径的药物的作用。分别选择葡萄糖输注控制和药物输注控制来代表葡萄糖和药物静脉给药的剂量率。最优控制的特性使我们能够研究各种情况下最优静脉输注方案的结构，并以尽可能低的费用预测最佳临床结果。
