title: Optimal control strategies of eradicating invisible glioblastoma cells after conventional surgery.
abstract: 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.
authors.affiliation: 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.
authors.forename: Aurelio A
authors.initials: AA
authors.lastname: de Los Reyes V
authors.affiliation: Department of Mathematics, Konkuk University, 1 Hwayang-dong, Gwangjin-gu, Seoul 143701, Republic of Korea junge@konkuk.ac.kr.
authors.forename: Eunok
authors.initials: E
authors.lastname: Jung
authors.affiliation: Department of Mathematics, Konkuk University, 1 Hwayang-dong, Gwangjin-gu, Seoul 143701, Republic of Korea Department of Mathematics, Ohio State University, Columbus, OH 43210, USA.
authors.forename: Yangjin
authors.initials: Y
authors.lastname: Kim
mesh_terms: D055372:AMP-Activated Protein Kinases / Q000378:metabolism; D000818:Animals; D000970:Antineoplastic Agents / Q000008:administration & dosage*; D001932:Brain Neoplasms / Q000188:drug therapy / Q000378:metabolism / Q000473:pathology / Q000601:surgery; D002465:Cell Movement / Q000187:drug effects; D002470:Cell Survival / Q000187:drug effects; D003198:Computer Simulation; D004305:Dose-Response Relationship, Drug; D004360:Drug Therapy, Computer-Assisted / Q000379:methods*; D005909:Glioblastoma / Q000188:drug therapy* / Q000378:metabolism* / Q000601:surgery; D005947:Glucose / Q000008:administration & dosage; D006801:Humans; D007262:Infusions, Intravenous; D035683:MicroRNAs / Q000378:metabolism; D008954:Models, Biological; D018365:Neoplasm, Residual; D011182:Postoperative Care; D016896:Treatment Outcome
chemical_list: D000970:Antineoplastic Agents; C531201:MIRN451 microRNA, human; D035683:MicroRNAs; D055372:AMP-Activated Protein Kinases; D005947:Glucose
keywords: cell proliferation and invasion; drug intravenous infusion; glioblastoma multiforme; glucose intravenous infusion; optimal control theory
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