On the control of cell migration and proliferation in glioblastoma

Glioblastoma multiforme (GBM) is an aggressive form of brain cancer with a median survival time of just about one year from the time of diagnosis. GBM is characterized by alternating phases of rapid proliferation and aggressive invasion as a response to metabolic stress in the microenvironment. In this paper, based on a recently formulated mathematical model for the relative balance of growth and invasion [13], we consider the control problem of maintaining a particular microRNA, miR-451, in an upregulated stage that prevents the migration of the cancer cells before surgery and leads to the localization of these cancer cells at the surgical site. These levels represent a state of the system and the control is given by dose rates of outside glucose administration. We formulate this as an optimal control problem with state-space constraints and analyze the structure of optimal and suboptimal treatment protocols.