November 15, 2018 at 16:30 the seminar on Mathematical Modeling in Biology and Medicine will be held under the guidance of prof. V. Volpert.
Speaker: Svetlana Kovalenko - Federal Science and Clinical Center of the Federal Medical and Biological Agency, scientific researcher
Topic: The optimization tasks for mathematical models of gliomas
Gliomas make up about half of the primary brain tumors. Tumor detection is now being performed using computed tomography and magnetic resonance imaging. Unfortunately, after a tumor is detected, doctors often have little time to cure this disease. There are various methods of treating gliomas. This They are chemotherapy, radiation therapy and surgery. Even with extensive surgical removal of tissue beyond the well-visible border of the tumor, regeneration occurs at the edge of the resection area. Over the course of time, chemotherapy and radiotherapy may acquire tumor resistance. Nevertheless, the study of mathematical models allowing to predict the development of the disease under the influence of drugs, as well as allowing to choose the optimal treatment regime, is very popular, because it allows you to choose the most optimal therapy strategy. Within the framework of this task, a mathematical problem of optimal control arises with phase constraints.
The speaker will consider the methods of solving optimal control problems in cases of various mathematical models of therapy. The problem of survival will be analyzed in detail, in which the phase constraints outline a certain area in the space of patient status indicators. The task of survival is to maximize the patient's lifetime, the search is conducted for precisely such treatment strategies that return the indicators to their original positions (and we see periodic trajectories in the graphs). Periodic trajectories suggest that the deadly disease has been transferred to the category of chronic.