Viable Therapy Strategies in a Spatial Mathematical Model of Glioma With Consideration of Oxygen Delivery
E. Fimmel Professor in the Faculty of Computer Science, Mannheim University of Applied Sciences Paul-Wittsack-Str. 10 68163 Mannheim, Germany firstname.lastname@example.org, A.S. Bratus Professor in the Faculty of Computer Science, Lomonosov Moscow State University Vorob´evy gory 119899 Moscow, Russia email@example.com, I. Samochin Faculty of Computer Science, Lomonosov Moscow State University Vorob´evy gory 119899 Moscow, Russia
The main aim of the talk is to identify treatment strategies for cancer using a spatial mathematical model described with the help of nonlinear PDE systems of parabolic type. The model considers the spatial dynamics of interaction between the drug and both malignant and healthy cells taking into account the resource (as oxygen and glucose) delivery through blood vessels. So, the model chosen defines the proliferation laws for malignant and healthy cells depending on the concentration of oxygen in blood. The chemoperapeutic agent spreads with the help of blood vessels and capillary and, thus, its amount is proportional to the amount of oxygen in blood, too.
We focus on such treatment strategies which secure a patient’s life as long as possible, i.e. they have to meet some restrictions on the total number of malignant cells (the upper bound), the total number of normal cells (the lower bound), the intensity of the therapy and on the total amount of chemotherapeutic agent during the whole treatment process. For every moment in time, these restrictions form some domain in the phase space. We will refer to this domain as the viable domain. A violation of the boundary of this domain by a phase variable means in reality the patient’s death.