Cellular Immunotherapy for High Grade Gliomas: Mathematical Analysis Deriving Efficacious Infusion Rates Based on Patient Requirements

To date, no effective cure has been found for high grade malignant glioma (HGG), current median survival for HGG patients under treatment ranging from 18 months (grade IV) to 5 years (grade III). Recently, T cell therapy for HGG has been suggested as a promising avenue for treating such resistant tumors, but clinical outcome has not been conclusive. For studying this new therapy option, a mathematical model for tumor–T cell interactions was developed, where tumor immune response was modeled by six coupled ordinary differential equations describing tumor cells, T cells, and their respective secreted cytokines and immune mediating receptors. Here we mathematically analyze the model in an untreated case and under T cell immunotherapy. For both settings we classify steady states, determine stability properties, and explore the global behavior of the model. Analysis suggests that in untreated patients, the system always converges to a steady state of a large tumor mass. An increase in the patient's pro-inflamm...