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-inflammatory activity only marginally reduces tumor load at steady state. This result suggests that the patient’s own immune system is never sufficient for eliminating HGG. In contrast, infusion of T cells above a certain level, Smin, renders a curative tumor-free steady state locally asymptotically stable. When the infusion rate is increased above a higher threshold, Smax, this steady state becomes globally stable, providing a cure from any initial state of the system. These thresholds, as well as the infusion time required for tumor elimination for different doses, are computed explicitly, and can be personalized using patient-specific parameters. Our results suggest that reduction of tumor load and even tumor elimination can be achieved, either by significantly encouraging the endogenous immune response or by T cell infusion. This work provides an insight and practical guidelines for improving the efficacy of brain cancer immunotherapy by T cell infusion, which should be further studied clinically.