Periodic treatment in a mathematical model of CAR-T cell therapy for glioblastoma

Abstract

In recent years, great progress has been made in the treatment of certain solid tumours with CAR-T (Chimeric Antigen Receptor T) cells. However, their implementation is more complicated than for non-solid tumours where this therapy has been shown to be effective (cf. [1, 2] for leukaemias and lymphomas). Encouraged by the positive results of the treatment, scientists are starting to test this therapy in various solid tumours, including glioblastoma - an aggressive primary brain tumour.

In our work, based on the mathematical model of CAR-T therapy proposed in [3], we study the results of periodic treatment regimen. We show that the model has a tumour-free periodic solution and study its stability. Using linearization and the Floquet theory we find a relationship between the portion of CAR-T cells and the period of application allowing for cure. Interestingly, the cure condition is the same as the condition guaranteeing local stability of the tumour-free steady state in the model with constant treatment.