International Journal of applied mathematics and computer science

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Paper details

Number 3 - September 2023
Volume 33 - 2023

On the analysis of a mathematical model of CAR-T cell therapy for glioblastoma: Insights from a mathematical model

Marek Bodnar, Urszula Foryś, Monika J. Piotrowska, Mariusz Bodzioch, Jose A. Romero-Rosales, Juan Belmonte-Beitia

Abstract
Chimeric antigen receptor T (CAR-T) cell therapy has been proven to be successful against different leukaemias and lymphomas. Its success has led, in recent years, to its use being tested for different solid tumours, including glioblastoma, a type of primary brain tumour, characterised by aggressiveness and recurrence. This paper presents an analytical study of a mathematical model describing the competition of CAR-T and glioblastoma tumour cells, taking into account their immunosuppressive capacity. The model is formulated in a general way, and its basic properties are investigated. However, most of the analysis considers the model with exponential tumour growth, assuming this growth type for simplicity. The existence and stability of steady states are studied, and the subsequent focus is on two different types of treatment: constant and periodic. Finally, protocols for CAR-T cell therapy of glioblastoma are numerically derived; these are aimed at preventing the tumour from reaching a critical size and at prolonging the patients’ survival time as much as possible. The analytical and numerical results provide theoretical support for the treatment of glioblastoma using CAR-T cells.

Keywords
glioblastoma, CAR-T cell therapy, mathematical modelling, periodic treatment

DOI
10.34768/amcs-2023-0027