A mathematical model of CAR-T cell therapy in combination with chemotherapy for malignant gliomas

TL;DR

This paper develops a mathematical model to analyze the combined effects of chemotherapy and CAR-T cell therapy on malignant gliomas, providing insights into optimal treatment strategies and tumor dynamics.

Contribution

It introduces a novel five-dimensional dynamical system model with impulsive inputs for combined MG therapies and explores optimal treatment protocols through in silico trials.

Findings

Constant combined therapy can eradicate tumors under certain conditions.

Tumor growth rate and therapy efficacy are key factors influencing survival.

In silico trials identify optimal treatment combinations for different tumor resistance profiles.

Abstract

We study the dynamics and interactions between combined chemotherapy and chimeric antigen receptor (CAR-T) cells therapy and malignant gliomas (MG). MG is one of the most common primary brain tumor, with high resistance to therapy and unfavorable prognosis. Here, we develop a mathematical model that describes the application of chemo- and CAR-T cell therapies and the dynamics of sensitive and resistant populations of tumor cells. This model is a five-dimensional dynamical system with impulsive inputs corresponding to clinical administration of chemo- and immunotherapy. We provide a proof of non-negativeness of solutions of the proposed model for non-negative initial data. We demonstrate that if we apply both therapies only once, the trajectories will be attracted to an invariant surface that corresponds to the tumor carrying capacity. On the other hand, if we apply both treatments constantly, we find regions of the parameter where the tumor is eradicated. Moreover, we study applications of different combinations of the above treatments in order to find an optimal combination at the population level. To this aim, we generate a population of $10^{4}$ virtual patients with the model parameters uniformly distributed in the medically relevant ranges and perform \emph{in silico} trials with different combinations of treatments. We obtain optimal protocols for several different relations of tumor growth rates between sensitive and drug resistant cells. We demonstrate that the tumor growth rate, efficacy of chemotherapy, and tumor immunosuppression are the parameters that mostly impact survival time in \emph{in silico} trials. We believe that our results provide new theoretical insights to guide the design of clinical trials for MG therapies.