Spatiotemporal dynamics of a glioma immune interaction model

Subhas Khajanchi,Juan J Nieto

doi:10.1038/s41598-021-00985-1

Subhas Khajanchi, Juan J Nieto

Open Access

https://doi.org/10.1038/s41598-021-00985-1

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Abstract

We report a mathematical model which depicts the spatiotemporal dynamics of glioma cells, macrophages, cytotoxic-T-lymphocytes, immuno-suppressive cytokine TGF-β and immuno-stimulatory cytokine IFN-γ through a system of five coupled reaction-diffusion equations. We performed local stability analysis of the biologically based mathematical model for the growth of glioma cell population and their environment. The presented stability analysis of the model system demonstrates that the temporally stable positive interior steady state remains stable under the small inhomogeneous spatiotemporal perturbations. The irregular spatiotemporal dynamics of gliomas, macrophages and cytotoxic T-lymphocytes are discussed extensively and some numerical simulations are presented. Performed some numerical simulations in both one and two dimensional spaces. The occurrence of heterogeneous pattern formation of the system has both biological and mathematical implications and the concepts of glioma cell progression and invasion are considered. Simulation of the model shows that by increasing the value of time, the glioma cell population, macrophages and cytotoxic-T-lymphocytes spread throughout the domain.

Highlights

We report a mathematical model which depicts the spatiotemporal dynamics of glioma cells, macrophages, cytotoxic-T-lymphocytes, immuno-suppressive cytokine Transforming growth factor β (TGF-β) and immunostimulatory cytokine IFN-γ through a system of five coupled reaction-diffusion equations
According to the 2016 World Health Organization (WHO) grading scheme for glioblastoma multiforme (GBM) of the Central Nervous System, the GBM is mainly classified into (i) isocitrate dehydrogenase (IDH)-wildtype glioblastoma that predominates in the patients over 55 years of age; (ii) IDH-mutant glioblastoma that preferentially arises in younger patients[4]
The biological motivation of this study is to investigate the heterogeneous nature of glioma cell population and immune components namely, macrophages and activated CD8+T cells

Summary

Introduction

We report a mathematical model which depicts the spatiotemporal dynamics of glioma cells, macrophages, cytotoxic-T-lymphocytes, immuno-suppressive cytokine TGF-β and immunostimulatory cytokine IFN-γ through a system of five coupled reaction-diffusion equations. The interaction between malignant gliomas and immune system is a nonlinear and highly complex phenomena This nonlinearity has attracted the attention of a significant number of scientists and researchers/oncologists in investigating the dynamics of glioma-immune system interactions throughout the world. To better understand such complex phenomenon, researchers have used mathematical models of gliomaimmune system response, over the last few decades. Swanson et al.[5,20,25,33,34,36] investigated the mathematical models that have been developed by M urray[35] and herself Their models quantify the spatiotemporal proliferation and invasion of malignant gliomas in the virtual human brain

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