Mathematical modeling applied to the growth and invasion of gliomas: A narrative review of methods and applications.

Abstract

e13591 Background: The study of glioma growth (gg) and invasion has greatly benefited from the application of mathematical models (MM) , which provide insights into the cellular and tissue mechanisms involved in tumor progression. Methods: The methodology consisted of a narrative review of articles on MM in gg and invasion, utilizing databases such as PubMed, Scopus, and Web of Science. The selected studies featured discrete, continuous, or hybrid approaches, considering variables such as cell proliferation and nutrient diffusion. Results: The review explores three modeling approaches for gliomas: discrete, continuous, and hybrid. Discrete models focus on cellular processes like chemotaxis and adhesion, while continuous models use reaction-diffusion equations for macroscopic variations. Hybrid models integrate these approaches, addressing heterogeneity and computational challenges. Numerical methods like Crank-Nicholson aid in solving differential equations, while 3D models reveal how the extracellular matrix influences the tumor microenvironment. Multiscale approaches link molecular changes to metabolism and tissue dynamics, incorporating factors like oxygen gradients and immune interactions, uncovering mechanisms of glioma progression. Conclusions: Mathematical modeling bridges theory and practice in oncology, simulating glioma growth, nutrient diffusion, and extracellular matrix interactions. It links theoretical insights with clinical observations, making it a key tool for advancing integrated and effective approaches against gliomas. Table of key contributions to mathematical modeling of gliomas. Year Contribution 2007 Continuous dispersion for invasive motility. 2009 Invasive growth with cell density and oxygen. 2011 Tumor model classification (discrete, continuous, hybrid). 2013 Three-dimensional avascular gg with phenotypic interactions. 2015 Glioma density in heterogeneous media via discontinuous diffusion. 2016 Systematization of gg models; compression mechanics in spheroids. 2017 GBM–microglia interaction mediated by growth factors. 2018 Molecular processes in diffusion-based tumor modeling. 2019 Integro-differential approach for proliferation and death. 2020 Crank–Nicolson method for one-dimensional glioma analysis. 2021 Mesh-free PDE approach for invasive tumor boundaries. 2022 Stochastic interface for multiscale glioma evolution. 2023 Three-dimensional simulation with necrosis, hypoxia, and invasion. 2024 Finite element studies in heterogeneous substrates for avascular tumors.