Modelo da dinâmica de crescimento de glioma em meio anisotrópico – influência das interações entre células proliferantes, quiescentes, necróticas e nutrientes no microambiente.

Abstract

Cancer is the leading public health issue WorldWide. According to the International Agency for Research on Cancer (IARC), an estimated 20 million new cancer cases and 9.7 million cancer- related deaths occurred globally in 2022. Gliomas are primary brain tumors originating in the cerebral parenchyma, characterized by their aggressive and infiltrative behavior. The diagnostic definition of adult gliomas is based on pathological anatomy, which includes morphological analysis (cell type, anaplasia, vascularization, presence of necrosis, and mitotic activity), immunohistochemical analysis (GFAP, AE1/AE3, IDH1, ATRX, p53, Ki67, H3K27M, H3G34, and H3K27me), and molecular analysis. Treatment is multimodal and involves surgery, radiotherapy, and systemic chemotherapy. This study proposes and validates a mathematical model based on partial differential equations (PDEs) to describe the spatio-temporal dynamics of glioma growth and dispersion, considering cellular interactions, nutritional limitations, and tissue anisotropy. The model was implemented in Wolfram Mathematica using NDSolve and NIntegrate, and integrates key parameters such as carrying capacity, proliferation, quiescence, and cell death rates, as well as diffusion coefficients specific to white and gray matter. Results indicate that tumor evolution is strongly modulated by nutrient availability and the structure of the tumor microenvironment. Glial and quiescent cells concentrate in the tumor core, whereas peripheral spread is constrained by less favorable