Non-Homogeneous Reaction-Diffusion Models of Tumour Growth

Abstract

This thesis develops and analyzes non-homogeneous reaction–diffusion models to investigate the growth and treatment dynamics of glioblastoma, an aggressive and highly invasive primary brain tumor. The work incorporates spatially varying diffusion, anisotropic migration informed by white matter structures, and logistic proliferation to capture realistic tumor behavior. A series of one- and two-dimensional numerical simulations were performed to examine baseline tumor progression and to evaluate the effectiveness of several therapeutic strategies, including chemotherapy, immunotherapy, surgical resection, and combined multi-modal protocols. The results demonstrate that treatment outcomes are highly sensitive to spatial heterogeneity, diffusion anisotropy, and timing of interventions. Integrated treatment strategies generally provide the greatest reduction in tumor burden, delay tumor recurrence, and slow propagation speed. This study highlights the importance of spatially informed mathematical modeling in understanding glioblastoma progression and optimizing treatment approaches.