Mathematical models for glioma growth and migration inside the brain
Gliomas are the most prevalent, aggressive, and invasive subtype of primary brain tumors, characterized by rapid cell proliferation and great infiltration capacity. De- spite the advances of clinical research, these tumors are often resistant to treatment, the median survival ranges between 9 and 12 months, and recurrence is the main cause of mortality. Glioma migration and invasion into the brain tissue is a complex phenomenon and little is still known about the underlying mechanisms that lead to tumor progression. In this thesis, we propose several mathematical models studying various aspects of glioma progression in relation to the microscopic and macroscopic scales charac- terizing this process. Exploiting the inherently multiscale nature of glioma evolution allows to define models based on dynamical systems, kinetic equations, and macro- scopic PDEs with different roles depending on the considered phenomena. The in- tegration of biological and clinical data with the mathematical models is one of the key objectives of this thesis. The experimental data at hand are obtained from mag- netic resonance and diffusion tensor images of the human brain and from in-vivo im- munofluorescence analysis of protein distributions in Drosophila, a reliable model for the study of glioblastoma dynamics. We analyze the anisotropic characteristics of the brain tissue, using the diffusion tensor data, and the influence of the fiber structures on tumor cell dynamics. We show how the fiber network directs cell migration along preferential paths, reproducing the branched and heterogeneous patterns typical of glioma evolution, and how multi- modal treatments can reduce this behavior. We study the interdependency of microenvironmental acidity and vasculature in tumor angiogenesis, defining a model capable of reproducing their influence on the emergence of phenotypic heterogeneity and hypoxia-related features (like necrosis) typical of glioma progression. This study enables the testing of a necrosis-based tumor grading and the investigation of multi-modal therapies with anti-angiogenic effects. We investigated the role of cell protrusions from a non-local perspective. We ex- plore their influence on the contact guidance phenomenon and on the emergence of collaborative or competitive effects between two cues driving cell velocity changes. Using the experimental analysis of protein distributions, we evaluate cell protru- sion relationship with integrins and proteases as leading mechanisms of glioblastoma progression. We show how the biochemical and biomechanical interactions of these agents result in the emergence of tumor propagation fronts, which can feature a dy- namical and heterogenous evolution in relation to environmental changes.