Glioma invasion and its interplay with nervous tissue and therapy: A multiscale model

•A multiscale model for glioma invasion, proliferation and treatment is presented.•Fully-anisotropic advection-diffusion equation for glioma density is investigated.•The role of the brain fiber distribution on influencing tumor spread is analyzed.•Three fiber distribution functions are analyzed and compared.•Using real DTI data, the impact of brain structures on tumor evolution is shown. A multiscale mathematical model for glioma cell migration and proliferation is proposed, taking into account a possible therapeutic approach. Starting with the description of processes occurring at the subcellular level, the equation for the mesoscopic level is formulated and a macroscopic model is derived, via parabolic limit and Hilbert expansions in the moment equations. After the model set up and the study of the well-posedness of this macroscopic setting, we investigate the role of the fibers in the tumor dynamics. In particular, we focus on the fiber density function, with the aim of comparing some common choices present in the literature and understanding which differences arise in the description of the actual fiber density and orientation. Finally, some numerical simulations, based on real data, highlight the role of each modelled process in the evolution of the solution of the macroscopic equation.