Glioma invasion and its interplay with the nervous tissue: a multiscale model
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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 taking place on the subcellular level, the equation for the mesoscopic level is formulated and, thus, the macroscopic model is derived, using a parabolic limit and the Hilbert expansions in the moment system. After the model set up and the study of the well-posedness of this macroscopic setting, we investigate the functions involved in the equations that highlight the role of the fibers in the tumor dynamics. In particular, we focus on the fiber density function, with the aim of comparing different possible choices present in literature and understanding which approach could better describe the actual fiber density and orientation. Finally some numerical simulations, based on real data, show the role of each modelled process in the evolution of the solution.