A PDE Model of Glioblastoma Progression: the Role of Cell Crowding and Resource Competition in Proliferation and Diffusion

Glioblastoma, the most aggressive form of primary brain tumor, presents significant challenges in clinical management and research due to its invasive nature and resistance to standard therapies. Mathematical modeling offers a promising avenue to understand its complex dynamics and develop innovative treatment strategies. Building upon previous research, this paper reviews and adapts some existing mathematical formulations to the modeling study of glioblastoma infiltration, utilizing the Partial Differential Equation (PDE) formalism to describe the time-varying and space-dependent cancer cell density. In particular, the role of cell diffusion and growth in the tumour progression and their limitation due to cell crowding and competition are investigated. Experimental data of glioblastoma taken from the literature are exploited for the identification of the model parameters. The improved data reproduction when the limitation of cell diffusion and growth is taken into account proves the relevant impact of the considered mechanisms on the spread of the tumour population. The numerical simulations highlight also that the proposed framework is promising for further investigations.