A simple agent-based hybrid model to simulate the biophysics of glioblastoma multiforme cells and the concomitant evolution of the oxygen field

Background and objectives: Glioblastoma multiforme (GBM) is one of the most aggressive cancers of the central nervous system. It is characterized by a high mitotic activity and an infiltrative ability of the glioma cells, neovascularization and necrosis. GBM evolution entails the continuous interplay between heterogeneous cell populations, chemotaxis, and physical cues through different scales. In this work, an agent-based hybrid model is proposed to simulate the coupling of the multiscale biological events involved in the GBM invasion, specifically the individual and collective migration of GBM cells and the concurrent evolution of the oxygen field and phenotypic plasticity. An asset of the formulation is that it is conceptually and computationally simple but allows to reproduce the complexity and the progression of the GBM micro-environment at cell and tissue scales simultaneously. Methods: The migration is reproduced as the result of the interaction between every single cell and its micro-environment. The behavior of each individual cell is formulated through genotypic variables whereas the cell micro-environment is modeled in terms of the oxygen concentration and the cell density surrounding each cell. The collective behavior is formulated at a cellular scale through a flocking model. The phenotypic plasticity of the cells is induced by the micro-environment conditions, considering five phenotypes. Results: The model has been contrasted by benchmark problems and experimental tests showing the ability to reproduce different scenarios of glioma cell migration. In all cases, the individual and collective cell migration and the coupled evolution of both the oxygen field and phenotypic plasticity have been properly simulated. This simple formulation allows to mimic the formation of relevant hallmarks of glioblastoma multiforme, such as the necrotic cores, and to reproduce experimental evidences related to the mitotic activity in pseudopalisades. Conclusions: In the collective migration, the survival of the clusters prevails at the expense of cell mitosis, regardless of the size of the groups, which delays the formation of necrotic foci and reduces the rate of oxygen consumption.