Mathematical modeling of glioma invasion: acid- and vasculature mediated go-or-grow dichotomy and the influence of tissue anisotropy

Starting from kinetic transport equations and subcellular dynamics we deduce a multiscale model for glioma invasion relying on the go-or-grow dichotomy and the influence of vasculature, acidity, and brain tissue anisotropy. Numerical simulations are performed for this model with multiple taxis, in order to assess the solution behavior under several scenarios of taxis and growth for tumor and endothelial cells. An extension of the model to incorporate the macroscopic evolution of normal tissue and necrotic matter provides a basis for performing tumor grading.