  We deduce a model for glioma invasion making use of DTI data and accounting
for the dynamics of brain tissue being actively degraded by tumor cells via
excessive acidity production, but also according to the local orientation of
tissue fibers. Our approach has a multiscale character: we start with a
microscopic description of single cell dynamics including biochemical and/or
biophysical effects of the tumor microenvironment, translated on the one hand
into cell stress and corresponding forces and on the other hand into receptor
binding dynamics; these lead on the mesoscopic level to kinetic equations
involving transport terms w.r.t. all kinetic variables and eventually, by
appropriate upscaling, to a macroscopic reaction-diffusion equation for glioma
density with multiple taxis, coupled to (integro-)differential equations
characterizing the evolution of acidity and macro- and mesoscopic tissue. Our
approach also allows for a switch between fast and slower moving regimes,
%diffusion- and drift-dominated regimes, according to the local tissue
anisotropy. We perform numerical simulations to investigate the behavior of
solutions w.r.t. various scenarios of tissue dynamics and the dominance of each
of the tactic terms, also suggesting how the model can be used to perform a
numerical necrosis-based tumor grading or support radiotherapy planning by dose
painting. We also provide a discussion about alternative ways of including cell
level environmental influences in such multiscale modeling approach, ultimately
leading in the macroscopic limit to (multiple) taxis.
