Christian Engwer, Alexander Hunt, Christina Surulescu

• Glioma is a common type of primary brain tumor, with a strongly invasive potential, often exhibiting nonuniform, highly irregular growth. This makes it difficult to assess the degree of extent of the tumor, hence bringing about a supplementary challenge for the treatment. It is therefore necessary to understand the migratory behavior of glioma in greater detail. In this paper we propose a multiscale model for glioma growth and migration. Our model couples the microscale dynamics (reduced to the binding of surface receptors to the surrounding tissue) with a kinetic transport equation for the cell density on the mesoscopic level of individual cells. On the latter scale we also include the proliferation of tumor cells via effects of interaction with the tissue. An adequate parabolic scaling yields a convection-diffusion-reaction equation, for which the coefficients can be explicitly determined from the information about the tissue obtained by diffusion tensor imaging. Numerical simulations relying on DTI measurements confirm the biological findings that glioma spreads along white matter tracts.