title: Effective equations for anisotropic glioma spread with proliferation: a multiscale approach and comparisons with previous settings.
abstract: Glioma is a common type of primary brain tumour, with a strongly invasive potential, often exhibiting non-uniform, highly irregular growth. This makes it difficult to assess the degree of extent of the tumour, hence bringing about a supplementary challenge for the treatment. It is therefore necessary to understand the migratory behaviour 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 tumour 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 (DTI). Numerical simulations relying on DTI measurements confirm the biological findings that glioma spread along white matter tracts.
authors.affiliation: Institute for Computational and Applied Mathematics, University of Münster, Orleans-Ring 10, D-48149 Münster, Germany.
authors.forename: Christian
authors.initials: C
authors.lastname: Engwer
authors.affiliation: Technische Universität Kaiserslautern, Fachbereich Mathematik, D-67653 Kaiserslautern, Germany hunt@mathematik.uni-kl.de.
authors.forename: Alexander
authors.initials: A
authors.lastname: Hunt
authors.affiliation: Technische Universität Kaiserslautern, Fachbereich Mathematik, D-67653 Kaiserslautern, Germany.
authors.forename: Christina
authors.initials: C
authors.lastname: Surulescu
mesh_terms: D001932:Brain Neoplasms / Q000000981:diagnostic imaging / Q000473:pathology*; D056324:Diffusion Tensor Imaging; D005910:Glioma / Q000000981:diagnostic imaging / Q000473:pathology*; D006801:Humans; D008962:Models, Theoretical
keywords: diffusion tensor imaging; glioma invasion; kinetic transport equations; macroscopic scaling; multiscale model; reaction–diffusion–transport equations