title: Glioma follow white matter tracts: a multiscale DTI-based model.
abstract: Gliomas are a class of rarely curable tumors arising from abnormal glia cells in the human brain. The understanding of glioma spreading patterns is essential for both radiological therapy as well as surgical treatment. Diffusion tensor imaging (DTI) allows to infer the white matter fibre structure of the brain in a noninvasive way. Painter and Hillen (J Theor Biol 323:25-39, 2013) used a kinetic partial differential equation to include DTI data into a class of anisotropic diffusion models for glioma spread. Here we extend this model to explicitly include adhesion mechanisms between glioma cells and the extracellular matrix components which are associated to white matter tracts. The mathematical modelling follows the multiscale approach proposed by Kelkel and Surulescu (Math Models Methods Appl Sci 23(3), 2012). We use scaling arguments to deduce a macroscopic advection-diffusion model for this process. The tumor diffusion tensor and the tumor drift velocity depend on both, the directions of the white matter tracts as well as the binding dynamics of the adhesion molecules. The advanced computational platform DUNE enables us to accurately solve our macroscopic model. It turns out that the inclusion of cell binding dynamics on the microlevel is an important factor to explain finger-like spread of glioma.
authors.affiliation: Institut für Numerische und Angewandte Mathematik, WWU Münster, Münster, Germany, christian.engwer@wwu.de.
authors.forename: Christian
authors.initials: C
authors.lastname: Engwer
authors.forename: Thomas
authors.initials: T
authors.lastname: Hillen
authors.forename: Markus
authors.initials: M
authors.lastname: Knappitsch
authors.forename: Christina
authors.initials: C
authors.lastname: Surulescu
mesh_terms: D016880:Anisotropy; D001932:Brain Neoplasms / Q000473:pathology*; D003198:Computer Simulation; D056324:Diffusion Tensor Imaging / Q000379:methods* / Q000706:statistics & numerical data; D005109:Extracellular Matrix / Q000473:pathology; D005910:Glioma / Q000473:pathology*; D006801:Humans; D055641:Mathematical Concepts; D008959:Models, Neurological; D009361:Neoplasm Invasiveness / Q000473:pathology; D066127:White Matter / Q000473:pathology*