Glioma follow white matter tracts: a multiscale DTI-based model

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 o...

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Bibliographic Details
Published in:Journal of mathematical biology 2015-09, Vol.71 (3), p.551-582
Main Authors: Engwer, Christian, Hillen, Thomas, Knappitsch, Markus, Surulescu, Christina
Format: Article
Language:English
Subjects:
Anisotropy
Applications of Mathematics
Brain Neoplasms - pathology
Computer Simulation
Diffusion Tensor Imaging - methods
Diffusion Tensor Imaging - statistics & numerical data
Extracellular Matrix - pathology
Glioma - pathology
Humans
Mathematical and Computational Biology
Mathematical Concepts
Mathematics
Mathematics and Statistics
Models, Neurological
Neoplasm Invasiveness - pathology
White Matter - pathology
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Summary: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.
ISSN:0303-6812
1432-1416
DOI:10.1007/s00285-014-0822-7