A multiscale model for glioma spread including cell-tissue interactions and proliferation

Christian  Engwer; Markus  Knappitsch; Christina Surulescu; Christian  Engwer; Markus  Knappitsch; Christina Surulescu

doi:10.3934/mbe.2015011

Mathematical Biosciences and Engineering

2016, Volume 13, Issue 2: 443-460. doi: 10.3934/mbe.2015011

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A multiscale model for glioma spread including cell-tissue interactions and proliferation

1.
WWU Münster, Institute for Computational und Applied Mathematics and Cluster of Excellence EXC 1003, Cells in Motion, Orleans-Ring 10, 48149 Münster
2.
Technische Universität Kaiserslautern, Felix-Klein-Zentrum für Mathematik, Paul-Ehrlich-Str. 31, 67663 Kaiserslautern

Received: 01 July 2015 Accepted: 29 June 2018 Published: 25 December 2015
MSC : Primary: 92C17, 92C50; Secondary: 35Q92.

Glioma is a broad class of brain and spinal cord tumors arising from glia cells, which are the main brain cells that can develop into neoplasms.They are highly invasive and lead to irregular tumor margins which are not precisely identifiable by medical imaging, thus rendering a precise enough resection very difficult.The understanding of glioma spread patterns is hence essential for both radiological therapy as well as surgical treatment.In this paper we propose a multiscale model for glioma growth including interactions of the cells with the underlying tissuenetwork, along with proliferative effects. Our current accounting for two subpopulations of cells to accomodate proliferation according to the go-or-grow dichtomotyis an extension of the setting in [16].As in that paper, we assume that cancer cells use neuronal fiber tracts as invasive pathways. Hence, the individualstructure of brain tissue seems to be decisive for the tumor spread. Diffusion tensor imaging (DTI) is able to provide suchinformation, thus opening the way for patient specificmodeling of glioma invasion. Starting from a multiscale model involving subcellular (microscopic) and individual (mesoscale)cell dynamics, we perform a parabolic scaling to obtain an approximating reaction-diffusion-transport equation on themacroscale of the tumor cell population. Numerical simulations based on DTI data are carried out in order to assess theperformance of our modeling approach.

Keywords:

diffusiontensor imaging,
Multiscale model,
macrosccopic scaling,
reaction-diffusion-transport equations.,
kinetic transport equations,
glioma invasion

Citation: Christian Engwer, Markus Knappitsch, Christina Surulescu. A multiscale model for glioma spread including cell-tissue interactions and proliferation[J]. Mathematical Biosciences and Engineering, 2016, 13(2): 443-460. doi: 10.3934/mbe.2015011

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Abstract

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