A Viscoelastic Model for Glioma Growth

J. R. Branco, J. A. Ferreira, P. de Oliveira

Abstract

In this paper we propose a mathematical model to describe the evolution of glioma cells in the brain taking into account the viscoelastic properties of brain tissue. The mathematical model is established considering that the glioma cells are of two phenotypes: migratory and proliferative. The evolution of the migratory cells is described by a diffusion-reaction equation of non Fickian type deduced considering a mass conservation law with a non Fickian migratory mass flux. The evolution of the proliferation cells is described by a reaction equation. Numerical simulations that illustrate the behaviour of the mathematical model are included.

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Paper Citation


in Harvard Style

R. Branco J., Ferreira J. and de Oliveira P. (2013). A Viscoelastic Model for Glioma Growth . In Proceedings of the 3rd International Conference on Simulation and Modeling Methodologies, Technologies and Applications - Volume 1: BIOMED, (SIMULTECH 2013) ISBN 978-989-8565-69-3, pages 689-695. DOI: 10.5220/0004632406890695


in Bibtex Style

@conference{biomed13,
author={J. R. Branco and J. A. Ferreira and P. de Oliveira},
title={A Viscoelastic Model for Glioma Growth},
booktitle={Proceedings of the 3rd International Conference on Simulation and Modeling Methodologies, Technologies and Applications - Volume 1: BIOMED, (SIMULTECH 2013)},
year={2013},
pages={689-695},
publisher={SciTePress},
organization={INSTICC},
doi={10.5220/0004632406890695},
isbn={978-989-8565-69-3},
}


in EndNote Style

TY - CONF
JO - Proceedings of the 3rd International Conference on Simulation and Modeling Methodologies, Technologies and Applications - Volume 1: BIOMED, (SIMULTECH 2013)
TI - A Viscoelastic Model for Glioma Growth
SN - 978-989-8565-69-3
AU - R. Branco J.
AU - Ferreira J.
AU - de Oliveira P.
PY - 2013
SP - 689
EP - 695
DO - 10.5220/0004632406890695