On a multiscale model involving cell contractivity and its effects on tumor invasion

Gülnihal Meral; Christian Stinner; Christina Surulescu

doi:10.3934/dcdsb.2015.20.189

Article Contents

2015, Volume 20, Issue 1: 189-213. Doi: 10.3934/dcdsb.2015.20.189

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On a multiscale model involving cell contractivity and its effects on tumor invasion

1.
Bülent Ecevit University, Faculty of Arts and Sciences, Department of Mathematics, 67100 Zonguldak
2.
Technische Universität Kaiserslautern, Felix-Klein-Zentrum für Mathematik, Paul-Ehrlich-Str. 31, 67663 Kaiserslautern

Received: July 2013

Revised: May 2014

Published: January 2015

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Abstract

Cancer cell migration is an essential feature in the process of tumor spread and establishing of metastasis. It characterizes the invasion observed on the level of the cell population, but it is also tightly connected to the events taking place on the subcellular level. These are conditioning the motile and proliferative behavior of the cells, but are also influenced by it. In this work we propose a multiscale model linking these two levels and aiming to assess their interdependence. On the subcellular, microscopic scale it accounts for integrin binding to soluble and insoluble components present in the peritumoral environment, which is seen as the onset of biochemical events leading to changes in the cell's ability to contract and modify its shape. On the macroscale of the cell population this leads to modifications in the diffusion and haptotaxis performed by the tumor cells and implicitly to changes in the tumor environment. We prove the (local) well posedness of our model and perform numerical simulations in order to illustrate the model predictions.

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Mathematics Subject Classification: Primary: 35Q92, 92C17; Secondary: 35K57.

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