On some models for cancer cell migration through
tissue networks

Jan Kelkel; Christina Surulescu; Jan Kelkel; Christina Surulescu

doi:10.3934/mbe.2011.8.575

Mathematical Biosciences and Engineering

2011, Volume 8, Issue 2: 575-589. doi: 10.3934/mbe.2011.8.575

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On some models for cancer cell migration through tissue networks

1.
IANS, University of Stuttgart, Pfaffenwaldring 57, 70569 Stuttgart
2.
INAM, University of Münster, Einsteinstrasse 62, 48149 Münster

Received: 01 February 2010 Accepted: 29 June 2018 Published: 01 April 2011
MSC : Primary: 35Q92 ; Secondary: 92B05.

We propose some models allowing to account for relevant processes at the various scales of cancer cell migration through tissue, ranging from the receptor dynamics on the cell surface over degradation of tissue fibers by protease and soluble ligand production towards the behavior of the entire cell population.
For a genuinely mesoscopic version of these models we also provide a result on the local existence and uniqueness of a solution for all biologically relevant space dimensions.
- Tumor cell migration,
- iterative method.,
- multiscale models
Citation: Jan Kelkel, Christina Surulescu. On some models for cancer cell migration throughtissue networks[J]. Mathematical Biosciences and Engineering, 2011, 8(2): 575-589. doi: 10.3934/mbe.2011.8.575

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Abstract

We propose some models allowing to account for relevant processes at the various scales of cancer cell migration through tissue, ranging from the receptor dynamics on the cell surface over degradation of tissue fibers by protease and soluble ligand production towards the behavior of the entire cell population.
For a genuinely mesoscopic version of these models we also provide a result on the local existence and uniqueness of a solution for all biologically relevant space dimensions.
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