Incompressible limit of a continuum model of tissue growth with segregation for two cell populations

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Title: Incompressible limit of a continuum model of tissue growth with segregation for two cell populations
Authors: Chertock, A
Degond, P
Hecht, S
Vincent, J-P
Item Type: Journal Article
Abstract: This paper proposes a model for the growth of two interacting populations of cells that do not mix. The dynamics is driven by pressure and cohesion forces on the one hand and proliferation on the other hand. Contrasting with earlier works which assume that the two populations are initially segregated, our model can deal with initially mixed populations as it explicitly incorporates a repul-sion force that enforces segregation. To balance segregation instabilities potentially triggered by the repulsion force, our model also incorporates a fourth order diffusion. In this paper, we study the influ-ence of the model parameters thanks to one-dimensional simulations using a finite-volume method for a relaxation approximation of the fourth order diffusion. Then, following earlier works on the single population case, we provide formal arguments that the model approximates a free boundary Hele Shaw type model that we characterise using both analytical and numerical arguments.
Issue Date: 22-Jun-2019
Date of Acceptance: 18-Jun-2019
URI: http://hdl.handle.net/10044/1/71636
DOI: https://dx.doi.org/10.3934/mbe.2019290
ISSN: 1547-1063
Publisher: American Institute of Mathematical Sciences
Start Page: 5804
End Page: 5835
Journal / Book Title: Mathematical Biosciences and Engineering
Volume: 16
Issue: 5
Copyright Statement: c 2019 the Author(s), licensee AIMS Press. This is an open access article distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/4.0)
Sponsor/Funder: The Royal Society
Engineering & Physical Science Research Council (EPSRC)
Engineering & Physical Science Research Council (EPSRC)
Engineering & Physical Science Research Council (EPSRC)
Funder's Grant Number: WM130048
EP/M006883/1
EP/N014529/1
EP/P013651/1
Keywords: Science & Technology
Life Sciences & Biomedicine
Mathematical & Computational Biology
tissue growth
two cell populations
incompressible limit
free boundary problem
SOLID TUMOR-GROWTH
BOUNDARY-PROBLEM
STABILITY
EQUATIONS
PHASE
q-bio.CB
q-bio.CB
0102 Applied Mathematics
0903 Biomedical Engineering
0904 Chemical Engineering
Bioinformatics
Publication Status: Published
Appears in Collections:Mathematics
Applied Mathematics and Mathematical Physics



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