A strongly degenerate diffusion‐haptotaxis model of tumour invasion under the go‐or‐grow dichotomy hypothesis

A strongly degenerate diffusion‐haptotaxis model of tumour invasion under the go‐or‐grow... We propose and study a strongly coupled PDE‐ODE‐ODE system modeling cancer cell invasion through a tissue network under the go‐or‐grow hypothesis asserting that cancer cells can either move or proliferate. Hence, our setting features 2 interacting cell populations with their mutual transitions and involves tissue‐dependent degenerate diffusion and haptotaxis for the moving subpopulation. The proliferating cells and the tissue evolution are characterized by way of ODEs for the respective densities. We prove the global existence of weak solutions and illustrate the model behaviour by numerical simulations in a 2‐dimensional setting. The numerical results recover qualitatively the infiltrative patterns observed histologically and moreover allow to establish a qualitative relationship between the structure of the tissue and the expansion of the tumour, thereby paying heed to its heterogeneity. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Mathematical Methods in the Applied Sciences Wiley

A strongly degenerate diffusion‐haptotaxis model of tumour invasion under the go‐or‐grow dichotomy hypothesis

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Publisher
Wiley Subscription Services, Inc., A Wiley Company
Copyright
Copyright © 2018 John Wiley & Sons, Ltd.
ISSN
0170-4214
eISSN
1099-1476
D.O.I.
10.1002/mma.4749
Publisher site
See Article on Publisher Site

Abstract

We propose and study a strongly coupled PDE‐ODE‐ODE system modeling cancer cell invasion through a tissue network under the go‐or‐grow hypothesis asserting that cancer cells can either move or proliferate. Hence, our setting features 2 interacting cell populations with their mutual transitions and involves tissue‐dependent degenerate diffusion and haptotaxis for the moving subpopulation. The proliferating cells and the tissue evolution are characterized by way of ODEs for the respective densities. We prove the global existence of weak solutions and illustrate the model behaviour by numerical simulations in a 2‐dimensional setting. The numerical results recover qualitatively the infiltrative patterns observed histologically and moreover allow to establish a qualitative relationship between the structure of the tissue and the expansion of the tumour, thereby paying heed to its heterogeneity.

Journal

Mathematical Methods in the Applied SciencesWiley

Published: Jan 1, 2018

Keywords: ; ; ; ; ; ;

References

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