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

Anna Zhigun, Christina Surulescu, Alexander Hunt

Research output: Contribution to journalArticle

5 Citations (Scopus)
155 Downloads (Pure)

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.
Original languageEnglish
Pages (from-to)2403-2428
Number of pages26
JournalMathematical Methods in the Applied Sciences
Volume41
Issue number6
Early online date21 Feb 2018
DOIs
Publication statusPublished - 01 Apr 2018

Keywords

  • cancer cell invasion
  • degenerate diffusion
  • global existence
  • go-or-grow dichotomy
  • haptotaxis
  • parabolic system
  • weak solution

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