Non-local parabolic and hyperbolic models for cell polarisation in heterogeneous cancer cell populations

Vasiliki Bitsouni (Lead / Corresponding author), Raluca Eftimie

Research output: Contribution to journalArticle

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Abstract

Tumours consist of heterogeneous populations of cells. The subpopulations can have different features, including cell motility, proliferation and metastatic potential. The interactions between clonal sub-populations are complex, from stable coexistence to dominant behaviours. The cell-cell interactions, i.e., attraction, repulsion and alignment, processes critical in cancer invasion and metastasis, can be influenced by the mutation of cancer cells. In this study, we develop a mathematical model describing cancer cell invasion and movement for two polarised cancer cell populations with different levels of mutation. We consider a system of non-local hyperbolic equations that incorporate cell-cell interactions in the speed and the turning behaviour of cancer cells, and take a formal parabolic limit to transform this model into a non-local parabolic model. We then investigate the possibility of aggregations to form, and perform numerical simulations for both hyperbolic and parabolic models, comparing the patterns obtained for these models.
Original languageEnglish
Pages (from-to)2600-2632
Number of pages33
JournalBulletin of Mathematical Biology
Volume80
Issue number10
Early online date22 Aug 2018
DOIs
Publication statusPublished - 1 Oct 2018

Fingerprint

Cell Population
cancer
Cancer
Polarization
polarization
Cells
Cell
Population
Neoplasms
subpopulation
cell movement
cells
mutation
Cell Communication
Cell Movement
Invasion
neoplasms
cell invasion
Model
Cell proliferation

Keywords

  • Aggregation patterns
  • Alignment
  • Cancer cells
  • Cell–cell interactions
  • Non-local hyperbolic model
  • Parabolic limit

Cite this

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title = "Non-local parabolic and hyperbolic models for cell polarisation in heterogeneous cancer cell populations",
abstract = "Tumours consist of heterogeneous populations of cells. The subpopulations can have different features, including cell motility, proliferation and metastatic potential. The interactions between clonal sub-populations are complex, from stable coexistence to dominant behaviours. The cell-cell interactions, i.e., attraction, repulsion and alignment, processes critical in cancer invasion and metastasis, can be influenced by the mutation of cancer cells. In this study, we develop a mathematical model describing cancer cell invasion and movement for two polarised cancer cell populations with different levels of mutation. We consider a system of non-local hyperbolic equations that incorporate cell-cell interactions in the speed and the turning behaviour of cancer cells, and take a formal parabolic limit to transform this model into a non-local parabolic model. We then investigate the possibility of aggregations to form, and perform numerical simulations for both hyperbolic and parabolic models, comparing the patterns obtained for these models.",
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Non-local parabolic and hyperbolic models for cell polarisation in heterogeneous cancer cell populations. / Bitsouni, Vasiliki (Lead / Corresponding author); Eftimie, Raluca.

In: Bulletin of Mathematical Biology, Vol. 80, No. 10, 01.10.2018, p. 2600-2632.

Research output: Contribution to journalArticle

TY - JOUR

T1 - Non-local parabolic and hyperbolic models for cell polarisation in heterogeneous cancer cell populations

AU - Bitsouni, Vasiliki

AU - Eftimie, Raluca

N1 - VB acknowledges support from an Engineering and Physical Sciences Research Council (UK) grant number EP/L504932/1. RE was partially supported by an Engineering and Physical Sciences Research Council (UK) grant number EP/K033689/1.

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AB - Tumours consist of heterogeneous populations of cells. The subpopulations can have different features, including cell motility, proliferation and metastatic potential. The interactions between clonal sub-populations are complex, from stable coexistence to dominant behaviours. The cell-cell interactions, i.e., attraction, repulsion and alignment, processes critical in cancer invasion and metastasis, can be influenced by the mutation of cancer cells. In this study, we develop a mathematical model describing cancer cell invasion and movement for two polarised cancer cell populations with different levels of mutation. We consider a system of non-local hyperbolic equations that incorporate cell-cell interactions in the speed and the turning behaviour of cancer cells, and take a formal parabolic limit to transform this model into a non-local parabolic model. We then investigate the possibility of aggregations to form, and perform numerical simulations for both hyperbolic and parabolic models, comparing the patterns obtained for these models.

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KW - Cell–cell interactions

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