Influences of Allee effects in the spreading of malignant tumours

Lotte Sewalt; Kristen Harley; Peter van Heijster; Sanjeeva Balasuriya

doi:10.1016/j.jtbi.2015.12.024

Influences of Allee effects in the spreading of malignant tumours

J Theor Biol. 2016 Apr 7:394:77-92. doi: 10.1016/j.jtbi.2015.12.024. Epub 2016 Jan 21.

Authors

Lotte Sewalt¹, Kristen Harley², Peter van Heijster², Sanjeeva Balasuriya³

Affiliations

¹ Mathematisch Instituut, Leiden University, 2300 RA, Leiden, The Netherlands. Electronic address: lotte@math.leidenuniv.nl.
² School of Mathematical Sciences, Queensland University of Technology, Brisbane, QLD 4001, Australia.
³ School of Mathematical Sciences, University of Adelaide, Adelaide, SA 5005, Australia.

PMID: 26802481
DOI: 10.1016/j.jtbi.2015.12.024

Abstract

A recent study by Korolev et al. [Nat. Rev. Cancer, 14:371-379, 2014] evidences that the Allee effect-in its strong form, the requirement of a minimum density for cell growth-is important in the spreading of cancerous tumours. We present one of the first mathematical models of tumour invasion that incorporates the Allee effect. Based on analysis of the existence of travelling wave solutions to this model, we argue that it is an improvement on previous models of its kind. We show that, with the strong Allee effect, the model admits biologically relevant travelling wave solutions, with well-defined edges. Furthermore, we uncover an experimentally observed biphasic relationship between the invasion speed of the tumour and the background extracellular matrix density.

Keywords: Allee effects; Canard theory; Geometric singular perturbation theory; Malignant tumour model; Travelling wave solutions.

Publication types

Research Support, Non-U.S. Gov't

MeSH terms

Computer Simulation
Extracellular Matrix / metabolism
Humans
Models, Biological*
Neoplasm Metastasis / pathology*
Neoplasms / pathology*