Influences of Allee effects in the spreading of malignant tumours

JOURNAL OF THEORETICAL BIOLOGY

卷:394

Article

Sewalt, Lotte¹  Harley, Kristen²  van Heijster, Peter²  Balasuriya, Sanjeeva³ 

[1] Leiden Univ, Math Inst, NL-2300 RA Leiden, Netherlands

[2] Queensland Univ Technol, Sch Math Sci, Brisbane, Qld 4001, Australia

[3] Univ Adelaide, Sch Math Sci, Adelaide, SA 5005, Australia

关键词: Malignant tumour model;    Allee effects;    Travelling wave solutions;    Geometric singular perturbation theory;    Canard theory;   

DOI  :  10.1016/j.jtbi.2015.12.024

来源: Elsevier

【 摘 要 】

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. (C) 2016 Elsevier Ltd. All rights reserved.

【 授权许可】

Free