Sewalt Lotte, Harley Kristen, van Heijster Peter, Balasuriya Sanjeeva
Mathematisch Instituut, Leiden University, 2300 RA, Leiden, The Netherlands.
School of Mathematical Sciences, Queensland University of Technology, Brisbane, QLD 4001, Australia.
J Theor Biol. 2016 Apr 7;394:77-92. doi: 10.1016/j.jtbi.2015.12.024. Epub 2016 Jan 21.
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.
科罗廖夫等人近期的一项研究[《自然综述：癌症》，14:371 - 379，2014年]表明，阿利效应——在其强形式中，即细胞生长需要最小密度——在癌性肿瘤扩散中很重要。我们提出了首个纳入阿利效应的肿瘤侵袭数学模型之一。基于对该模型行波解存在性的分析，我们认为它是对同类先前模型的改进。我们表明，在强阿利效应下，该模型允许具有明确边界的生物学相关行波解。此外，我们揭示了肿瘤侵袭速度与细胞外基质背景密度之间实验观察到的双相关系。
