A mathematical analysis of a model for capillary network formation in the absence of endothelial cell proliferation

被引：18

作者：

Sleeman, BD ^{[1
]}

Anderson, ARA

Chaplain, MAJ

机构：

[1] Univ Leeds, Sch Math, Leeds LS2 9JT, W Yorkshire, England

[2] Univ Dundee, Dept Math, Dundee DD1 4HN, Scotland

来源：

APPLIED MATHEMATICS LETTERS | 1999年 / 12卷 / 08期

基金：

英国生物技术与生命科学研究理事会;

关键词：

angiogenesis; endothelial cells; chemotaxis; haptotaxis; Sturm-Liouville problem;

D O I：

10.1016/S0893-9659(99)00132-9

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

An analysis of a parabolic partial differential equation modelling capillary network formation is presented. The model includes terms representing cell random motility, chemotaxis, and haptotaxis due to the presence of chemical stimuli: tumour angiogenic factors and fibronectin. The analysis provides an underlying insight into mechanisms of cell migration which are crucial for tumour angiogenesis. Specific 1 and 2D examples are discussed in detail. (C) 1999 Elsevier Science Ltd. All rights reserved.

引用

页码：121 / 127

页数：7

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