UNSPECIFIED (1997) A mathematical model for the capillary endothelial cell-extracellular matrix interactions in wound-healing angiogenesis. IMA JOURNAL OF MATHEMATICS APPLIED IN MEDICINE AND BIOLOGY, 14 (4). pp. 261-281. ISSN 0265-0746

Full text not available from this repository.

Abstract

Angiogenesis, the process by which new blood capillaries grow into a tissue from surrounding parent vessels, is a key event in dermal wound healing, malignant-tumour growth, and other pathologic conditions. In wound healing, new capillaries deliver vital metabolites such as amino acids and oxygen to the cells in the wound which are involved in a complex sequence of repair processes. The key cellular constituents of these new capillaries are endothelial cells: their interactions with soluble biochemical and insoluble extracellular matrix (ECM) proteins have been well documented recently, although the biological mechanisms underlying wound-healing angiogenesis are incompletely understood. Considerable recent research, including some continuum mathematical models, have focused on the interactions between endothelial cells and soluble regulators (such as growth factors). In this work, a similar modelling framework is used to investigate the roles of the insoluble ECM substrate, of which collagen is the predominant macromolecular protein. Our model consists of a partial differential equation for the endothelial-cell density (as a function of position and time) coupled to an ordinary differential equation for the ECM density. The ECM is assumed to regulate cell movement (both random and directed) and proliferation, whereas the cells synthesize and degrade the ECM. Analysis and numerical solutions of these equations highlights the roles of these processes in wound-healing angiogenesis. A nonstandard approximation analysis yields insight into the travelling-wave structure of the system. The model is extended to two spatial dimensions (parallel and perpendicular to the plane of the skin), for which numerical simulations are presented. The model predicts that ECM-mediated random motility and cell proliferation are key processes which drive angiogenesis and that the details of the functional dependence of these processes on the ECM density, together with the rate of ECM remodelling, determine the qualitative nature of the angiogenic response. These predictions are experimentally testable, and they may lead towards a greater understanding of the biological mechanisms involved in wound-healing angiogenesis.

Item Type:	Journal Article
Subjects:	Q Science > QA Mathematics
Journal or Publication Title:	IMA JOURNAL OF MATHEMATICS APPLIED IN MEDICINE AND BIOLOGY
Publisher:	OXFORD UNIV PRESS
ISSN:	0265-0746
Date:	December 1997
Volume:	14
Number:	4
Number of Pages:	21
Page Range:	pp. 261-281
Publication Status:	Published
URI:	http://wrap.warwick.ac.uk/id/eprint/16162

Data sourced from Thomson Reuters' Web of Knowledge

Request changes to a record

Actions (login required)

View Item