Qualitative analysis of a mathematical model for capillary formation in tumor angiogenesis


Pamuk S.

MATHEMATICAL MODELS & METHODS IN APPLIED SCIENCES, vol.13, no.1, pp.19-33, 2003 (SCI-Expanded) identifier identifier

Abstract

Qualitative analysis of a mathematical model for capillary formation is presented under assumptions that enzyme and fibronectin concentrations are in quasi-steady state. The aim of this paper is to prove mathematically that the long-time tendency of endothelial cells will be towards the transition probability density function of enzyme and fibronectin. Endothelial cell steady-state solution is obtained and a numerical simulation is provided to show that there is a close agreement between the steady-state solution obtained analytically and the numerically calculated steady-state of the related initial value problem, which provides strong evidence for the stability of this steady-state.