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


Pamuk S.

MATHEMATICAL MODELS & METHODS IN APPLIED SCIENCES, cilt.13, ss.19-33, 2003 (SCI İndekslerine Giren Dergi) identifier identifier

  • Cilt numarası: 13 Konu: 1
  • Basım Tarihi: 2003
  • Doi Numarası: 10.1142/s0218202503002362
  • Dergi Adı: MATHEMATICAL MODELS & METHODS IN APPLIED SCIENCES
  • Sayfa Sayıları: ss.19-33

Özet

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.