Mathematical Models and Methods in Applied Sciences · 2003 · 24 citations · 17 references
MedicineBiophysicsCancer BiologyBiological Systems ModelingCell BiophysicsTumor MicroenvironmentAngiogenesisAngiogenesis In CancerInitial ConditionsMathematical BiologySteady-state AnalysisVascular TissueAngiogenesis ModelingInitial Value Problem FormulationLong-time BehaviorNumerical SimulationQuasi-steady-state ApproximationSteady-state SolutionsTumor Angiogenesis ModelsTumor Growth Modeling
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.
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