This paper presents an extended mathematical model for tumor angiogenesis incorporating oxygen dynamics as a main regulator. We enhance a five-component PDE system describing endothelial cells, proteases, inhibitors, extracellular matrix, and oxygen concentration, with a focus on their spatiotemporal interactions. We establish existence, uniqueness, and boundedness of solutions through a mathematical analysis. A numerical scheme using method of lines and fourth-order Runge-Kutta methods is developed, with proven stability constraints and convergence properties. Numerical experiments demonstrate biologically plausible vascular formation with oxygen-mediated regulation.
Keywords: Angiogenesis; Convergence analysis; Numerical methods for PDEs; Partial differential equations.
© 2025. The Author(s).