Analytical and numerical properties of an extended angiogenesis PDEs model
Pasquale De Luca, Livia Marcellino
TL;DR
This paper introduces a new mathematical model for tumor angiogenesis that includes oxygen dynamics and proves its mathematical properties.
Contribution
The novel contribution is extending an angiogenesis model with oxygen dynamics and proving its mathematical properties.
Findings
The model establishes existence, uniqueness, and boundedness of solutions.
A stable numerical scheme with convergence properties is developed.
Numerical experiments show biologically plausible vascular formation regulated by oxygen.
Abstract
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.
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Taxonomy
TopicsMathematical Biology Tumor Growth · Kruppel-like factors research · Angiogenesis and VEGF in Cancer