ArticleJournal of mathematical biology2025
Analytical and numerical properties of an extended angiogenesis PDEs model.
Article in Journal of mathematical biology, 2025. The graph could read no effect estimate from its abstract, so it casts no vote on the map. Cited by 1 paper.
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The abstract states no effect estimate the extractor could read, or names no intervention and outcome on the map, so this paper lights no cell and moves no belief. It is still indexed, cited and linked below.
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Who cites it
1 citing paper in PubMed.
- Numerical analysis & modelling in the life sciences: a topical collection in honor of Ezio Venturino.Journal of mathematical biology · 2026Article
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2 authors.
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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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