Tumour induced angiogenesis as a reinforced random walk: Modelling capillary network formation without endothelial cell proliferation

DOI10.1016/S0895-7177(02)00129-2zbMath1021.92016OpenAlexW1972477563MaRDI QIDQ1410106

I. P. Wallis, Sleeman, Brian D.

Publication date: 14 October 2003

Published in: Mathematical and Computer Modelling (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/s0895-7177(02)00129-2

zbMATH Keywords

reinforced random walkschemotaxishaptotaxistumour angiogenesis

Mathematics Subject Classification ID

Medical applications (general) (92C50) Applications of Brownian motions and diffusion theory (population genetics, absorption problems, etc.) (60J70) Cell movement (chemotaxis, etc.) (92C17)

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Cites Work

• Unnamed Item
• A mathematical model for capillary network formation in the absence of endothelial cell proliferation
• Continuous and discrete mathematical models of tumor-induced angiogenesis
• A mathematical analysis of a model for tumour angiogenesis
• A mathematical analysis of a model for capillary network formation in the absence of endothelial cell proliferation
• A System of Reaction Diffusion Equations Arising in the Theory of Reinforced Random Walks
• Aggregation, Blowup, and Collapse: The ABC's of Taxis in Reinforced Random Walks
• Reinforced random walk
• A mathematical model for the roles of pericytes and macrophages in the initiation of angiogenesis. I: The role of protease inhibitors in preventing angiogenesis
• Mathematical modeling of the onset of capillary formation initiating angiogenesis