A 2D mathematical model for tumor angiogenesis: the roles of certain cells in the extra cellular matrix

DOI10.1016/j.mbs.2018.10.007zbMath1408.35064OpenAlexW2898274060WikidataQ58546672 ScholiaQ58546672MaRDI QIDQ669096

İrem Çay, Serdal Pamuk, Ali Sazcı

Publication date: 20 March 2019

Published in: Mathematical Biosciences (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.mbs.2018.10.007

zbMATH Keywords

mathematical modelingnumerical solutiontumor angiogenesiscapillary formation

Mathematics Subject Classification ID

Reaction-diffusion equations (35K57) Initial-boundary value problems for second-order parabolic equations (35K20) PDEs in connection with biology, chemistry and other natural sciences (35Q92) Cell movement (chemotaxis, etc.) (92C17)

Cites Work

• Mathematical modeling of capillary formation and development in tumor angiogenesis: penetration into the stroma
• Modelling and mathematical problems related to tumor evolution and its interaction with the immune system
• A mathematical model of tumor hypoxia targeting in cancer treatment and its numerical simulation
• Coupled modelling of tumour angiogenesis, tumour growth and blood perfusion
• A mathematical model of tumour angiogenesis, regulated by vascular endothelial growth factor and the angiopoietins
• A survey of models for tumor-immune system dynamics
• QUALITATIVE ANALYSIS OF A MATHEMATICAL MODEL FOR CAPILLARY FORMATION IN TUMOR ANGIOGENESIS
• A mathematical model for the roles of pericytes and macrophages in the initiation of angiogenesis. I: The role of protease inhibitors in preventing angiogenesis

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