A mathematical analysis of a model for capillary network formation in the absence of endothelial cell proliferation

DOI10.1016/S0893-9659(99)00132-9zbMath0963.92025OpenAlexW2086817170MaRDI QIDQ1975322

M. A. J. Chaplan, Sleeman, Brian D., Alexander R. A. Anderson

Publication date: 9 April 2000

Published in: Applied Mathematics Letters (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/s0893-9659(99)00132-9

zbMATH Keywords

angiogenesischemotaxisendothelial cellsSturm-Liouville problemhaptotaxis

Mathematics Subject Classification ID

Initial-boundary value problems for second-order parabolic equations (35K20) PDEs in connection with biology, chemistry and other natural sciences (35Q92) Medical applications (general) (92C50) Cell biology (92C37)

Related Items (9)

Mathematical models of tumour angiogenesis ⋮ Tumour induced angiogenesis as a reinforced random walk: Modelling capillary network formation without endothelial cell proliferation ⋮ Stochastic transitions in a mathematical model for capillary network formation ⋮ QUALITATIVE ANALYSIS OF A MATHEMATICAL MODEL FOR CAPILLARY FORMATION IN TUMOR ANGIOGENESIS ⋮ COMPUTING HIGHLY ACCURATE SOLUTIONS OF A TUMOUR ANGIOGENESIS MODEL ⋮ The decomposition method for continuous population models for single and interacting species ⋮ A review of mathematical models for the formation of vascular networks ⋮ Steady-state solutions of a generic model for the formation of capillary networks ⋮ A chemotaxis model motivated by angiogenesis

Cites Work

• A mathematical model for capillary network formation in the absence of endothelial cell proliferation
• Continuous and discrete mathematical models of tumor-induced angiogenesis
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