QUALITATIVE ANALYSIS OF A MATHEMATICAL MODEL FOR CAPILLARY FORMATION IN TUMOR ANGIOGENESIS

DOI10.1142/S0218202503002362zbMath1043.92014MaRDI QIDQ3043522

Serdal Pamuk

Publication date: 6 August 2004

Published in: Mathematical Models and Methods in Applied Sciences (Search for Journal in Brave)

zbMATH Keywords

stabilityangiogenesisprobability density functionquasi-steady stateCapillary

Mathematics Subject Classification ID

PDEs in connection with biology, chemistry and other natural sciences (35Q92) Signal detection and filtering (aspects of stochastic processes) (60G35) Medical applications (general) (92C50) Oscillation, zeros of solutions, mean value theorems, etc. in context of PDEs (35B05)

Related Items (10)

Numerical solution of a mathematical model for capillary formation in tumor angiogenesis via the tau method ⋮ The method of lines for the numerical solution of a mathematical model for capillary formation: The role of endothelial cells in the capillary ⋮ Solution of the porous media equation by Adomian's decomposition method ⋮ A 2D mathematical model for tumor angiogenesis: the roles of certain cells in the extra cellular matrix ⋮ MATHEMATICAL TOPICS ON THE MODELLING COMPLEX MULTICELLULAR SYSTEMS AND TUMOR IMMUNE CELLS COMPETITION ⋮ Solutions of a linearized mathematical model for capillary formation in tumor angiogenesis: an initial data perturbation approximation ⋮ The decomposition method for continuous population models for single and interacting species ⋮ An application for linear and nonlinear heat equations by Adomian's decomposition method ⋮ Steady-state analysis of a mathematical model for capillary network formation in the absence of tumor source ⋮ Gaussian curvature: a growth parameter for biological structures

Cites Work

• Mathematical modeling of capillary formation and development in tumor angiogenesis: penetration into the stroma
• A mathematical model for capillary network formation in the absence of endothelial cell proliferation
• Analysis of a mathematical model for the growth of tumors
• A mathematical analysis of a model for capillary network formation in the absence of endothelial cell proliferation
• ON THE EXISTENCE OF SPATIALLY PATTERNED DORMANT MALIGNANCIES IN A MODEL FOR THE GROWTH OF NON-NECROTIC VASCULAR TUMORS
• 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
• Unnamed Item

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