Numerical simulation of capillary formation during the onset of tumor angiogenesis

Michael W. Smiley; Howard A. Levine; Marit Nilsen Hamilton

doi:10.3934/proc.2003.2003.817

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2003, Volume 2003: 817-826. Doi: 10.3934/proc.2003.2003.817 open access

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Numerical simulation of capillary formation during the onset of tumor angiogenesis

1.
Department of Mathematics, Iowa State University
2.
Department of Biophysics, Biochemistry & Molecular Biology, Iowa State University

Received: August 31, 2002

Published: March 2003

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Abstract

A recently proposed mathematical model for turor angiogenesis consists of a coupled system of ordinary and partial differential equations, some of which are strongly convection dominated diffusion equations. A numerical method based on the use of characterics, which is mass conserving, can be used to effectively handle this feature. The model and the numerical method are presented.

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Mathematics Subject Classification: 35K55, 65M06, 65M25, 92C17, 92C45.

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