American Institute of Mathematical Sciences

Advanced
2003, 2003(Special): 817-826. doi: 10.3934/proc.2003.2003.817

Numerical simulation of capillary formation during the onset of tumor angiogenesis

Michael W. Smiley 1, , Howard A. Levine 1, and  Marit Nilsen Hamilton 2,

1. 

Department of Mathematics, Iowa State University, United States, United States
2. 

Department of Biophysics, Biochemistry & Molecular Biology, Iowa State University, United States

Received  September 2002 Published  April 2003

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.
Keywords: convection-dominated diffusion, conservative characteristic method., angiogenesis, chemotaxis.
Mathematics Subject Classification: 35K55, 65M06, 65M25, 92C17, 92C4.
Citation: Michael W. Smiley, Howard A. Levine, Marit Nilsen Hamilton. Numerical simulation of capillary formation during the onset of tumor angiogenesis. Conference Publications, 2003, 2003 (Special) : 817-826. doi: 10.3934/proc.2003.2003.817
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