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Numerical simulation of capillary formation during the onset of tumor angiogenesis

Pages: 817 - 826, Issue Special, July 2003

 Abstract        Full Text (180.7K)              

Michael W. Smiley - Department of Mathematics, Iowa State University, United States (email)
Howard A. Levine - Department of Mathematics, Iowa State University, United States (email)
Marit Nilsen Hamilton - Department of Biophysics, Biochemistry & Molecular Biology, Iowa State University, United States (email)

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.

Keywords:  angiogenesis, chemotaxis, convection-dominated diffusion, conservative characteristic method.
Mathematics Subject Classification:  35K55, 65M06, 65M25, 92C17, 92C45.

Received: September 2002; Published: April 2003.