TITLE:
Analysis on a Mathematical Model for Tumor Induced Angiogenesis
AUTHORS:
Richard C. Ewool, Zachariah Sinkala
KEYWORDS:
Explicit Stabilized Runge-Kutta Methods, Angiogenesis, Inhibitors, Rat Cornea, Source Term
JOURNAL NAME:
Journal of Applied Mathematics and Physics,
Vol.2 No.7,
June
25,
2014
ABSTRACT: Tumor-induced angiogenesis is the process by which unmetastasized tumors
recruit red blood vessels by way of chemical stimuli to grow towards the tumor
for vascularization and metastasis. We model the process of tumor-induced
angiogenesis at the tissue level using ordinary and partial differential
equations (ODEs and PDEs) that have a source term. The source term is
associated with a signal for growth factors from the tumor. We assume that the
source term depends on time, and a parameter (time parameter). We use an explicit
stabilized Runge-Kutta method to solve the partial differential equation. By
introducing a source term into the PDE model, we extend the PDE model used by
H. A. Harrington et al. Our results
suggest that the time parameter could play some role in understanding
angiogenesis.