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A mathematical model for pathological angiogenesis

Authors: M. M. Soares, R. D. M. Travasso, A. Diehl

Ref.: XXXVI National Meeting on Condensed Matter Physics, São Paulo, Brasil. (2013)

Abstract: Angiogenesis is an important biological phenomena responsible for many pathologies and have been an intensive target of research in all the world. The knowledge about tumor induced angiogenesis is a challenging problem with relevant consequences for diagnosis and treatment of cancer. In this current work we used a multi-scale phase-field model, proposed by Travasso et al (2011), for understanding the mechanical and biological process behind the endothelial growth. The model focuses in one important protein: Vascular Endothelial Growth Factor (VEGF). This factor have the task of activate endothelial tip cell (ETC), sprouting new vascularization and working to regulate ETCs migration/proliferation. In the other words, VEGF is the principal motor force of angiogenesis. These principles are taken in consideration and were introduced into mathematical model, where is need a computational approach because of their complexity. The familiar form of equations allows to use a simple method of integration, through of finite differences. Furthermore, we uses parallel programming with Message Passing Interface (MPI) to improve the computational efficiency. published results show that this is a good model to describe angiogenesis, providing forecast about endothelial morphology, branches density and diameter vessel of newly formed vascular networks. We show the results for the new parallel version of code in three dimensions.