3D CA model of tumor-induced angiogenesis

Abstract

Tumor-induced angiogenesis is the formation of new sprouts from preexisting nearby parent blood vessels. Computationally, tumor-induced angiogenesis can be modeled using cellular automata (CA), partial differential equations, etc. In this present study, a realistic physiological approach has been made to model the process of angiogenesis by using 3D CA model. CA technique uses various neighborhoods like Von-Neumann neighborhood, Moore neighborhood, and Margolus neighborhood. In our model Von-Neumann neighborhood has used for distribution of some significant chemical and non-chemical tumor angiogenic factors like vascular endothelial growth factor, endothelial cells, O2, extracellular matrix, fibronectin, etc., and Moore neighborhood is used for distribution of matrix metalloproteinase. In vivo tumor environment all the factors are not distributed equally in the extracellular matrix. Distributions of those chemical and nonchemical factors depend on their source, nature and function. To keep similarity with the biological tumor environment, we have formulated initial distributions of the chemical and non-chemical factors accordingly. We have started the simulation in MATLAB with this initial distribution. Number of sprouts randomly varies from one run to another. We observed that sprouts are not originating from the same locations in each simulation. A sprout has high sensitivity of VEGF and fibronectin concentrations. sVEGFR-1 always tries to regress the sprout. When two or more sprouts come closer, they merge with each other leading to anastomosis. Sufficient number of tip cells may cause sprout towards tumor.