  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.
