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In tumors, angiogenesis (conformation of a new vasculature from another primal one) is produced with the releasing of tumor angiogenic factors from hypoxic cells. These angiogenic substances are distributed around the tumor micro-environment by diffusion. When they reach the primal blood vessel bed, the sprouting and branching of a new micro-vascular network is produced. These new capillaries will supply oxygen to cells so that their hypoxic state is overcome. In this work, a new and simple 3D agent-based model to simulate tumor-induced angiogenesis is presented. In this approach, the evolution of the hypoxic conditions in cells along the related conformation of the new micro-vessels is considered. The importance that the relative position of the primal vasculature and tumor structure takes in the final distribution of the new micro-vasculature has also been addressed. The diffusion of angiogenic factors and oxygen has been modelled at the targets by numerical convolution superposition of the analytical solution from the sources. Qualitative and quantitative results show the importance of tip endothelial cells in overcoming hypoxic conditions in cells at early stages of angiogenesis. At final stages, anastomosis plays an important role in the reduction of hypoxia in cells.

A simple agent-based model to simulate 3D tumor-induced angiogenesis considering the evolution of the hypoxic conditions of the cells