Emergence of Taxis and Synergy in Angiogenesis

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Abstract
Angiogenesis, the expansion of the vascular system feeding a tumor, is crucial to both primary tumors long-time growth and for the successful implantation of metastases. We formulate a model that relates the energetic requirements of the cancer cells to the production and diffusion of an angiogenic factor and to the ensuing evolution of neighboring endothelial cells. The model yields predictions for the development of neovascularization and for the increase in the blood flow to the tumor. We show that the directed growth of the vascular net is an emergent property and that therapies targeting different stages of the angiogenic process might have a synergistic effect.