Abstract
Cancer cells require higher oxygen levels and nutrition than normal cells. Cancer cells induce angiogenesis (the development of new blood vessels) from preexisting vessels. This biological process depends on the special, chemical, and physical properties of the microenvironment surrounding tumor tissues. The complexity of these properties hinders an understanding of their mechanisms. Various mathematical models have been developed to describe quantitative relationships related to angiogenesis. We developed a three-dimensional mathematical model that incorporates angiogenesis and tumor growth. We examined angiopoietin, which regulates the spouting and branching events in angiogenesis. The simulation successfully reproduced the transient decrease in new vessels during vascular network formation. This chapter describes the protocol used to perform the simulations.
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