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. Author manuscript; available in PMC: 2014 Jan 7.
Published in final edited form as: Annu Rev Biomed Eng. 2011 Aug 15;13:10.1146/annurev-bioeng-071910-124729. doi: 10.1146/annurev-bioeng-071910-124729

Figure 6.

Figure 6

Macroscopic-scale functional relationships as emergent phenomena from microscopic models. The volume-averaged behavior of an agent-based model of ductal carcinal in situ (DCIS)—a type of breast cancer where growth is constrained to a breast duct—was analyzed to postulate a Michaelis-Menten type relationship between oxygen (σ) and proliferation (PI) as an emergent phenomenon of the model (80)—see the solid curves above. This hypothesized relationship was later validated by analyzing post-mastectomy Ki-67 immunohistochemical data for proliferation in two separate breast ducts (dashed curves), with excellent qualitative and quantitative agreement (81).