Scaling in Vascular Networks: Curvature, Finite-Size Effects, and Applications to Tumor Angiogenesis and Growth

Van Savage (September 1, 2010)

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Metabolic rate, heart rate, and lifespan depend on body size according to scaling relationships that extend over ~21 orders of magnitude and that represent diverse taxa and environments. These relationships for body mass have long been approximated by power laws, but there has been intense debate about the values of exponents (e.g., 1/4 versus 1/3). I will show for mammals that these scaling relationships exhibit systematic curvature in logarithmic space. This curvature explains why different studies find different power-law exponents. I will also show how existing optimal network theory can be modified using finite-size corrections and hydrodynamical considerations to predict curvature. I will distinguish among potential physiological mechanisms by comparing model predictions for the direction and magnitude of the curvature with results from empirical data. For the final half of the talk, I will develop modified network models to describe tumor angiogenesis and vascular structure. These new models will help to compare tumor with normal vasculature, to understand different phases (pre- and post-angiogenesis) of tumor growth, and to describe the formation of a necrotic core.