Flow-correlated dilution of a regular network leads to a percolating network during tumor-induced angiogenesis

Regular Article


We study a simplified stochastic model for the vascularization of a growing tumor, incorporating the formation of new blood vessels at the tumor periphery as well as their regression in the tumor center. The resulting morphology of the tumor vasculature differs drastically from the original one. We demonstrate that the probabilistic vessel collapse has to be correlated with the blood shear force in order to yield percolating network structures. The resulting tumor vasculature displays fractal properties. Fractal dimension, Micro-Vascular Density (MVD), blood flow and shear force have been computed for a wide range of parameters.


87.18.-h Biological complexity 64.60.ah Percolation 61.43.Hv Fractals; macroscopic aggregates (including diffusion-limited aggregates) 


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Copyright information

© EDP Sciences, SIF, Springer-Verlag Berlin Heidelberg 2009

Authors and Affiliations

  1. 1.Department of Neurobiology, Physiology and BehaviorUniversity of CaliforniaDavisUSA

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