Flow-correlated dilution of a regular network leads to a percolating network during tumor-induced angiogenesis.
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.
Paul
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Department of Neurobiology, University of California, Davis, CA 95616, USA. rpaul@ucdavis.edu
D043925:Angiogenesis Inducing Agents / Q000097:blood / Q000378:metabolism*; D003198:Computer Simulation; D017709:Fractals; D006801:Humans; D008954:Models, Biological; D009369:Neoplasms / Q000097:blood / Q000098:blood supply* / Q000473:pathology*; D009389:Neovascularization, Pathologic / Q000097:blood / Q000473:pathology*; D012039:Regional Blood Flow; D012212:Rheology; D033081:Shear Strength; D013269:Stochastic Processes
D043925:Angiogenesis Inducing Agents