https://doi.org/10.1140/epje/i2009-10513-8
Regular Article
Flow-correlated dilution of a regular network leads to a percolating network during tumor-induced angiogenesis
Department of Neurobiology, Physiology and Behavior, University of California, 95616, Davis, CA, USA
* e-mail: rpaul@ucdavis.edu
Received:
14
April
2009
Revised:
24
June
2009
Accepted:
2
September
2009
Published online:
24
September
2009
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.
PACS: 87.18.-h Biological complexity – / 64.60.ah Percolation – / 61.43.Hv Fractals; macroscopic aggregates (including diffusion-limited aggregates) –
© EDP Sciences, SIF, Springer-Verlag Berlin Heidelberg, 2009