PoC - Physics of Cancer - Annual Symposium
Contributed Talk, Friday, 11:45 – 12:00  
Physical determinants of vascular network remodeling during tumor growth

Michael Welter, Heiko Rieger

Saarland University, Theoretical Physics, PF 151150, 66041 Saarbrücken, Germany

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Tissues in living organisms need a persistent supply with oxygen and other nutrients provided by the vascular blood flow through the vessel network threading the tissue. Fast proliferating cells in a growing tumor have an increased oxygen/nutrient demand, for which reason tumors usually cannot grow beyond a size of 1-2mm3 without modifying the original vasculature. This modification, comprising a substantial increase of microvascular density (MVD) in the growth zone of the tumor, is denoted as angiogenesis, the creation of new blood vessels from existing ones. 
The emerging tumor vasculature is in many respects different from the hierarchically organized arterio-venous blood vessel network in normal tissues. The expected increase in MVD is usually observed in the periphery of the tumor, whereas the morphology of the vasculature in the tumor center is characterized by decreased MVD, dilated vessels, and regions of necrotic tumor tissue. The resulting tumor-specific capillary network is very heterogeneous, composed of dense and void regions, and has geometric properties different from normal arterio-venous or normal capillary networks. 
Besides pro- and anti-angiogenic molecular factors, mechanical, hydrodynamical and collective processes must be involved in the process that transforms or remodels the original arterio-venous blood vessel network into a tumor-specific vasculature. In this paper we want, with the help of a theoretical model [1-4] to address the physical determinants of the dynamical evolution, final morphology and blood flow properties of an emerging tumor blood vessel network. in which a growing tumor transforms a hierarchically organized arterio-venous blood vessel network into a tumor specific vasculature is analyzed. The determinants of this remodeling process involve the morphological and hydrodynamic properties of the initial network, generation of new vessels (sprouting angiogenesis), vessel dilation (circumferential growth), blood flow correlated vessel regression, tumor cell proliferation and death, and the interdependence of these processes via spatio-temporal changes of blood flow parameters, oxygen / nutrient supply and growth factor concentration fields. The emerging tumor vasculature is non-hierarchical and compartmentalized into different zones. It displays a complex geometry with necrotic zones and "hot spots" of increased vascular density and blood flow of varying size. The origin of these hot spots is discussed. The blood vessel network transports drug injections efficiently, but the computation of the interstitial fluid flow shows that most of the drug is quickly washed out from the tumor after extravasation.
 
Fig. 1: Visualization of the vessel and tumor configuration generated by a simulation of the model at different times (100h, 400h, 500h). A cut through the cubic simulation volume is shown. The vessels are depicted as cy-linders which are color coded by their blood pressure (blue = 0 kPa; red = 12 kPa). Non-circulated vessels are shown in gray. The yellow spheroid in the center shows the tumor with necrotic regions in the later stage. 
 
[1] D.-S. Lee, K. Bartha, H. Rieger, Phys. Rev. Lett. 96: 058104 (2006).
[2] K. Bartha, H. Rieger, J. Theor. Biol. 241: 903 (2006).
[3] M. Welter, K. Bartha, H. Rieger, J. Theor. Biol. 259: 405 (2009).
[4] M. Welter, H. Rieger, Europ. Phys. J. E 33: 149 (2010).
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