Vascular remodelling of an arterio-venous blood vessel network during solid tumour growth

Abstract

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On the importance of the submicrovascular network in a computational model of tumour growth

“…The interdistance measured between the vessels in a same plane is around 100 μm. This corresponds to data from the literature (Secomb et al, 2004;Welter et al, 2008Welter et al, , 2009). We will consider two cases in the simulations, one without the SMVN, related to a weakly oxygenated tissue, and the other one integrating this SMVN (in addition to the microvascular network extracted from the experimental images).…”

“…Vessel sprouting Endothelial cells forming the parent vessel walls start to detach from one another, proliferate, migrate and invade to form some sprouts under the stimulating effect of VEGF (Qutub and Popel, 2009;Welter et al, 2009). We define a sprout as the tip of a growing vessel.…”

“…Vessel sprouting inside the tumour is different than in the normal tissue. Indeed, the tumour changes the nature of the vessel wall by stopping angiogenic sprouting after a time delay t EC (switch) following the growth of the tumour over the considered vessel (Welter et al, 2009). …”

“…In particular, when the wall shear stress τ w is too low, vessels tend to collapse. In our computational model, we assume that if the wall shear stress falls below a threshold value τ coll , that is τ w b τ coll then the vessel has a mean survival time t EC (death) (Welter et al, 2009). The expression of τ w is given next.…”

Modeling the effect of chemotaxis on glioblastoma tumor progression

“…Capillary vessels were added to connect arteries with veins when the distance between nodes was less than 200 lm, each node has less than three vessels, and the radius of those vessels was less than 20 lm. The radius of the vessels was calculated using Murray's rule r 71 where p, s1 and s2 indicate the parent and the children vessels, respectively. The oxygen concentration was computed by solving a PDE similar to the one described in the next subsection.…”