Computational Models of Vascularization and Therapy in Tumor Growth - Mechanical and Chemical Signaling in Angiogenesis - page 233

Fig. 5 Schematic view of
the model downstream the
VEGFR receptor leading to
the activation of the calcium
channel. Adapted from [ 56 ]
diffusion of VEGF in the extracellular domain, the reception of signals via VEGF
receptors located in the membrane subcompartment of the cell and their inter-
nalization and recycling, the activation of mechanotransduction pathways via the
formation of cadherin-cadherin junctions, and the activation of the related sig-
naling cascades within the cytosol. The expressions of specific molecules then
feedback on the value of the modeling parameters of the cellular Potts model
determining motility, adhesion and polarization. A schematic view of the multi-
scale structure of the model is proposed Fig. 6 .
b. Computational models of cell and vascular network organization.
Another aspect that should be included in attempting a multiscale description of
angiogenesis is the modeling of vascular network organization and structure.
It is known that in the embryo, the primitive vascular plexus forms through the
process of vasculogenesis. In this process mesoderm-derived precursors of endo-
thelial cells assemble by directed cell migration and cohesion. The resulting
organization is a network characterized by a polygonal structure having a precise
size that is found to be functional for oxygen transport into the tissues. In spite of the
subsequent remodeling processes, this characteristic is maintained in the adult body
where the capillary network embedded in the tissues and stemmed by the vascular
tree has the same geometric shape of the minimal unit participating in the formation
of the embryonic vascular network and is optimal for metabolic exchange.
The ability to form networking capillary tubes is a cell autonomous property of
endothelial cells. At the site of vessel formation, soluble stimuli released by
neighbouring cells modify the genetic program of endothelial cells allowing them
to be responsive to permissive cues coming from the extracellular environment
[ 66 ]. Several in vitro models support this concept. In particular, it is well known
that culturing endothelial cells on a gel-scaffold markedly accelerates their mor-
phological differentiation in to geometric tubular networks, which are almost