Computational Modeling of Angiogenesis: Towards a Multi-Scale Understanding of Cell–Cell and Cell–Matrix Interactions - Mechanical and Chemical Signaling in Angiogenesis - page 161

Fig. 1 Overview of vascular network formation. a Shows a vasculature grown in vitro with
HUVEC on Matrigel. b Illustrates the networks formed with the mechanical continuum model [ 4 ].
c Shows the outcome of the chemical continuum model [ 5 ]. d and e Show the networks formed with
the chemical cell-based model, respectively with contact inhibition (d)[ 14 ] or cell elongation
(e)[ 13 ]. f Illustrates the networks formed with the cell-based model with preferential attraction to
elongated structures [ 9 ]. All images were reproduced with the publishers permission
be required for network formation which contradicts the observations by Manoussaki
et al. [ 3 ].
Both previous models consider mechanical interactions between cells and the
matrix to be the driving forces for network formation. Serini et al. [ 5 , 17 ] proposed
that chemotaxis is the driving force of network formation [ 5 ]. In the in vitro
models cells move predominantly towards regions of high cell density suggesting
that the cells are attracted by a chemoattractant secreted by the cells. Therefore,
the computational model assumes that cells secrete a chemoattractant to which
cells move preferentially. This model produces network-like patterns as shown in
Fig. 1 c. Two important predictions are made based on this model. First, the model
predicts an optimal cell density for the formation of stable vascular networks and
second, the size of the meshes in the network depend on the diffusivity and decay
rate of the chemoattractant.
The mechanical and chemical hypotheses for vascular network formation have
also been combined in one mechanochemical model [ 18 ]. This continuum model
hypothesizes that network formation consists of two stages. First, cells move
upwards chemical gradients. Second, at higher local cell density, the cells do not
sense the gradient, but the high cell density signals them to start remodeling the
matrix. This then attracts cells to the high density regions. The mechanochemical