Computational Modeling of Angiogenesis: Towards a Multi-Scale Understanding of Cell–Cell and Cell–Matrix Interactions - Mechanical and Chemical Signaling in Angiogenesis - page 164

models [ 13 , 14 , 22 , 23 ] suggest that autocrine chemotaxis, combined with cell
properties such as contact inhibition of cell elongation, may drive angiogenesis.
Other cell-based angiogenesis model [ 7 , 9 , 10 ] have suggested that autocrine
chemotaxis may not be necessary at all. Moreover, mechanical interactions
between cells and the matrix have not yet been modeled with a cell-based model.
Adding this mechanical interaction to cell-based angiogenesis models will help to
gain a true understanding of the mechanisms involved in angiogenesis
2.2 Sprouting
Sprouting angiogenesis is the formation of new vessels by creating a sprout in the
wall of the existing vessel. This form of angiogenesis is often observed in the
vicinity of hypoxic tissue that secretes angiogenic factors, e.g., a growing tumor,
which activate and attract endothelial cells from the existing vessels [ 25 ].
By stimulating the formation of a new vasculature, a tumor is able to grow and
proliferate. The mechanisms underlying the dynamics of sprouting angiogenesis
are still poorly understood. What mechanisms guide the growing sprout? How do
biochemical and biomechanical interactions of the ECM with cells effect sprout-
ing? Is proliferation required and where is proliferation located in the sprout? How
are tip cells selected in the vessel and what causes sprouts to branch? Computa-
tional models have contributed to a better understanding of these issues.
In corneal angiogenesis sprouting is restricted in absence of proliferation;
sprouts will not reach a tumor when cells are not able to divide [ 26 ]. A continuum
model [ 2 ] describes the change in cell density over time due to cell migration
driven by cell diffusion, chemotaxis and haptotaxis. The initial configuration of the
simulation consists of a blood vessel at one side and a tumor at the other side of the
simulation domain. This tumor secretes a chemoattractant, resulting in a gradient
of chemoattractant that attracts cells towards the tumor. Haptotaxis is induced by
fibronectin that the cells secrete themselves. The highest levels of fibronectin are
present where the cell density is maximum. Therefore, haptotaxis and chemotaxis
work in opposite directions. The continuum model suggests that, in absence of
proliferation, the sprouting is restricted. The authors propose that this is caused
because haptotaxis outweighs chemotaxis and increasing the number of cells
would increase the chemotactic response.
A problem with this model is that it describes cells as a density field, hence it
cannot describe how the sprout breaks up due to lack of proliferation. Therefore,
a discrete modeling approach has been introduced to study cell proliferation in the
sprout [ 8 ]. As illustrated in Fig. 2 a the model mimics a cornea with a lesion in the
center from which VEGF is secreted. A sprout grows from the periphery and
consist of multiple cell types; one leading tip and multiple following stalk cells.
The tip cell migrates towards the center induced by the VEGF gradient. Tip cell
migration is limited by the elasticity of the tip cell and the strength of the adhesion
between stalk cells. Adding proliferation enables unlimited sprout extension.