Biomedical Engineering Reference
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since the curves related to different quantities of the growth factor have al-
most the same slope and do not differ much in the particular values, but may
also be related to the number of cells forming the studied island (as shown in
Figure 2.13 (bottom line, left panel)). For this reason, some simulations are
performed starting with colonies with different densities.
As the number of cells increases, the lattice is taken wider, to avoid over-
lapping problems. For low densities (say, n < 60) the branches are quite long
and thin, so that it can be hypothesized that the colony assumes a star-shaped
configuration, with a little main corpus. For high densities (say, n > 60) the
sprouts tend to become shorter and thicker, while at still higher densities
(say, n > 130) there are limit thresholds for both length and thickness. The
decrement of the length and the relative increment of the thickness are almost
specular and has the consequence that the area of a virtual branch remains
almost constant, independently of the cell density, which can only lead to a
bigger main corpus of the island. The cell density affects also the number of
the branches developing in a time-lapse of 24 h: for very low values (say, n < 8)
there is no development of sprouts, and for high densities (say, n > 108) there
is a constant value for their quantity, as shown in Figure 2.13 (bottom line,
right panel). In the medium range, the number of branches increases with the
number of cells forming the island. The higher quantity of sprouts appearing
in bigger colonies may have two explanations: first, bigger colonies have more
cells available for branching, and then they have wider external surfaces and
so more space for the growth of the sprouts.
In the model it is assumed that the MLP-29 decision to whether extend
or retract a pseudopod depends on the concentration difference between the
retracted and extended position of the pseudopods, regardless the absolute
concentration of the HGF. However, at higher concentrations, we can hypoth-
esize that most HGF receptors will saturate, thus becoming insensitive to
HGF levels, a situation that occurs experimentally and that is possible to find
also in the sprouting process of blood vessel [260]. It is possible to hypothesize
that the viscoelastic properties of the matrix substrate, as well as its chem-
ical composition, may affect the diffusive behavior of the HGF, ultimately
resulting in delayed scattering phenomena with unstable branches.
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