Biomedical Engineering Reference
In-Depth Information
in [250], the movement of cells has been biased towards direction of principal
strains of the underlying matrix, while in [289], the authors have added a
cell sensitivity to matrix density gradients (i.e., the haptotactic mechanism)
and long-range interactions in matrix stretching, due to its fibrous nature.
In this regard, the mechanical and topological properties of the substrate
could also be characterized. For example, dense protein matrices, trapping a
number of growth factor molecules, slow the diffusion of the morphogen and,
causing steeper gradients, alter cell chemical responses. Moreover, anisotropic
substrates drive cell migration and interfere with the network formation, es-
pecially in a three-dimensional patterning.
The constitutive relations linking the Potts parameter to the internal state
of cell compartments are the same as in the case of the motion of the single cell
described in the previous chapter. In particular, it is useful to underline that,
in a multicellular system, the relation assumed for the chemotactic coecient
represents a further strong improvement of this work with respect to classic
CPMs (see, for example [259, 260, 261]). In fact, therein, all the cells of the
same type feature the same chemical sensitivity, despite of their individuality
and their internal state (here defined by the intracellular calcium level).
7.2.2 Molecular-Level Model
VEGF evolution is again described by Equation (6.5). However, the growth
factor is no longer produced by an exogenous source, but is autocrinally se-
creted by TECs at a constant rate
v
(see [360]). The VEGF production term
therefore reads as
S = S(x;t) =
v
;
(7.1)
where x belongs to the external surface of the cell PM (i.e., (
(
x
)
) = M
and 9x
0
2
0
x
: (
(
x
0
)
) = C). The model of the agonist-induced intracellu-
lar dynamics is also the same as in the case of the single cell. In particular,
Equations (6.7), (6.8), and (6.10) work for each individual, and the extracel-
lular calcium profile is again given by (6.14), with the flux exchanges to be
considered obviously with all cells.
7.3 Simulations in Standard Conditions
The domain consists in a 500 500 square lattice, where each site is equiv-
alent to 4 m
2
. Therefore, represents a section of a 24-well plate of size
L
= 1 mm. The experimental time is set to 10 s per MCS: for this choice
the simulated TECs move with nearly the experimental velocity of vascular
cells ( 25 m/h [261, 309]) and the overall patterning has a comparable time
scale ( 12 h [133]).
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