Biomedical Engineering Reference
In-Depth Information
viduals are represented as standard discrete CPM objects
of type = C.
They reside in an isotropic homogeneously distributed extracellular matrix,
a generalized object of type = M. The ARO colony evolves following the
rules given in relation (1.2), where T is an overall motility of the culture and
the Hamiltonian reads as
H(t) = H
adhesion
(t) + H
shape
(t) = H
adhesion
(t) + H
volume
(t) + H
surface
(t);
(2.1)
which, expanding all terms for readers' convenience, becomes:
X
X
H(t)
=
J
C;C
+
J
C;M
+
x
;
x
0
2
0
x
;
x
0
2
0
x
:
(@
x
2@
)\(@
x
0
2@
0
)6=;
(
(
x
)
)=(
0
(
x
0
)
)=C
x
:
(@
x
2@
)\(@
x
0
2@
0
)6=;
(
(
x
)
)=C^(
0
(
x
0
)
)=M
X
surface
(a
surface
(t) A
surface
C
)
2
+
+
X
perimeter
(a
perimeter
(t) A
perimeter
C
)
2
:
+
(2.2)
H
adhesion
(t) has the same form as in Equation (1.5): in particular, since there
is only one type of cell placed in an extracellular medium, the Js reduce to
cell{matrix J
C;M
and cell{cell J
C;C
adhesive strengths. The terms in H
shape
(t)
are instead the energetic constraints regulating the changes in cell dimensions
and shape and are given as in Equation (1.6). Indeed, the target dimensions,
corresponding to the initial measures, and the elastic moduli are the same for
all ARO individuals, i.e., for all
such as (
) = C:
8
<
A
surface
= A
surface
C
;
A
perimeter
= A
perimeter
C
;
:
surface
=
surface
C
;
perimeter
=
perimeter
C
:
In particular, following the experimental observations provided in the previous
section, both the growth rate and the elasticity of the AROs are here assumed
to be negligible, and therefore we set high values of
surface
C
=
perimete
C
.
In the case of ARO aggregates, HGF stimulation is modeled only through
its effects both on the motility of individuals and on their adhesive inter-
actions. In particular, we preliminarily hypothesize a directed proportionality
between the amount of HGF added in the culture and the model parameters T
and J
C;C
: increasing doses of growth factor therefore correspond to increasing
values of the cell agitation rate T and of the intercellular adhesion coecient,
which results in weaker cell{cell contact junctions. J
C;M
remains instead fixed
in each simulation, as HGF stimulation has not been demonstrated to affect
the expression of the activity of integrin molecules.
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