Biomedical Engineering Reference
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dynamics are explicitly approached with a continuous model, which follows
the approaches presented in the literature, based on experimental data mainly
obtained from electrophysiological and fluorometric measurements, provided
on different cell lines [132, 194, 217, 283, 371]. All the levels of the model are
as usual explicitly integrated and fed back over the whole simulations.
6.2.1 Cell-Level Model
The TEC is a three-dimensional compartmentalized individual of type
() = E, as depicted in Figure 6.2. In particular, it is dierentiated in the
nucleus, of type = N and in the surrounding cytosol, of type = C. In
this case, the plasma envelope is not explicitly identified. The extracellular
medium is classically represented as a generalized cell = M, which is as-
sumed to be static, passive, and homogenously distributed throughout the
simulation domain, forming no large-scale structures and thus without geo-
metric constraints.
The internal state vectors of the sub-cellular compartments are as follows:
for
such that (
) 2fC;Ng, s
;
(x;t) = (a(x;t);n(x;t);c(x;t)) 2
R
3
+
, where a(x;t) corresponds to the local concentration of AA, n(x;t)
of NO, and c(x;t) of Ca
2+
.
The system Hamiltonian is given by:
H(t) = H
shape
(t) + H
adhesion
(t) + H
chemotaxis
(t) + H
persitence
(t): (6.1)
H
shape
= H
volume
+ H
surface
takes into account of cell shape growth and
deformations with elastic-like terms in the form of (4.6), where the target
dimensions of the sub-units are their initial measures. Cell volume fluctuations
are kept negligible, within a few percent, by high constant values for
volume
;
for
such that (
) 2 fC;Ng, as done in [259]. Moreover, because cell
nuclei do not strongly deform, we set a high value also for
surface
;
=
surface
;N
when (
) = N. Instead, when (
) = C,
surface
;
is a measure of the
ease with which the TEC changes its shape due to cytoskeletal remodeling.
As shown in [32], this is mediated by the actin{myosin interactions and re-
organizations that is in turn facilitated by the presence of free calcium ions.
Therefore, for (
) = C, we set:
s
sur
;
(x;t) = s
sur
;A
(x;t) = (c(x;t));
;
(s
sur
;A
;
(x;t)) = f
sur
(s
sur
;A
;
(x;t)) =
sur
0
e
k
e
c
(t)
;
where c
(t) = [c
(t)=C
0
] 1 is a positive value, since c
(t) =
P
x
2
c(x;t)
corresponds to the total concentration of the ion in cell at time t, and
surface
;
(t) =
surface
;
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