Biomedical Engineering Reference
In-Depth Information
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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