Biomedical Engineering Reference
In-Depth Information
The simulated cancer cells, called of type = E, are dened as bicom-
partmentalized units, composed of the nucleus, = N, and the surrounding
cytosol, = C. Also, in this case, they are not assigned an internal vector:
the purpose of the model is to analyze the influence on their movement of
geometrical and elastic characteristics and not of their molecular state. The
extracellular environment is dierentiated into a medium-like state, = M,
and a polymeric-like state, = P. The medium-like state represents the stan-
dard mixture of soluble components, which, together with the water solvent,
compose the interstitial fluid. The polymeric state reproduces instead the
structured wafer, which, after subsequent replica molding processes, is typi-
cally covered with fibronectin-based solutions and used in the standard micro-
fabricated channel migration chip; see [332] and the references therein.
The system Hamiltonian is defined as
H(t) = H
shape
(t) + H
adhesion
(t) + H
persistence
(t):
(10.1)
For each cell , H
shape
models the geometrical attributes of its subcellular
compartments, which are written as nondimensional relative deformations in
the quadratic form of Equation (4.6). Assuming that cells do not significantly
grow during migration (which is consistent with the time-scale of the phe-
nomenon of our interest), the fluctuations of their volumes are again kept
negligible with high constant values
volume
;N
=
volume
;C
1;
for any individual and for
such that (
) 2fN;Cg. The stiness of the
intracellular compartments (given, respectively, by
surface
;
=
surface
;C
, for
(
) = C and
surface
=
surface
;N
, for (
) = N) will be instead discussed
;
in the results section.
H
adhesion
is differentiated in the contributions due to either the generalized
contact tension between the nucleus and the cytoplasm within the same cell,
or to the effective adhesion between cells or between a cell and a channel wall.
In particular, J
int
N;C
0 implicitly models the forces exerted by intermediate
actin filaments and microtubules to anchor the nucleus to the cell cytoskeleton,
preventing cells from fragmenting. A null contribution is instead given to the
adhesive interactions between a moving cell and an extracellular component
(i.e., we assume J
ext
E;M
= J
ext
E;P
= 0). This choice, successfully used in another
similar model of in vitro cell migration [350], is done to analyze the direct
influence of cell deformability on its motile behavior, and is consistent with
the experimental literature, which widely demonstrates that most cell lines
display sustained amoeboid motility in confined environments in a poorly
adhesive mode [172, 225, 332]. J
ext
E;E
is nally kept high to avoid cell{cell
adhesive interactions that may affect the early phases of their movement (i.e.,
on the flat surface outside the channels).
Finally, if moving cells are able to polarize, i.e., to differentiate in a lead-
ing and a trailing surface, they display a directional movement dictated by
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