Biomedical Engineering Reference
In-Depth Information
their longer axis, implemented with a term analogous to Equation (2.4). In
particular, t = 60 MCS, whereas
pers
, which controls the persistence time,
is again a function of the length of the cell:
L
(t)
L
0
1
pers
(t) =
pers;0
;
(10.2)
As in Equation (6.4), L
is the current length of the longer axis of the cell,
which is approximated with an ellipsoid [260], and L
0
is the initial cell diame-
ter. Obviously L
L
0
, since we have assumed that the cell deforms but does
not grow during migration.
Given the Hamiltonian, the transition probability of a spin flip has the form
of Equation (4.24). In particular, we use p(T
(t)) = tanh(T
(t)). Indeed,
for each cell and for (
) = N, T
;
= T
;N
gives the agitation rate
of its nucleus, while, for (
) = C, T
;
= T
;C
is as usual a measure of
the intrinsic motility of the overall individual. Indeed, for each cell, T
;N
is a
low value (< 1), resulting in the passive motion of the nucleus, which, unable
to move autonomously, is dragged by the surrounding cytosol, characterized
instead by a high T
C
1 (see Chapter 6). The matrix structure is instead
fixed (i.e., T
P
= 0). A summary of the parameters used in the model is given
in Table C.11.
10.3 Simulations
The simulation domain R
3
is a 480 288 48 regular grid, with periodic
boundary conditions in the y direction and no flux in the others. The charac-
teristic size of each grid site is 1 m. The lattice reproduces a micro-fabricated
device with channel structures of various widths and a planar surface just out-
side their entrances; see Figure 10.1. This architecture is typically used in the
literature to analyze cell migration both on open spaces and through precisely
confined environments; see [332] and the references therein. The temporal res-
olution of the model is an MCS, which is set to correspond to 2 s in order to
compare the simulated cellular dynamics with the relative experimental ob-
servations. The overall observation time is set equal to 8 h ( 14400 MCS) to
ensure the development of suciently long migration paths, as done again in
[332]. Initially, the cells are seeded on the planar substrate in close proximity
of the channel entrances and display an unpolarized morphology. Indeed, they
are hemispheres with a diameter of 30 m, while the nucleus, whose location
and geometry is estimated from experimental images, is a central sphere with
a diameter of 10 m. These dimensions, given in Table C.11, reect the mean
measures of human pancreatic epithelial cancer cells (Panc-1) [28, 332].
Following the definition used in [332], we here distinguish cell migratory
behavior as follows:
Search WWH ::
Custom Search