Biomedical Engineering Reference
In-Depth Information
in most experimental cases to avoid cell overlapping and to compensate for
the absence of mitosis. In fact, to model a pure migration assay, the overall
observation period is set equal to 12 h. This choice ensures a sucient distance
from critical events, such as culture splitting and cell cycle synchronization.
For the same reason, we also neglect cell apoptosis.
The boundary conditions of domain are zero ux at the lateral sides (i.e.,
at x = 0 and x = 350) and periodic at the others (i.e., at y = 0 and y = 500).
The no-flux assumption at x = 0 is appropriate as the cell population has
grown to confluence, and therefore there is no space for cells to move in that
direction. The periodic boundary conditions at the top and the bottom of the
lattice are also reasonable since the model is intended to examine a section
of a much larger well. The no-flux condition at x = 350 is caused by the fact
that this border reproduces the wall of the experimental dish.
Initially, the extracellular level of HGF is zero, as well as the intracellular
amounts of messenger proteins. The basal properties of the cells, listed in Table
C.5, have been evaluated following biological considerations listed both in the
previous section and in Chapter 2. Indeed, they have been determined through
preliminary simulations that showed the model consistency in a wide range of
parameters. As usually done, the position of each ARO cell is established
by calculating the position of its center of mass. Similarly, its path is defined
as the path of its center of mass and its speed, v, as the speed of its center of
mass.
The directional component of cell motion is measured by the linearity L,
which is defined as the ratio between the x-component of the final displacement
of a cell (i.e., of its center of mass, in the direction of the wound) and the total
length of its path within the observation period [251]. Its value ranges from
0 to 1, being close to 0 when the cell movement is almost isotropic, with no
directional trend, and getting larger for motions clustered toward the center
of the wound.
In the circular charts, the final displacement of a cell is represented by
the polar coordinates of the final position of its center of mass, as in [23]. As
is typically done in experimental works, the healing capacity of the overall
population is calculated by measuring the mean percentage of the recolonized
scratch over time:
X
1
N
1
d
i
(t)
d
0
D(t) =
100;
(5.10)
i=1
where d
0
is the initial width of the scratch (175 px 0.35 mm) and d
i
(t)
is the distance across the wound between a cell at the front and the right
border of the domain . The number 100 is used to avoid the biases toward
accounting for outlier individuals. Obviously, D(t
final
) quantifies the invasive
distance at the end of the observation period. Results of the healing capacity
of the culture are shown as means with standard deviations (SDs) over 20
independent simulations.
The statistical analysis of the migratory properties of the three subpop-
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