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target cytokine secretion amount (which increases the cytokine concentration in
the position where the cell is located),
ψ
out
max
is the maximum secretion allowed
and
α
is the cell activation level. The secretion function is shown in figure 4, for
two maximum secretion values (
ψ
out
max
=2and
ψ
out
max
=8).
Δψ
(
α
)
out
=
ψ
out
max
·
α
(8)
This equation has been chosen for both simplicity and ease of calculation, so
that the simulation of the model is not limited by an excessive computational
load. As previously mentioned, no assertion about the validity of this modelling
can be performed for now, due to the absence of numerical experimental data.
5
Results and Discussion
In order to verify the response of the designed model, a simple simulation scenario
was selected. The artificial tissue is represented by a 3x3 square region, with the
cell positioning shown in figure 5, where
E
and
R
are used to designate the
cell type (effector and regulatory, respectively), and the number located right
under the cell type designates the cell number, to be used when analysing the
simulation results, with the x and y axis in the horizontal and vertical directions,
respectively.
Fig. 5.
Artificial tissue where the simulation took place
The cell populations for the simulation are composed of, according to figure
5, 6 effector cells and 1 regulatory cell. Therefore, the initial cell population is
composed of 14.3% of regulatory cells, a number close to values verified experi-
mentally [9].
Before starting the simulation, the cell identified by number 2 in figure 5 was
stimulated, by setting its activation level to 0
.
999. This could be caused by the
recognition of an antigen, for example. The remaining cells were initialized with
an activation level equals to 1
10
−
4
. Afterwards, the simulation was executed
for 30 iterations, with a time step of 1 second. The diffusion rates of stimulation
and regulatory cytokines were chosen as 1.5 and 2, respectively, while decay rates
were chosen as 0.25 and 0.05, respectively. Therefore, regulatory cytokines diffuse
more easily and decay less into the environment than stimulation cytokines.
·
