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In-Depth Information
4.2
Cytokine Absorption
Following the cytokine diffusion and decay in the tissue, each cell in the popu-
lation proceeds to absorb cytokines located in the position where it is located.
According to the model being simulated, effector cells can absorb both IFN-
γ
and IL-10, while regulatory cells can only absorb IFN-
γ
. For simplicity, this pro-
cess has been modelled by a first degree polynomial of the cell activation level,
according to equation 3. This equation determines the absorption rate, that is,
the relative amount of a given cytokine to be absorbed, where
φ
i
max
is the max-
imum cytokine input rate, to be absorbed when the cell is fully activated,
φ
i
min
is the minimum cytokine input rate, absorbed when the cell has received little
or no stimulation and
α
is the cell activation level. As mentioned, the value
given by equation 3 is relative to the total cytokine concentration located in the
position where the cell is located. Therefore, to determine the absolute amount
of cytokine to be absorbed, the total cytokine concentration is determined, and
multiplied by
φ
(
α
)
in
, as shown in equation 4. To illustrate the function used to
determine the absorption rate, it is shown in figure 2, for two different values of
φ
i
min
and
φ
i
max
.
φ
(
α
)
in
=
φ
i
min
+(
φ
i
max
−
φ
i
min
)
·
α
(3)
Δψ
(
x, y, t, α
)
in
=
φ
(
α
)
in
·
ψ
(
x, y, t
)
(4)
Fig. 2.
Plots of the cytokine absorption rate as a function of cell activation for
ψ
i
min
=
0
.
1
,ψ
i
max
=0
.
5and
ψ
i
min
=0
.
3
,ψ
i
max
=0
.
5
4.3
Determination of the New Activation Level
After cytokine absorption, the simulation continues to determine the new activa-
tion level for each cell, given as a function of the cytokine inputs. As previously
discussed, effector cells have
ψ
i
stimulation
≥
0 (because they
can absorb both IFN-
γ
and IL-10), and regulatory cells have
ψ
i
stimulation
0and
ψ
i
regulation
≥
0
and
ψ
i
regulation
= 0 (because regulatory cells can absorb only IFN-
γ
). In the
≥
