nr. 477 - 2011 - Institut for Natur, Systemer og Modeller (NSM)

5.8 Discussion of Parameters 37
Figure 5.9 shows simulations of the DuCa model with activation due to necrotic cells. Initial
conditions correspond to a healthy rest state, i.e. (M, Ma, Ba, Bn, C) = (4.77 × 10 5 , 0, 0, 0, 0).
mately 13, at which point the growth decreases. Without this activation, cf. figure 5.3,
the growth starts to decrease at 12. Thus with the additional activation more resting
macrophages become activated within the same time interval as without additional activation.
This implies that more apoptotic β-cells are phagocytized during the same
amount of time as before, thus less are left to become necrotic, which in turn implies
fewer necrotic cells, and thereby less cells to facilitate the detrimental cycle.
When we turn the graphs that are made based on NOD parameters, we see that there
is very little, if any, difference between the original DuCa model, and the one with
activation from necrotic cells – the concentration of apoptotic β-cells does not go to
zero. This is not very surprising, since there is no difference in the phagocytosis rate
between activated and resting macrophages in the NOD mouse.
Thus the moral of the tale is that when there is a difference between the phagocytosis
rate of a resting and an activated macrophage, it does make a slight difference in the
initial behavior to include activation due to necrotic cells.
5.8 Discussion of Parameters
Some parameter values are notoriously hard to measure, and therefore they are often
associated with estimates, or they may be known to lie within a given range. The
parameters in table 5.1 are no different. In table 5.2 we have gathered values from
different articles. It is interesting to see how much some of the values differ. An
obvious example is the difference in the efflux rate, c. Marée et al. (2006) report that
Furth and den Dulk (1984) find the turnover rate of resting macrophages to be in the
range (0.07 − 0.25) d −1 , and based on this they estimate c ≈ 0.1d −1 (Marée et al.,
2006, p.1275). We have, however, not been able to locate this range in the article of
Furth and den Dulk (1984), and have based our value stated in table 5.2 on the value
that Furth and den Dulk (1984) report at the very end of their discussion (and in their
abstract), where they state that (Furth and den Dulk, 1984, p.1282)
The mean turnover time calculated with the value for the efflux of spleen