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

5 The DuCa Model
In the following we give an account of the background of the full model of Marée et al.
(2006), which we have coined the DuCa model since it is a Dutch-Canadian collaboration.
We will also present the compartment system and the system of differential
equations as they have presented it in their article. While doing so we will comment or
clarify when we find it necessary. Afterwards, in sections 5.5 and 5.7, we discuss and
give a critical appraisal of the DuCa model and the assumptions/simplifications made
with it.
5.1 Background for the DuCa Model
The model proposed by Marée et al. (2006) is partly based on an earlier work by Marée
et al. (2005) and findings by Trudeau et al. (2000).
In Marée et al. (2005) they conclude that Balb/c macrophages are generally more efficient
at phagocytizing apoptotic β-cells than NOD macrophages. Furthermore they
found that the Balb/c macrophages undergo an activation step after they have engulfed
their first apoptotic β-cell. After the activation step, their phagocytosis rate increases;
see table 5.1. In NOD-mice no activation step was observed, i.e. the NOD macrophages
do not become more efficient at phagocytizing after engulfment of an apoptotic β-cell.
Trudeau et al. (2000) found that a wave of apoptosis 1 occurs in the pancreatic β-cells
in neonatal mice and other rodents as well. These findings led the scientific community
to hypothesize that the reason why T1D is more prevalent in NOD-mice (relative to
Balb/c-mice) is due to the poor phagocytosis rate of their macrophages (e.g. Trudeau
et al. (2000), Mathis et al. (2001)).
The greater phagocytosis rate in Balb/c-mice implies that the macrophages are able
to accommodate the increased amount of apoptotic β-cells during the apoptotic wave,
whereas this is not the case in NOD-mice. Here some of the apoptotic β-cells are left
uncleared long enough for the cells to become necrotic. 2
When an activated macrophage engulfs a necrotic β-cell it secretes cytokines of which
some are cytotoxic to β-cells (Stoffels et al. (2004)). Thus more β-cells undergo apoptosis,
yielding a higher concentration of apoptotic β-cells to be phagocytized. The NOD
macrophages are already incapable of clearing the cells that entered the system during
the apoptotic wave, and so more cells become necrotic and the cycle continues. In
other words a feedback loop is initiated in the NOD-mice, which eventually leads to
the decimation of the β-cell population. The more efficient phagocytosis of the Balb/c
1 An apoptotic wave is when an elevated rate of cells undergo apoptosis over a short interval of time
relative to the lifespan of the organism in which it takes place.
2 This also happens in the Balb/c mice, but only during a brief period.
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