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

6.3 Recapitulation of The Analysis of the IM 63
6.3 Recapitulation of The Analysis of the IM
On the basis of the analysis of the IM we have reached an understanding of what kind
of dynamics that the people of Marée et al. (2006) were looking for when modifying the
CPH model and at the same time gained insight into the problems they were facing in
this process. To summarize: the CPH model was extended to the IM for the purpose of
testing the hypothesis that impaired phagocytosis makes the difference between health
and disease. For the hypothesis to be confirmed the model should be able to exhibit
two kinds of dynamics by changing the values of the parameters f1 and f2. The two
types of dynamics were dubbed Balb/c and NOD dynamics respectively and refers to
the classification of the mice that are prone to develop T1D (NOD-mice) and those who
are not (Balb/c-mice). In the case where the estimated Balb/c phagocytosis rates were
applied, the model was expected to show Balb/c dynamics. This implies the existence
of a healthy rest state, where there is no activated macrophages and no apoptotic βcells,
as the only fixed point in the physiological relevant region of the phase space.
This fixed point should furthermore be stable such that any stimulated inflammation
will be nonpermanent. When using the estimated phagocytosis rates for NOD-mice
the model was expected to exhibit NOD dynamics which is more eventful than the
former. Here the possibility for a permanent and nonpermanent inflammation should
be open, since not all NOD-mice develop T1D. In addition the chronic inflammation
should be bounded such that the concentration of neither the activated macrophages
nor the apoptotic β-cells tends towards infinity. These expectations are reached when,
besides the stable healthy rest state, there is a saddle point that together with its stable
manifold comprises a separatrix. Below the separatrix the inflammation is damped, i.e.
nonpermanent, whereas, if the separatrix is traversed, the inflammation will escalate.
The escalating inflammation needs to be bounded, so a third fixed point must exist
that has to be stable.
These are the two types of dynamics that the model should be able to exhibit when
using the estimated Balb/c and NOD parameters. However as discussed in section
6.1 this is not the case, since the IM also exhibits Balb/c dynamics when applying
the estimated NOD parameters. By this realization the people of Marée et al. (2006)
suggest to implement the role of necrosis in the model. We will proceed by embarking
on an analysis of this model, i.e. the DuCa model, in the following sections.