The cytodynamic model follows the one outlined in [3] and is depicted in Figure 6.8. This model is only used for the cell population in the liver compartment

**Figure 6.8:** Cytodynamic model used in the case study.

In this model, stem cells (S) may give rise to premalignant cells (P), who,
in turn, can mutate to malignant cells (M). But due to toxic effects, stem
cells may also die or lose their ability to divide. In this case they are
placed in a pool of 'dead' cells (D). Furthermore, cells from a reservoir (R)
can replace stem cells, but also mutate into premalignant cells of a different
type (Q). Denoting the population sizes by , the
system of ordinary differential equations governing the cell populations
is as follows:

where *c* := 1/ 8760, ,
and

Obviously, we start with a completely healthy system. Moreover, the mutation
rates are affine functions of the pollutant mass in the liver. In case
a constant background pollution is assumed, one should better calculate
an equilibium distribution for the compartments and a corresponding
equilibrium point of the system above, which can then serve as a starting
point.

Wed Dec 22 12:25:31 CET 1999