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Cytodynamics

 

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

 figure1022
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 tex2html_wrap_inline3457, the system of ordinary differential equations governing the cell populations is as follows:
eqnarray1015
where c := 1/ 8760, tex2html_wrap_inline3461, tex2html_wrap_inline3463 and
displaymath4323
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.


next up previous contents
Next: The Effect Function Up: Modeling Issues Previous: Chemokinetics

Joerg Fliege
Wed Dec 22 12:25:31 CET 1999