Results of this model are shown in Fig. 9.3. The thyroid level declines to a stable
level with the input rate. Change the external input rate to one tenth of the stable
level and plot the result. This level represents an extremely deficient iodine level.
This very basic model of a complex and important process demonstrates how
one can model simply yet accurately. Note that we did not use the idea of the mass
action law here. Why not? Can you see here where some flows are recipientcontrolled and some are donor-controlled? This identification of the state variable
controls early in the modeling process can be very helpful.
We have begun this part of the book on physical and biochemical with simple
chemical reactions and proceeded to catalyzed processes, the activities of an
individual cell, and the distribution of chemical substances among different compartments. Let us return in the following chapter to chemical reactions and combine
our insight into oscillatory system behavior of Chap. 4 with our knowledge about
chemical processes.
9.2 Iodine Compartment Model Equations
EXTRA_TISSUE_IODINE(t) ¼ EXTRA_TISSUE_IODINE(t À dt) + (FLOW_6
À FLOW_5) * dt
INIT EXTRA_TISSUE_IODINE ¼ 682 {micrograms}
INFLOWS:
FLOW_6 ¼ K2 * THYROID
Fig. 9.3
9.2 Iodine Compartment Model Equations
83