The model uses Michaelis Menten Kinetics to simulate the production of Thyroid Stimulating Hormone $($TSH$),$ secreted by the pituitary gland, and the thyroxine hormone $($TH$),$ secreted by the thyroid gland, which in return inhibits TSH production.

a$)$ Convert the Berkeley Madonna code listed below to a Forrester Diagram.

METHOD RK$4$

DT$=1$e$-4$

STOPTIME$=200$

$\{$ conc $=$ ug$/$l $\}$

INIT TSH $=1\mathrm{.}5$

INIT TH $=30$

Qmax$=2$

Kth$=50$

Ktsh$=1$

Rth$=0\mathrm{.}031$

Rtsh$=5.$

Mth$=20$

Smax$=10$

n$=3$

d$/$dt $($TH$)=$ THsecr$-$THremoval

THsecr $=$ Qmax$*$TSH$/(($Ktsh$+$TSH$))$

THremoval $=$ Rth$*$Mth

d$/$dt $($TSH$)=$ TSHsecr $-$ TSHremoval

TSHsecr $=$ Smax$*$ Kth$^$n$/($Kth$^$n $+$ TH$^$n$)$

TSHremoval $=$ Rtsh $*$ TSH