# non dimensionalize pharmacodynamics

#### dwsmith

##### Well-known member
$$\frac{dG}{dt} = k_{inG} - k_{outG}\cdot G\cdot (1 + S_{Ins}[n]\cdot I)$$
$$\frac{dI}{dt} = k_{inI}[m]\cdot (1 + S_G[r]\cdot (G - G_0)) - k_{outI}\cdot I$$

The units for the first equation are $k_{inG} = \frac{mg(week)}{dl}$, $k_{outG} = \frac{1}{week}$, $G = \frac{mg(week)^2}{dl}$, $S_{Ins}[n] = \frac{ml}{ng}$ and $I = \frac{ng}{ml}$
The second are $k_{inI} = \frac{ng(week)}{ml}$, $S_G[r] = \frac{dl}{mg}$, $G = G_0$, and $k_{outI} = \frac{1}{week}$

I am not sure how to do this very well since I didn't get a response to my Buckingham Pi Theorem question which would help me understand how to do this.