Table 1.

Initial value problems (IVPs) of interest for single- and two-compartment models

Model	Input	IVP
M1	Beq	$\begin{array}{cc}\frac{d{a}_c}{\mathit{dt}}\hfill & =-k_e{a}_c+g_B(t),\hfill \\ a_c(0)\hfill & =0.\hfill \end{array}$
M1	BeqL	$\begin{array}{cc}\frac{d{a}_c}{\mathit{dt}}\hfill & =-k_e{a}_c+g_{\mathit{BL}}(t),\hfill \\ a_c(0)\hfill & =0.\hfill \end{array}$
M1	Ieq	$\begin{array}{cc}\frac{d{a}_c}{\mathit{dt}}\hfill & =-k_e{a}_c+g_I(t),\hfill \\ a_c(0)\hfill & =0.\hfill \end{array}$
M2	Beq	$\begin{array}{cc}\frac{d{a}_b}{\mathit{dt}}\hfill & =-k_a{a}_b+g_B(t),\hfill \\ \frac{d{a}_c}{\mathit{dt}}\hfill & =k_a{a}_b-k_e{a}_c,\hfill \\ a_b(0)\hfill & =a_c(0)=0.\hfill \end{array}$
M2	BeqL	$\begin{array}{cc}\frac{d{a}_b}{\mathit{dt}}\hfill & =-k_a{a}_b+g_{\mathit{BL}}(t),\hfill \\ \frac{d{a}_c}{\mathit{dt}}\hfill & =k_a{a}_b-k_e{a}_c,\hfill \\ a_b(0)\hfill & =a_c(0)=0.\hfill \end{array}$

Here, $\delta$ is the Dirac delta function, M is the number of doses given, and T is the dosing interval for bolus doses. Model and Input labels refer to Figs. 1 and 2