The mathematical equations for the components involved are shown in Eq. 1-5:

1. \(\frac{dA_1}{dt} = X_0 - K_{10} \cdot X_1 - \frac{V_m \cdot X_1}{K_m + X_1} - K_{12} \cdot (X_1 - X_2) \quad (1)\)

2. \(\frac{dA_2}{dt} = K_{21} \cdot (X_1 - X_2) \quad (2)\)

3. \(X_0 = \frac{D_0}{I_t} \quad (3)\)

4. \(X_1 = \frac{A_c}{V_1} \quad (4)\)

5. \(X_2 = \frac{A_p}{V_2} \quad (5)\)

Where \(A_1\) and \(A_2\) represent the amount of drug in the central and peripheral compartments, respectively. The units for drug concentrations are microgram/milliliter (µg/ml). \(D_0\) represents the administration dose. \(I_t\) symbolizes the infusion rate time (0.6 mg/min for the 10 mg/kg IV single dose and 6.6 mg/min for the 100 mg/kg IV single dose). \(X_0\) represents the initial drug concentration after administration. \(X_1\) and \(X_2\) denote the drug concentration in the central and peripheral compartments, respectively. Parameters \(V_1\) and \(V_2\) represent the volume of central and peripheral compartments, respectively. \(Cl\) represents the clearance from the central compartment, while \(Q\) denotes the distribution clearance between the central and peripheral compartments. Kinetic parameters for non-linear elimination are characterized by \(K_m\) (the Michaelis constant) and \(V_m\) (which characterizes the maximum velocity achieved by the system at maximum [saturating] substrate concentrations).
