Linear 1-compartment


Linear 1-compartment, bolus
Parameters
\(CL\) Clearance. Ratio of the drug’s elimination rate from the body over its circulating concentration, [L/h]
\(V\) Volume of distribution. Ratio of the drug’s amount present in the body over its circulating concentration, [L]
\(k_e\) \(=\frac{CL}{V}\)
Equations
Equation: \(\frac{dC}{dt} = -{k_e} C = -\frac{CL}{V} C\)
Initial conditions: \(C(t_0) = C_{residual} + \frac{D}{V}\)


Linear 1-compartment, infusion
Parameters
\(CL\) Clearance. Ratio of the drug’s elimination rate from the body over its circulating concentration, [L/h]
\(V\) Volume of distribution. Ratio of the drug’s amount present in the body over its circulating concentration, [L]
\(T_{inf}\) Infusion time, [h]
\(k_e\) \(=\frac{CL}{V}\)
\(k_0\) \(=\frac{D}{T_{inf}}\)
Equations
Equation: \( \begin{align*}
\frac{dC}{dt} &=
\begin{cases}
\frac{k_0}{V} – k_e C ,
&\text{for $t\leq t_0 + T_{inf}$}\\
- k_e C,
&\text{for $t> t_0 + T_{inf}$}
\end{cases}
\end{align*}
\)
Initial conditions: \(C(t_0) = C_{residual}\)

Linear 1-compartment, extravascular
Parameters
\(CL\) Clearance. Ratio of the drug’s elimination rate from the body over its circulating concentration, [L/h]
\(V\) Volume of distribution. Ratio of the drug’s amount present in the body over its circulating concentration, [L]
\(k_a\) Absorption rate constant. Relative rate constant of the drug’s absorption into the body, [h⁻¹]
\(F\) Bioavailability. Fraction of the drug’s administered dose that reaches unchanged the systemic circulation, [%]
\(k_e\) \(=\frac{CL}{V}\)
Equations
Equation: \( \begin{align*}
\frac{dC_1}{dt} &= k_a C_2 – k_e C_1 \\
\frac{dC_2}{dt} &= -k_a C_2
\end{align*}
\)
Initial conditions: \(
\begin{align*}
C_1(t_0) &= C_{1residual} \\
C_2(t_0) &= C_{2{residual}} + \frac{F D}{V}
\end{align*}\)