| Linear 2-compartments, bolus | ||
|---|---|---|
| Parameters | ||
| \(CL\) | Clearance. Ratio of the drug’s elimination rate from the body over its circulating concentration, [L/h] | |
| \(V_1\) | Central Volume of distribution. Volume into which the drug distributes initially without delay after its delivery into the circulation, [L] | |
| \(V_2\) | Peripheral volume of distribution, second compartment. Volume into which a drug is considered to distribute secondly with retardation, from and back to the central compartment, [L] | |
| \(Q\) | Inter-compartmental clearance. Ratio of the drug’s distribution rate between the central compartment and the peripheral compartments over its circulating concentration , [L/h] | |
| \(k_e\) | \(=\frac{CL}{V_1}\) | |
| \(k_{12}\) | \(=\frac{Q}{V_1}\) | |
| \(k_{21}\) | \(=\frac{Q}{V_2}\) | |
| Equations | ||
| Equation: | \(\begin{align*} \frac{dC_1}{dt} &= k_{21} C_2 – k_{12} C_1 – k_e C_1 \\ \frac{dC_2}{dt} &= k_{12} C_1 -k_{21} C_2 \end{align*}\) |
|
| Initial conditions: | \(\begin{align*} C_1(t_0) &= C_{1residual} + \frac{D}{V_1} \\ C_2(t_0) &= C_{2{residual}} \end{align*}\) |
|
| Linear 2-compartments, infusion | |
|---|---|
| Parameters | |
| \(CL\) | Clearance. Ratio of the drug’s elimination rate from the body over its circulating concentration, [L/h] |
| \(V_1\) | Central Volume of distribution. Volume into which the drug distributes initially without delay after its delivery into the circulation, [L] |
| \(V_2\) | Peripheral volume of distribution, second compartment. Volume into which a drug is considered to distribute secondly with retardation, from and back to the central compartment, [L] |
| \(Q\) | Inter-compartmental clearance. Ratio of the drug’s distribution rate between the central compartment and the peripheral compartments over its circulating concentration , [L/h] |
| \(T_{inf}\) | Infusion time, [h] |
| \(k_e\) | \(=\frac{CL}{V_1}\) |
| \(k_{12}\) | \(=\frac{Q}{V_1}\) |
| \(k_{21}\) | \(=\frac{Q}{V_2}\) |
| \(k_0\) | \(=\frac{D}{T_{inf}}\) |
| Equations | |
| Equation: | \(\begin{align*} \frac{dC_1}{dt} &= \begin{cases} k_{21} C_2 – k_{12} C_1 – k_e C_1 + \frac{k_0}{V_1}, &\text{for $t\leq t_0 + T_{inf}$}\\ k_{21} C_2 – k_{12} C_1 – k_e C_1, &\text{for $t> t_0 + T_{inf}$} \end{cases} \\ \frac{dC_2}{dt} &= k_{12} C_1 -k_{21} C_2 \end{align*} \) |
| Initial conditions: | \(\begin{align*} C_1(t_0) &= C_{1residual} \\ C_2(t_0) &= C_{2{residual}} \end{align*}\) |
| Linear 2-compartments, extravascular | |
|---|---|
| Parameters | |
| \(CL\) | Clearance. Ratio of the drug’s elimination rate from the body over its circulating concentration, [L/h] |
| \(V_1\) | Central Volume of distribution. Volume into which the drug distributes initially without delay after its delivery into the circulation, [L] |
| \(V_2\) | Peripheral volume of distribution, second compartment. Volume into which a drug is considered to distribute secondly with retardation, from and back to the central compartment, [L] |
| \(Q\) | Inter-compartmental clearance. Ratio of the drug’s distribution rate between the central compartment and the peripheral compartments over its circulating concentration , [L/h] |
| \(T_{inf}\) | Infusion time, [h] |
| \(k_a\) | 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, [%] |
| \(k_e\) | \(=\frac{CL}{V}\) |
| \(k_{12}\) | \(=\frac{Q}{V_1}\) |
| \(k_{21}\) | \(=\frac{Q}{V_2}\) |
| Equations | |
| Equation: | \(\begin{align*} \frac{dC_1}{dt} &= k_{21} C_2 – k_{12} C_1 + k_a C_3 – k_e C_1 \\ \frac{dC_2}{dt} &= k_{12} C_1 -k_{21} C_2 \\ \frac{dC_3}{dt} &= -k_{a} C_3 \end{align*} \) |
| Initial conditions: | \( \begin{align*} C_1(t_0) &= C_{1residual} \\ C_2(t_0) &= C_{2residual} \\ C_3(t_0) &= C_{3residual} + \frac{F D}{V_1} \end{align*}\) |