| Michaelis-Menten 1-compartment, bolus | ||
|---|---|---|
| Parameters | ||
| \(V\) | Volume of distribution. Ratio of the drug’s amount present in the body over its circulating concentration, [L] | |
| \(V_m\) | Maximum rate of elimination. Maximum rate of elimination of the drug from the circulation through a saturable pathway, [mg/h] | |
| \(K_m\) | Michaelis-Menten constant. Substrate concentration at which a saturable elimination rate reaches half of its maximum value, [mg/L] | |
| Equations | ||
| Equation: | \(\frac{dC}{dt} = -\frac{\frac{V_m}{V}\times C}{K_m + C}\) | |
| Initial conditions: | \(C(t_0) = C_{residual} + \frac{D}{V}\) | |
| Michaelis-Menten 1-compartment, infusion | |
|---|---|
| Parameters | |
| \(V\) | Volume of distribution. Ratio of the drug’s amount present in the body over its circulating concentration, [L] |
| \(V_m\) | Maximum rate of elimination. Maximum rate of elimination of the drug from the circulation through a saturable pathway, [mg/h] |
| \(K_m\) | Michaelis-Menten constant. Substrate concentration at which a saturable elimination rate reaches half of its maximum value, [mg/L] |
| \(T_{inf}\) | Infusion time, [h] |
| Equations | |
| Equation: | \( \begin{align*} \frac{dC}{dt} &= \begin{cases} \frac{k_0}{V} – \frac{\frac{V_m}{V}\times C}{K_m + C} , &\text{for $t\leq t_0 + T_{inf}$}\\ -\frac{\frac{V_m}{V}\times C}{K_m + C}, &\text{for $t> t_0 + T_{inf}$} \end{cases} \end{align*} \) |
| Initial conditions: | \(C(t_0) = C_{residual}\) |
| Michaelis-Menten 1-compartment, extravascular | |
|---|---|
| Parameters | |
| \(V\) | Volume of distribution. Ratio of the drug’s amount present in the body over its circulating concentration, [L] |
| \(V_m\) | Maximum rate of elimination. Maximum rate of elimination of the drug from the circulation through a saturable pathway, [mg/h] |
| \(K_m\) | Michaelis-Menten constant. Substrate concentration at which a saturable elimination rate reaches half of its maximum value, [mg/L] |
| \(k_a\) | Absorption rate constant. Relative rate constant of the drug’s absorption into the body, [h⁻¹] |
| Equations | |
| Equation: | \(\begin{align*} \frac{dC_1}{dt} &= k_a C_2 -\frac{\frac{V_m}{V}\times C_1}{K_m + C_1} \\ \frac{dC_2}{dt} &= – k_a C_2 \end{align*} \) |
| Initial conditions: | \( \begin{align*} C_1(t_0) &= C_{1residual} \\ C_2(t_0) &= C_{2residual} + \frac{F D}{V} \\ \end{align*}\) |