Michaelis-Menten 1-compartment, bolus | ||
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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 | |
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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 | |
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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: | \( \begin{align*} C_1(t_0) &= C_{1residual} \\ C_2(t_0) &= C_{2residual} + \frac{F D}{V} \\ \end{align*}\) |