First-pass effect: nonlinear concept comprising an explicit solution of integrated Michaelis-Menten equation.

The first-pass effect results from metabolism during the first liver passage of a drug given by mouth. The metabolism is described by the Michaelis-Menten equation, but the integrated form of the Michaelis-Menten equation has no explicit solution for concentration and its handling requires a computer. However, the presented nonlinear equation of the first-pass effect is an explicit integration of the Michaelis-Menten equation and involves only general mathematics. However, the problem of evaluating the Michaelis-Menten constants Vm and Km is not resolved. Therefore, linear equations are also derived, which correspond to previous clearance models.