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

Saturable first-pass kinetics of propranolol

Reduced bioavailability (F) due to hepatic first-pass extraction of an oral dose (D) is a well-known pharmacokinetic phenomenon. An integrated solution for Michaelis-Menten kinetics of the first-pass effect is derived from the maximal metabolic rate (Vm), volume of distribution (Vd), first order absorption rate constant (ka), Michaelis constant (Km), and liver blood flow (Q). F = 1 - VmVd/kaD ln (1 + kaD/QKm) This equation for single dosage can also be extended to steady state kinetics after multiple dosing in which the amount of a drug present in the hepatic circulation is considered. According to the literature, the bioavailability of a single 80 mg oral dose of propranolol (F = 0.22) increases after multiple doses Fss = 0.36). Based on the first pass equations for single dosage and multiple dosing, the maximal metabolic rate (Vm = 0.043 mg l-1 h-1) corresponding to 310 mg per day and the Michaelis constant (Km = 0.10 mg/l) were calculated for propranolol. Incorporation of nonlinear plasma protein binding in this concept may explain the lack of threshold phenomenon for a single dose of less than 40 mg propranolol. Zero order absorption kinetics could explain why cumulation kinetics seem linear even at an excessive dosage of 960 mg propranolol per day. From these derivations it may be concluded that multiple dosing, increase in plasma protein binding, high absorption rate, and increased portal venous blood flow will increase bioavailability, whereas slow release formulations, fractional drug dosage, and saturable absorption kinetics will decrease bioavailability of first-pass drugs like propranolol.

Theoretical considerations in the calculation of bioavailability of drugs exhibiting Michaelis-Menten elimination kinetics

Two approaches used for bioavailability determination of drugs with Michaelis-Menten elimination kinetics were examined by computer simulation. The first method involved treating the drug as though its clearance remained constant during elimination, and the conventional method of taking the ratio of areas under the curve resulting from the oral and intravenous doses was used to calculate bioavailability. The second approach involved using the Michaelis parameters, Vmax and Km, to determine concentration dependent clearance values, but based these calculations on peripheral drug concentrations rather than on concentrations entering or in the liver. We have developed a simulation method that was used to test the accuracy of the above two methods. In the simulations described, Vmax, Km, and hepatic blood flow were chosen to represent a drug with an extraction ratio of 0.9 under linear conditions, but with Michaelis-Menten kinetics occurring at the doses given. Absorption was assumed to be first-order, and metabolism was assumed to occur only in the liver. These simulations showed that the most accurate determination of bioavailability requires knowledge of the direct contribution of oral absorption to the concentration of drug entering the liver. Unexpectedly, the results also showed that if a drug has a large volume of distribution or a large absorption rate constant, or both, use of the much simpler conventional method of bioavailability determination may be appropriate even in cases where the degree of saturation is substantial.