Haiyung Cheng

Mean residence time concepts for pharmacokinetic systems with nonlinear drug elimination described by the Michaelis-Menten equation

Equations for the mean residence time (MRT) of drug in the body and related functions are derived for drugs which are intravenously administered into a one- or two-compartment system with Michaelis–Menten elimination. This MRT is a function of the steady-state volume of distribution and time-average clearance obtained from the dose and area under the curve (dose/AUC). The differences between the MRT calculated by the proposed method and by using the moment theory method (AUMC/AUC) are demonstrated both mathematically and by computer simulations. The validity of the proposed method for calculation of MRT and its relationship to the moment theory result have also been assessed by examining the percentage of the administered dose eliminated and the percentage of the total area attained at MRT and at AUMC/AUC in relation to the dose. The equations evolved should be helpful in clarifying residence time derivations and in defining the disposition characteristics and differences between linear and nonlinear systems. Direct methods are provided for calculation of Michaelis–Menten parameters based on the relationship between MRT and dose.

Two-compartment basophil cell trafficking model for methylprednisolone pharmacodynamics

A two-compartment closed model was used to characterize the movement of basophils between blood and extravascular sites resulting from methylprednisolone (MP) exposure. This model is consistent with the view that corticosteroids cause a decrease in the recirculation of these cells from peripheral compartments. Methylprednisolone (Solu-Medrol) was given to healthy males at doses of 10, 25, and 40 mg. Blood samples were collected and assayed for MP by HPLC for pharmacokinetic analysis. Whole blood histamine, an index of circulating basophils, was assessed by RIA over 32 hr. Nonlinear least-squares analysis was carried out to solve for the model parameters reflecting cell movement between compartments and sensitivity (IC50)to the steriod. This model quantitates the fall and return pattern of biologic response to corticosteroids with a minimal number of parameters which jointly fit several dose/response curves and yields a mean IC50value of 8.1 ng/ml similar to receptor binding of MP. Properties of the temporal and integrated response curve and model extrapolations over a wide dose range were explored with simulations. Because corticosteroids exert similar effects on other cells in blood, this model may be applicable to various regulatory and immunosuppressive effects.

Mean residence times and distribution volumes for drugs undergoing linear reversible metabolism and tissue distribution and linear or nonlinear elimination from the central compartments

Equations for the mean residence times in the body (MRT) and in the central compartment (MRTc) are derived for bolus central dosing of a drug and its metabolite which undergo linear tissue distribution and linear reversible metabolism but are eliminated either linearly or nonlinearly (Michaelis–Menten kinetics) from the central compartments. In addition, a new approach to calculate the steady-state volumes of distribution for nonlinear systems (reversible or nonreversible) is proposed based on disposition decomposition analysis. The application of these equations to a dual reversible two-compartment model is illustrated by computer simulations.

Mean Residence Time of Oral Drugs Undergoing First-Pass and Linear Reversible Metabolism

Equations for the mean residence times in the body (MRT) and AUMC/AUC of a drug and its metabolite have been derived for an oral drug undergoing first-pass and linear reversible metabolism. The mean residence times of the drug or interconversion metabolite in the body after oral drug are described by equations which include the mean absorption time (MAT), the mean residence times of the drug or metabolite in the body after intravenous administration of the drug, the fractions of the dose entering the systemic circulation as the parent drug and metabolite, and the systemically available fractions of the drug (Fpp) or metabolite (Fmp). Similarly, the AUMC/AUC of the drug and metabolite after oral drug can be related to the MAT, ratios of the fraction of the dose entering the systemic circulation to the systemically available fraction, the first-time fractional conversion of each compound, and AUMC/AUC ratios after separate intravenous administration of each compound. The Fpp and Fmp values, in turn, are related to the first-pass availabilities of both drug and metabolite and the first-time fractional conversion fractions. The application of these equations to a dual reversible two-compartment model is illustrated by computer simulations.

Mean interconversion times and distribution rate parameters for drugs undergoing reversible metabolism

The mean interconversion time and recycling numbers are introduced as intrinsic metabolic interconversion and distribution parameters for drugs undergoing linear reversible metabolism. Equations for these parameters, the distribution clearance, and the mean transit time in the central and peripheral compartments are derived for a metabolic pair where interconversion and elimination occur in central compartments. These parameters can be calculated from plasma concentration versus time slopes and intercepts, AUC, and AUMC data of parent drug and its metabolite partner following iv administration of each compound. The mean time analysis is illustrated with disposition data obtained previously for methylprednisolone and methylprednisone in the rabbit. Examination of mean times and additional properties of the system reveals that total exposure time of methylprednisolone is weakly influenced by the metabolic interconversion process, whereas the total exposure time of methylprednisone is strongly influenced by the process. In addition, the tissue distribution processes moderately influence the total exposure times of both compounds. The derived mean time parameters, along with previously evolved equations for clearances, volumes of distribution, moments, and mean residence times allow comprehensive analysis of linear, multicompartmental reversible metabolic systems.

Uptake and Stereoselective Binding of the Enantiomers of MK-927, a Potent Carbonic Anhydrase Inhibitor, by Human Erythrocytes in Vitro

MK-927 [5,6-dihydro-4H-4(isobutylamino)thieno(2,3-B)thiopyran-2-sulfonamide-7.7 dioxide], a potent carbonic anhydrase inhibitor, contains a chiral center and exists as a racemate. In order to understand the kinetic behavior of the enantiomers of MK-927 in the body, the uptake and binding of these compounds were studied in human erythrocytes in vitro. Since no degradation or metabolism of the enantiomers occurred during incubation in blood, one can describe the equilibration of the drugs between plasma and erythrocytes by a closed two-compartment system. Erythrocytes were considered as a compartment composed of two parts: one in which free drug is exchangeable to plasma and the other in which drug is tightly bound to carbonic anhydrase in a Michaelis–Menten type binding. After the addition of the enantiomers individually to fresh blood, they were taken up by erythrocytes rapidly in a concentration-dependent manner. The time to achieve equilibrium decreased as the concentration increased, suggesting saturation of binding sites. With the assumption of simple diffusion, the binding and transfer kinetics were determined simultaneously by computer fitting. There were no Stereoselective differences in the transfer process of the enantiomers across the erythrocyte membrane, while binding of the enantiomers exhibited stereoselectivity. The penetration of the unbound enantiomer across the erythrocyte cell membrane was rapid, with a mean transit time of about 3 sec. The S-( + )-enantiomer was bound to the high-affinity carbonic anhydrase isoenzyme more strongly than the R-( – )-enantiomer by approximately 10-fold. For the low-affinity isoenzyme, the R-( – )-enantiomer was bound more strongly than the S-( + )-enantiomer.

Application of mean residence-time concepts to pharmacokinetic systems with noninstantaneous input and nonlinear elimination.

Equations describing the mean residence time (MRT) of drugs in the body are derived for drugs that are administered by first-and zero-order rates into systems with Michaelis–Menten elimination. With computer simulations, the validity of these equations, the differences between them, and the conventional approach using the AUMC/AUC or the summation of mean times are demonstrated by examining calculations of the percentage of the administered dose eliminated at the MRT and AUMC/AUC. The effects of the absorption rate on the AUC and on the approximate and true MRT values in a nonlinear pharmacokinetic system are also illustrated with computer simulations. It was previously found that the true MRTiv = Vss · AUCiv/dose for an iv bolus. The total MRT (sum of input and disposition) of a drug after noninstantaneous administration was found to be a function of the MRTiv, two values of AUC (iv and non-iv), and exactly how the drug is administered expressed as the mean absorption time (MAT). In addition, a theoretical basis is proposed for calculation of the bioavailability of drugs in both linear and nonlinear pharmacokinetic systems.

Constant-Rate Intravenous Infusion Methods for Estimating Steady-State Volumes of Distribution and Mean Residence Times in the Body for Drugs Undergoing Reversible Metabolism

Equations for the steady-state volumes of distribution (Vss) and the mean residence times in the body (MRT) are derived for a drug and its metabolite subject to reversible metabolism and separately infused intravenously at a constant rate to steady state of both compounds. The Vss and MRT parameters are functions of the integrals of plasma concentrations, plasma concentrations at steady state, and times to reach steady state of both drug and metabolite. In addition, the MRT values are functions of the infusion rates. These equations were validated by computer simulations and comparison with IV bolus dose parameters. These relationships extend the ability to assess the pharmacokinetics of linear reversible metabolic systems.

An area function method for calculating the apparent elimination rate constant of a metabolite

A simple method for determination of the apparent elimination rate constant of a metabolite (km) has been developed. This procedure requires calculation of area intervals under the plasma concentration-time curves of the parent drug and its derived metabolite. The method has been evaluated and compared with the Chan moment method using both errorless and errant data. The approach is accurate for various ratios of elimination rate constants of drug and metabolite, allows several values of km to be averaged, but works best using data prior to the metabolite tax.

Pharmacokinetics of Linear Reversible Metabolic Systems

The role of reversible metabolism in pharmacology and pharmacokinetics has been gradually appreciated. Many compounds undergo this process. For example, commonly-used drugs such as captopril [1, 2], sulindac [3, 4], methylprednisolone [5, 6], lovastatin [7, 8], procainamide [9–11], imipramine [12, 13], and clofibric acid [14–16] have interconversion metabolites. Additional examples of drugs [17–31] which undergo reversible metabolism are listed in Table I. These compounds can be generally categorized according to their metabolically affected groups as: sulfides, sulfoxides, alcohols, lactones, arylamines, tertiary amines, and carboxylic acids.