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 (F _p ^p) or metabolite (F _m ^p). 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 F _p ^p and F _m ^p 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.     

A method for calculating the mean absorption time of drugs undergoing reversible and first-pass metabolism

A method has been derived for calculating the mean absorption time of an oral drug and its interconversion metabolite which is generated from the drug systemically and presystemically. The method evolves from the convolution integral and requires plasma AUC and AUMC values after separate intravenous administration of the drug and its interconversion metabolite and oral administration of the drug. It can also be used to calculate the mean input time of a drug undergoing reversible metabolism and administered by any other extravascular route. Results of a simulation study using both errorless and errant data indicate that, when the absorption rate constant of a drug or its interconversion metabolite is not much larger than the apparent elimination rate constant, the proposed method performs satisfactorily. However, when the absorption rate constant of a drug or its interconversion metabolite is much larger than the apparent elimination rate constant, the proposed method appears to be inaccurate.     

An algorithm and computer program for calculating the mean transit time and distribution rate parameters of generated metabolites undergoing linear tissue distribution and linear or non-linear central elimination

A method is described for calculating the mean transit time and distribution rate parameters of a generated primary metabolite undergoing linear distribution and linear or non-linear central elimination, and of catenary metabolites with any precursor order. It is also applicable to a drug and its interconversion metabolite and does not require separate administration of the metabolite. The method allows steady-state volume of distribution and distribution clearance of a metabolite to be calculated, provided that the central volume of distribution of the metabolite is known. An algorithm and computer program to implement the proposed method are presented. The calculations require the plasma concentration versus time curves of the metabolite and its precursor. The method is applied to both published and simulated data.     

Volume of distribution at steady state for a linear pharmacokinetic system with peripheral elimination

The problem of finding the steady-state volume of distribution V(ss) for a linear pharmacokinetic system with peripheral drug elimination is considered. A commonly used equation V(ss) = (D/AUC)*MRT is applicable only for the systems with central (plasma) drug elimination. The following equation, V(ss) = (D/AUC)*MRT(int), was obtained, where AUC is the commonly calculated area under the time curve of the total drug concentration in plasma after intravenous (iv) administration of bolus drug dose, D, and MRT(int) is the intrinsic mean residence time, which is the average time the drug spends in the body (system) after entering the systemic circulation (plasma). The value of MRT(int) cannot be found from a drug plasma concentration profile after an iv bolus drug input if a peripheral drug exit occurs. The obtained equation does not contain the assumption of an immediate equilibrium of protein and tissue binding in plasma and organs, and thus incorporates the rates of all possible reactions. If drug exits the system only through central compartment (plasma) and there is an instant equilibrium between bound and unbound drug fractions in plasma, then MRT(int) becomes equal to MRT = AUMC/AUC, which is calculated using the time course of the total drug concentration in plasma after an iv bolus injection. Thus, the obtained equation coincides with the traditional one, V(ss) = (D/AUC)*MRT, if the assumptions for validity of this equation are met. Experimental methods for determining the steady-state volume of distribution and MRT(int), as well as the problem of determining whether peripheral drug elimination occurs, are considered. The equation for calculation of the tissue-plasma partition coefficient with the account of peripheral elimination is obtained. The difference between traditionally calculated V(ss) = (D/AUC)*MRT and the true value given by (D/AUC)*MRT(int) is discussed.     

Derivation of general equations for linear mammillary models when the drug is administered by different routes

A general disposition equation for a linear mammillary model consisting of ncompartments is derived. This equation is used to derive disposition equations for the central compartment when drug input occurs into the central compartment and when drug input occurs into a peripheral compartment. The derivation of equations that describe the entire time course of drug in a particular compartment after intravenous, intramuscular, oral, and rectal drug administration is also presented.     

Determination of volume of distribution at steady state with complete consideration of the kinetics of protein and tissue binding in linear pharmacokinetics

The assumption of an instant equilibrium between bound and unbound drug fractions is commonly applied in pharmacokinetic calculations. The equation for the calculation of the steady-state volume of distribution V(ss) from the time curve of drug concentration in plasma after intravenous bolus dose administration, which does not assume an immediate equilibrium and thus incorporates dissociation and association rates of protein and tissue binding, is presented. The equation obtained V(ss) = (Dose/AUC)*MRT(u) looks like the traditional equation, but instead of mean residence time MRT calculated using the total drug concentration in plasma, it contains mean residence time MRT(u) calculated using the plasma concentration of the unbound drug. The equation connecting MRT(u) and MRT is derived. If an immediate equilibrium between bound and unbound drug fractions occurs, MRT(u) and MRT are the same, but in general, MRT(u) is always smaller than MRT. For drugs with high protein affinity and slow dissociation rate MRT(u) may be of an order of several hours smaller than MRT, so that V(ss) can be considerably overestimated in the traditional calculation.     

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.     

A multi-mechanistic drug release approach in a bead dosage form and in vivo predictions

Our previous study has successfully prepared a combination of immediate release, enteric coated, and controlled release (CR) beads and mathematically modeled in vitro drug release characteristics of the combination based on the release profiles of individual beads. The objectives of the present study are to evaluate the combination and individual beads in vivo and to mathematically model in vivo drug input characteristics of the combination based on the in vivo input of individual beads. Beagle dogs were used as an animal model, and theophylline as a model drug. In vivo percent drug absorbed at different times (input function) after administration of a capsule bead dosage form was calculated using the Wagner-Nelson deconvolution method using intravenous injection of theophylline in each dog as a reference. The in vivo input functions of individual beads were each fitted to appropriate mathematical equations. The in vivo input function of the bead combination dosage form was calculated based on the individual mathematical equations (expected), and verified experimentally in vivo (experimental). The results showed that all bead dosage forms behave in vivo as defined in vitro. Enteric coated beads significantly delay the time to reach the maximum concentration of drug (tmax=4.9 h) compared to uncoated immediate release beads (2 h). The lag time of enteric coated beads is 1.1 h. CR beads showed both longer tmax (6 h) and mean residence time (MRT=9.7 h) compared to the uncoated immediate release beads (tmax=2 h and MRT=7.1 h) as designed in vitro. The in vivo input functions for the three individual beads can be fitted to equations as a function of square root of time. The combined bead dosage form showed tmax of 2.4 h and MRT of 7.9 h. The experimental and expected in vivo input profiles agreed to within +/- 12% (residues at individual data points). Our results suggest that the drug input function of a combined multi-mechanism oral dosage form can be predicted from the in vivo performance of individual formulations using the dog as an in vivo model.     

The ratio of first to zeroth moments of the plasma profile of an oral drug undergoing first-pass and linear reversible metabolism

Based on the convolution integral, equations have been drived for the ratio of the first to the zeroth moments of the plasma concentration—time curve (AUMC/AUC) parameters for a drug (p) undergoing first-pass and reversible metabolism and its reversible metabolite (m). According to these equations, the AUMC/AUC of a drug administered orally and of its reversible metabolite can be related to the mean absorption times, the ratios of the fraction of the dose entering the systemic circulation to the bioavailability, the first-time fractional conversion of each compound, and the AUMC/AUC ratios after intravenous administration of each compound. The proposed approach allows a more generalized derivation method for AUMC/AUC of a drug administered orally and undergoing first-pass and reversible metabolism. It is also applicable to any other extravascular route.     

Effects of First-Pass Metabolism on Metabolite Mean Residence Time Determination After Oral Administration of Parent Drug

Metabolite kinetics after oral drug administration can be determined, without separate metabolite administration, using the concepts of mean residence time (MRT). The MRT of parent drug and metabolite after oral administration of the parent drug, MRTp,p(oral) and MRTm,p(oral), can be calculated directly from the drug and metabolite profiles. The difference between MRTm,p(oral) and MRTp,p(oral), termed Delta MRT, yields an estimate of MRT of metabolite when the metabolite is given as an iv bolus, MRTm,m(iv). The calculation is simple for drugs that are known to undergo negligible first-pass metabolism. Correction can also be made when extent of first-pass metabolism is known. Ambiguity is encountered, however, when the degree of first-pass metabolism is unknown. When the delta MRT is negative, then first-pass metabolism must be considered. A positive value of delta MRT, on the other hand, is not a definitive indication of the absence of first-pass metabolism. It may occur in the presence or absence of first-pass metabolism. Ignoring the possibility of first-pass metabolism when a positive value of delta MRT occurs may lead to an incorrect estimate of MRTm, m(iv). The estimation error is relatively small, however, when MRTm,m(iv) MRTp,p(iv), even when first-pass metabolism is extensive. This situation may apply to the administration of a prodrug.     

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 MRT_iv = V _ss · AUC_iv/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 MRT_iv, 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.     

A Multi‐mechanistic Drug Release Approach in a Bead Dosage Form and In Vivo Predictions

Our previous study has successfully prepared a combination of immediate release, enteric coated, and controlled release (CR) beads and mathematically modeled in vitro drug release characteristics of the combination based on the release profiles of individual beads. The objectives of the present study are to evaluate the combination and individual beads in vivo and to mathematically model in vivo drug input characteristics of the combination based on the in vivo input of individual beads. Beagle dogs were used as an animal model, and theophylline as a model drug. In vivo percent drug absorbed at different times (input function) after administration of a capsule bead dosage form was calculated using the Wagner–Nelson deconvolution method using intravenous injection of theophylline in each dog as a reference. The in vivo input functions of individual beads were each fitted to appropriate mathematical equations. The in vivo input function of the bead combination dosage form was calculated based on the individual mathematical equations (expected), and verified experimentally in vivo (experimental). The results showed that all bead dosage forms behave in vivo as defined in vitro. Enteric coated beads significantly delay the time to reach the maximum concentration of drug (t_max = 4.9h) compared to uncoated immediate release beads (2h). The lag time of enteric coated beads is 1.1h. CR beads showed both longer t_max (6h) and mean residence time (MRT = 9.7h) compared to the uncoated immediate release beads (t_max = 2h and MRT = 7.1h) as designed in vitro. The in vivo input functions for the three individual beads can be fitted to equations as a function of square root of time. The combined bead dosage form showed t_max of 2.4h and MRT of 7.9h. The experimental and expected in vivo input profiles agreed to within ± 12% (residues at individual data points). Our results suggest that the drug input function of a combined multi‐mechanism oral dosage form can be predicted from the in vivo performance of individual formulations using the dog as an in vivo model.     

The pharmacokinetics of escitalopram after oral and intravenous administration of single and multiple doses to healthy subjects

The pharmacokinetics of escitalopram (S-citalopram) and its principal metabolite, S-demethylcitalopram (S-DCT), were investigated after intravenous and oral administration to healthy subjects. After intravenous infusion of escitalopram, the mean systemic clearance and volume of distribution were 31 L/h and 1,100 L, respectively. After oral administration of single or multiple doses, the absorption was relatively fast, with the maximum observed plasma or serum concentration (C(max)) attained after 3 to 4 hours. The mean half-lives were 27 and 33 hours, respectively; steady state was attained within 10 days. The area under the plasma or serum concentration time curve from time zero to 24 hours and C(max) was both linear and proportional to the dose. The apparent volume of distribution was around 20 L/kg. Comparison of the systemic and oral clearance implied a high absolute bioavailability. There was no evidence of interconversion from S-citalopram to R-citalopram either in plasma or in urine. Concurrent intake of food had no effect on the pharmacokinetics of escitalopram or its metabolite. All treatments were well tolerated.     

Disposition of pentopril, a new orally active angiotensin-converting enzyme inhibitor, and its active metabolite in rats

The disposition characteristics of pentopril (the ethyl ester) and its active carboxylic acid metabolite (CGS 13934) were determined in conscious rats after separate intravenous administrations of both compounds. The relationship between plasma concentration and pharmacological effect was also evaluated. The extent of apparent bioavailability of the active metabolite was determined after oral administration of pentopril. Pharmacokinetic parameters were calculated from the plasma concentration-time data for both the parent drug and its active metabolite after their separate intravenous administrations using a one-compartment model for the drug and a two-compartment model for the metabolite. The elimination half-life for the drug was approximately 1 min. The elimination half-life for the metabolite was 13 min (SD, +/- 3.5, n = 4) after its direct intravenous administration, but increased to an apparent half-life of 20 min (SD +/- 5, n = 5) when formed in vivo as a metabolite. Comparison of the formation rate of the metabolite and the elimination rate of the parent drug indicated that the parent drug was rapidly and completely hydrolyzed to the acid metabolite as soon as it reached the systemic circulation. No parent drug was detected in plasma after its oral administration. The apparent bioavailability of the acid metabolite was 66% after oral drug administration. A close relation between inhibition of pressor response to angiotensin I (AI) and plasma concentration of the active metabolite was observed when plotted against time after drug or metabolite administration. A Michaelis-Menten function correlated (multiple r2:0.995) well between effect and plasma metabolite concentration with mean concentration for 50% of maximum inhibition, IC50, of 3.6 X 10(-7) M (0.11 microgram/mL).     

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 (V _ss) 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 V _ss 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.     

Serum concentrations and urinary excretion of pinacidil and its major metabolite, pinacidil pyridine-N-oxide following i.v. and oral administration in healthy volunteers.

Serum concentrations of pinacidil and its major metabolite pinacidil pyridine-N-oxide were determined following administration of both an intravenous solution and a sustained release oral preparation to healthy volunteers. Mean bioavailability of pinacidil was 57.1 +/- 13.7%. Following intravenous administration, the mean AUC0-8 h metabolite/AUC 0-8 h pinacidil ratio was 0.559 +/- 0.272 and after oral administration, 0.825 +/- 0.656. Only one subject had serum metabolite concentrations in excess of pinacidil during the intravenous study whereas three subjects achieved metabolite concentrations in excess of pinacidil during the oral study. The mean serum elimination half-life of metabolite was significantly longer than parent drug following intravenous administration (P less than 0.01) but not after oral administration. No significant difference was found in the maximum measured metabolite concentration (Cmax.m) between the studies. The time to Cmax.m was significantly delayed (P less than 0.001) following oral dosage. Twenty four hour urinary excretion of metabolite was significantly increased (P less than 0.001) following oral administration whilst that of pinacidil was decreased (P less than 0.02). These results suggest that pinacidil pyridine-N-oxide may be a 'first-pass' metabolite of pinacidil. In most patients pinacidil pyridine-N-oxide is unlikely to contribute significantly to the hypotensive effect of pinacidil.     

Pharmacokinetic study of the novel, synthetic trioxane antimalarial compound 97-78 in rats using an LC-MS/MS method for quantification

The present study has been designed to investigate the pharmacokinetic parameters of the novel trioxane antimalarial 97-78 (US Patent 6316493 B1, 2001) in male and female rats after single oral and intravenous administration. The pharmacokinetic profile of 97-78 was investigated in the form of its completely converted metabolite 97-63 after dose administration. Quantification of metabolite 97-63 in rat plasma was achieved using a simple and rapid LC-MS/MS method. The LC-MS/MS method has been validated in terms of accuracy, precision, sensitivity and recovery for metabolite 97-63 in rat plasma. The intra- and interday accuracy (% bias) and precision (% RSD) values of the assay were less than 10% for metabolite 97-63. The chromatographic run time was 4.0 min and the weighted (1/x2) calibration curves were linear over the range 1.56-200 ng/ml. This method was successfully applied for analysis of pharmacokinetic study samples. Maximum plasma concentrations of 97-63 at 47 mg/kg oral administration in male and female rats were 1986.6 ng/ml and 4086.7 ng/ml at time (Tmax) 0.92 h and 0.58 h, respectively. The area under the curve (AUC(0-infinity)), elimination half-life (t(1/2) beta) and mean residence time (MRT) were 4669.98 ng x h/ml, 2.8 h and 4.2 h in male and 11786.0 ng x h/ml, 4.52 h and 4.32 h in female rats respectively. After single oral and intravenous administration of 97-78 to male and female rats significant differences were observed in pharmacokinetic parameters (AUC and t (1/2) beta) for metabolite 97-63.     

A general model of metabolite kinetics following intravenous and oral administration of the parent drug

A model of metabolite pharmacokinetics is developed in terms of residence time distributions and derived non-compartmental measures. It provides quantitative insight into factors determining the concentration-time curve of metabolite following intravenous and oral administration of the precursor drug. The AUCs and higher curve moments (mean residence times and relative dispersions) are calculated/predicted and their dependence on mean absorption time, fraction of first-pass metabolism and intrinsic disposition residence times of the parent drug and metabolite, respectively, is discussed. An AUC-based method for the determination of the first-pass effect is proposed which is not influenced by drug absorption. The approach is valid for linear pharmacokinetic systems exhibiting hepatic and renal elimination of the precursor drug; it is not restricted to specific compartmental models. Limitations of previous concepts of metabolite kinetics are defined. Criteria are presented for the appearance of concave metabolite curves in a semi-logarithmic scale.     

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.     

Pharmacokinetics of tramadol in rat plasma and cerebrospinal fluid after intranasal administration

We have evaluated the potential of intranasal administration of tramadol. The pharmacokinetic behaviour of tramadol in rat plasma and cerebrospinal fluid (CSF) after intranasal administration was determined and compared with those after intravenous and oral administration. Serial plasma and CSF samples were collected for 6 h, and the drug concentrations were assayed by an HPLC-fluorescence method. The plasma absolute bioavailability values of tramadol after intranasal and oral administration were 73.8% and 32.4%, respectively, in conscious rats. The Cmax (maximum concentration) value after the intranasal dose was lower (P<0.05), and the MRT (mean retention time) was longer (P<0.05) than the values obtained after intravenous administration. A pharmacokinetic study of tramadol in plasma and CSF was undertaken in anaesthetized rats. The absolute bioavailability values in plasma and CSF after intranasal administration were 66.7% and 87.3%, respectively. The Cmax values in plasma and CSF after a nasal dose were lower (P<0.05) than after the intravenous dose. The values of Cmax and AUC0-->6 h in plasma and CSF after intranasal administration were higher than after the oral dose. The mean drug-targeting efficiency after intranasal administration was significantly greater than after the oral dose. In conclusion, intranasal administration of tramadol appeared to be a promising alternative to the traditional administration modes for this drug.