Mean residence time of drugs administered non-instantaneously and undergoing linear tissue distribution and reversible metabolism and linear or non-linear elimination from the central compartment

Based on disposition decomposition analysis (DDA), equations for the mean residence times (MRT) in the body are derived for a drug and its interconversion metabolite that undergo linear tissue distribution and linear or non-linear elimination from the central compartment after non-instantaneous administration of the drug. The MRT of the drug after non-instantaneous input can be related to the MRT of the drug after intravenous administration, the ratio of the total area under the plasma concentration—time curve of the drug after non-instantaneous administration to that after intravenous administration, the bioavailability of the drug, and the mean input time of the drug. Similar relationships also exist for the MRT of the interconversion metabolite after non-instantaneous input of the drug. The application of these equations to a non-linear reversible metabolic system is illustrated with computer simulations.     

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.     

Troleandomycin effects on methylprednisolone and methylprednisone interconversion and disposition in the rabbit

A study of the effects of troleandomycin (TAO) on the disposition of intravenous methylprednisolone in rabbits was performed in order to develop an animal model to further evaluate the mechanism of TAO/steroid beneficial effects in severe asthma. The plasma concentration-time profiles of methylprednisolone and methylprednisone were determined in the presence and absence of single and multiple dose TAO regimens. Pharmacokinetic analysis revealed a significant decrease in total plasma clearance of methylprednisolone in the presence of multiple dose TAO. Alterations in the disposition of the reversible metabolite, methylprednisone, were also observed. The TAO-methylprednisolone interaction may involve decreasing the degree of interconversion between the steroid and its reversible metabolite. TAO also decreases metabolite turnover more than three-fold. The antibiotic does not cause marked deviation from linear biexponential elimination of methylprednisolone as observed in man. The rabbit may serve as a useful animal model for further studies of the TAO/methylprednisolone interaction.     

Bioavailability and nonlinear disposition of methylprednisolone and methylprednisone in the rat.

Bioavailability of low (10 mg/kg) and high (50 mg/kg) doses of methylprednisolone was determined after oral administration of the free alcohol of methylprednisolone and iv administration of methylprednisolone sodium succinate. Plasma concentrations of methylprednisolone and methylprednisone (reversible metabolite) were measured by HPLC. Methylprednisolone systemic availability (F) was 49-57% after iv administration and approximately 35% after oral administration. Solubilization of steroids with PEG:ethanol had no effect on their disposition. Apparent systemic clearance (CL) of methylprednisolone was 21 mL/min (low dose), approximately twice the liver blood flow. Dose-dependent changes in steady-state volume of distribution (Vdss) and central volume of distribution (Vdc), volumes, and apparent CL were observed. The methylprednisolone-to-methylprednisone AUC ratio decreased with dose due to saturation of methylprednisone formation clearance (CL12), but this is a minor metabolic pathway. The mean residence time (MRT) increased threefold with dose. Graphical estimates of the Michaelis-Menten capacity (Vmax) and affinity (Km) constants were in reasonable agreement with CL values for the low-dose experimental data. Low systemic availability of iv methylprednisolone sodium succinate was in part due to sequential first-pass hepatic metabolism of the methylprednisolone formed. Methylprednisolone disposition is complex in the rat due to extensive first-pass effects, nonlinear elimination, nonlinear distribution, and reversible metabolism.     

General treatment of mean residence time,clearance, and volume parameters in linear mammillary models with elimination from any compartment

A general treatment for mean residence time, clearance, and volume parameters in linear mammillary models which includes the possibility of first-order elimination from compartments other than the central compartment is presented. The interrelationship between noncompartmentally derived parameters and compartmentally derived pharmacokinetic microconstants is described. The concept of exit site dependent and exit site independent parameters is introduced in the development of these treatments. Explications of mean residence time in terms of elimination rate, amount eliminated, and amount in the body are presented together with demonstrations of their utility.Supported in part by NIH grants GM 26691 and HL 32243.     

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.     

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.     

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.     

Methylprednisolone disposition in rabbits. Analysis, prodrug conversion, reversible metabolism, and comparison with man

Methodology was evolved for comparison of methylprednisolone disposition in man and rabbit. Methylprednisolone, methylprednisone, and methylprednisolone hemisuccinate ester concentrations in plasma were measured by HPLC methodology after iv administration of each compound to rabbits. Methylprednisolone hemisuccinate is rapidly and completely hydrolyzed to methylprednisolone with a half-life of 10 min. Dosing with the free alcohol or ester produces identical disposition curves for methylprednisolone. Methylprednisolone was found to undergo rapid and reversible metabolism with methylprednisone, a phenomenon also seen in man. Plasma concentrations of methylprednisolone are appreciably greater than the metabolite regardless of the form of steroid given. Administration of the metabolite yields 67% availability of methylprednisolone. The occurrence of reversible metabolism produces an apparent clearance which is about 71% of the value of the "real" elimination clearance for both steroids. Man and rabbit show identical plasma protein binding of methylprednisolone (77%). Small differences in apparent clearance (man, 5.74 ml/min/kg; rabbit, 7.93 ml/min/kg) can be accounted for by the animal scale-up principle (body weight0.89). The rabbit is thus a useful animal model for further assessing mechanisms of drug- or disease-steroid interactions which occur in man.     

Methylprednisolone versus prednisolone pharmacokinetics in relation to dose in adults

Summary The disposition and plasma binding of methylprednisolone were examined in seven normal volunteers following the administration of 5, 20 and 40 mg of intravenous methylprednisolone sodium succinate. Methylprednisolone exhibits linear plasma protein binding averaging 77%. The mean plasma methylprednisolone clearance of 337 ml·h^–1. kg^–1 was independent of dose. The steroid appears to moderately distribute into tissue spaces with a mean volume of distribution of 1.41·kg^–1. Methylprednisolone disposition parameters were compared with the non-transcortin bound parameters for prednisolone. The prednisolone plasma clearance based on the transcortin free-drug is similar to methylprednisolone total plasma clearance. However, the corrected volume of distribution of prednisolone is only one-half that of methylprednisolone. The disposition rate of these two steroids is thus similar, in spite of their metabolic control by different enzymatic pathways and major influence of saturable transcortin binding on prednisolone elimination.     

General treatment of mean residence time, clearance, and volume parameters in linear mammillary models with elimination from any compartment

A general treatment for mean residence time, clearance, and volume parameters in linear mammillary models which includes the possibility of first-order elimination from compartments other than the central compartment is presented. The interrelationship between noncompartmentally derived parameters and compartmentally derived pharmacokinetic microconstants is described. The concept of exit site dependent and exit site independent parameters is introduced in the development of these treatments. Explications of mean residence time in terms of elimination rate, amount eliminated, and amount in the body are presented together with demonstrations of their utility.     

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.     

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.     

Definitions and applications of mean transit and residence times in reference to the two-compartment mammillary plasma clearance model

The mean transit time (MTT) and the mean residence time (MRT) values of a linear two-compartment plasma clearance model were evaluated using definitions originally proposed by Rescigno and Gurpide. The MRT of the total body (MRTB) can be viewed as comprising the MRT in the central compartment (MRTC) and the MRT in the peripheral tissue compartment (MRTT). The MTT and MRT of each compartment can be envisioned as the average interval of time spent by a drug particle during a single passage and in all passages through it. Hence, the MRT is the product of MTT and the mean number of passages of a drug particle through the central (R + 1) or tissue (R) compartments. Physiologically, each MTT parameter is related to its apparent volume divided by all its clearance processes, reversible and irreversible (if any exist). Each MRT parameter is related to its apparent volume divided by only the sum of irreversible exit clearances. Applications of the five MTT/MRT parameters were made to disposition data for digoxin and gentamicin to assess their use as indicators of tissue persistency. This report provides additional physiological and pharmacokinetic insights into the disposition properties of drugs and reconciles various treatments of the two-compartment model using rate constants, volume/clearance terms, and transit/residence times.     

Drug redistribution and mean transit time concepts for nonlinear pharmacokinetic systems

Equations for the mean number of cycles through the peripheral system (R) and the mean transit time through the central compartment (MTTc) are derived for intravenous drugs with linear distribution and linear or nonlinear central elimination. This R is a function of distribution clearance (CLD), dose, and area under the plasma concentration-time curve (AUC). The MTTc is a function of the central volume of distribution, CLD, dose, and AUC. The application of the proposed calculations of R and MTTc was illustrated by computer simulations.     

The use of Weibull distribution to describe thein vivo absorption kinetics

The drug in vivoabsorption rate reflects the distribution of drug molecules absorption times. For the latter the Weibull distribution is suggested and some examples taken from the literature are used to support the proposal. Cumulative absorption data for theophylline in man and pantothenic acid in rats are linearized in the double log coordinates, and the Weibull absorption model parameters are estimated by linear regression. The mean absorption time values calculated from these parameters are in close agreement with those assessed by the model-independent method.     

Mean residence time for drugs subject to enterohepatic cycling

A physiologically realistic model of enterohepatic cycling (EHC) which includes separate liver and gallbladder compartments, discontinuous gallbladder emptying and first-order absorption from both an oral formulation and secreted bile (k_a ^po and k_a ^b, respectively) has been developed. The effect of EHC on area under the first-moment curve (AUMC) of drug concentration in plasma and on parameters derived from the AUMC was investigated. Unlike AUC, AUMC is dependent on the time and time-course of gallbladder emptying, increasing as the interval between gallbladder emptying increases. Consequently, mean residence time (MRT) is also a time-dependent parameter. Analytical solutions for MRT^iv and MRT^po were derived. Mean absorption time (MAT = MRT^po — MRT^ivj is also time-dependent, contrary to findings previously published for a model of EHC with a continuous time lag. MAT is also dependent on k _a ^po , k _a ^b and the hepatic extraction ratio. The difference between MRT _po ^s two formulations with unequal k _a ^po values may deviate from the difference in the inverse of their absorption rate constants. Implications for design and interpretation of pharmacokinetic studies include (i) MAT values may be dominated by the time-course of recycling rather than the time-course of the initial absorption, depending on the extent of EHC and (ii) the unpredictable nature of the time of gallbladder emptying will contribute to intrasubject variability in derived parameters during crossover studies. Knowledge of the extent of EHC is invaluable in deciding whether modification of the in vitro release characteristics of an oral formulation will have any effect on the overall time-course of absorption in vivo. Techniques to monitor or control gallbladder emptying may be helpful for reducing variability in pharmaco-kinetic studies for compounds which are extensively cycled in bile.     

Mean residence time in the body versus mean residence time in the central compartment

Mean residence time in the body may be determined by noncompartmental methods following any type of input process into the sampled compartment. Mean residence time in the central compartment can be determined following an intravenous bolus dose, as it requires calculation of the concentration at zero time. For any other input process the mean residence time in the central compartment can be calculated from the elimination rate constant from the central compartment if one accepts the same restrictions used to calculate mean residence time in the body. Publication supported in part by NIH grant GM 26691.