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 initial slope method for model structure: Independent estimation of the elimination rate constant of a metabolite

A model structure-independent method for calculating the true elimination rate constant of a primary metabolite is presented. It does not require direct metabolite administration and uses data on drug and metabolite blood (plasma) concentrations after a bolus drug input. The method has been tested and compared with the moment method and the area function method using errorless and errant data simulated on the basis of one- and two-compartment models of the metabolite kinetics. In contrast to known methods the proposed method provided exact estimates of the elimination rate constant in the case of errorless data of both one- and two-compartment models. However the estimates are sensitive to random errors in the concentration data.     

An initial slope method for model structure: independent estimation of the elimination rate constant of a metabolite

A model structure-independent method for calculating the true elimination rate constant of a primary metabolite is presented. It does not require direct metabolite administration and uses data on drug and metabolite blood (plasma) concentrations after a bolus drug input. The method has been tested and compared with the moment method and the area function method using errorless and errant data simulated on the basis of one- and two-compartment models of the metabolite kinetics. In contrast to known methods the proposed method provided exact estimates of the elimination rate constant in the case of errorless data of both one- and two-compartment models. However the estimates are sensitive to random errors in the concentration data.     

The Influence of Liposomal Encapsulation on Sodium Cromoglycate Pharmacokinetics in Man

The pharmacokinetics of pulmonary-administered sodium cromoglycate (SCG) has been studied in five healthy volunteers. SCG, 20 mg, was inhaled as a solution and encapsulated in dipalmitoyl phosphatidylcholine/cholesterol (1:1) liposomes. Liposomal SCG produced detectable drug levels in plasma from four volunteers taken 24 and 25 hr after inhalation. Inhaled SCG solution, although producing peak plasma levels more than sevenfold greater than liposomal drug, was not detectable in 24-hr samples from any volunteer. The decline in plasma levels following inhalation of liposomal SCG (reflecting the absorption phase) was best described by a biexponential equation. The two absorption rate constants differed by more than an order of magnitude. The rapid absorption phase was probably due to free or surface-adsorbed SCG in the liposomal formulation, since the absorption rate constant for this phase did not differ significantly from the absorption rate constant for SCG in solution. The phase of slow drug absorption may then be attributed to absorption of drug released from vesicles. The data indicate that encapsulation of SCG prior to pulmonary administration prolonged drug retention within the lungs and altered its pharmacokinetics.     

Pharmacokinetics of pentobarbital after intravenous and oral administration

The plasma levels in humans of pentobarbital were determined after intravenous administration of a 50 mg dose. It was found that pentobarbital is distributed in at least two kinetically distinct body compartments: a central, or “serum” compartment and a peripheral, or “tissue,” compartment. By use of established mathematical techniques, values were assigned to the rate constants controlling the distribution and overall elimination of the drug from the body. The oral absorption of pentobarbital in fasted and nonfasted subjects was determined by mathematical analysis of the plasma level data following oral administration of a 50 mg dose. It was found that the presence of food significantly reduces the apparent absorption rate constant but not the amount absorbed. The absorption of a second dose, given 1.5 hr after the first dose, in nonfasted subjects was not affected, and a rapid increase in plasma levels occurred after this administration.     

The Area Function Method for Assessing the Drug Absorption Rate in Linear Systems with Zero-Order Input

A noncompartmental approach for determination of the apparent zero-order absorption rate constant (k ₀) has been developed. The procedure evolves from the convolution integral and requires individual oral-dose plasma concentration values and calculation of area intervals under the plasma concentration–time curves after intravenous administration. The proposed method was evaluated and compared with the Wagner–Nelson, Loo–Riegelman, deconvolution, nonlinear regression, and moment methods using errorless and errant simulation data for one- or two-compartment models. The area function method is generally equal to the best of these techniques (nonlinear regression) and superior to the weaker methods (moment, deconvolution, Loo–Riegelman), especially for errant two-compartment data. Coupled with a companion procedure for constructing fraction absorbed versus time plots and assessing first-order absorption rate constants, the area function methods offer direct and accurate means of discerning drug absorption kinetics without the need for assignment of a disposition model for drugs with linear elimination kinetics.     

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 tmax.     

Linear pharmacokinetic models and vanishing exponential terms: Implications in pharmacokinetics

A series of models more closely related than classical models to known facts about drug absorption and disposition are presented. It is shown that mathematically such models require the same number of exponential terms in the equation describing the plasma concentration following intravenous administration as in that describing the plasma concentration following oral administration. However, it is also shown that one or two of the exponential terms of the intravenous, and sometimes the oral, equation often are relatively unimportant and appear to vanish on stripping or fitting of data. This phenomenon leads to ambiguity concerning which model to assign to one or more sets of data. The number of potential models in a given situation has now been greatly increased. It is also shown that if data obey these models then neither the Wagner-Nelson nor the Loo-Riegelman method provides estimates of absorption rate constants when the A_t/V_p, t data are analyzed by conventional methods.Supported in part by Public Health Service Grant 5P11 GM 15559.     

Multiplicative dependence of the first order rate constant and its impact on clinical pharmacokinetics and bioequivalence.

The purpose of the study was to investigate the factors upon which the first order rate constant depends in order to assess the impact on the body-drug concentration when it changes throughout a treatment. A reasoning for linking the first order rate constants with several factors in a multiplicative way was proposed out taking into account kinetic and thermodynamic aspects. A multi-compartment model for drug disposition was analyzed and compartment mean drug concentrations at steady state were obtained as a function of the model kinetic constants. At the moment, only four factors were identified as responsible for the actual rate constant value. Apart from an intrinsic kinetic constant, they are the inverse of compartment volume, the transfer surface area, the fraction of mass able to be transferred, and the fraction of mass that effectively can be transferred. In clinical practice some of these factors might change throughout time (because of chronophysiological rhythms or drug availability at the action sites) and consequently, an inconstant extra-plasma/plasma drug concentration ratio could be obtained. In conclusion, therapeutic response prediction for a treatment does not upon plasma drug concentration monitoring. Equivalence in plasma drug exposure should not mean therapeutic equivalence, because differences in the rate and in the extent between test and reference products may induce a change in the action site/plasma drug concentration ratio.     

Estimation of Oral Bioavailability of a Long Half-Life Drug in Healthy Subjects

Purpose. To estimate and compare the oral bioavailability of a drug (BMS-187745) administered as single doses of oral solution of either the parent drug or its prodrug (BMS-188494). Methods. A single-dose, two-period, three-treatment, control-balanced, residual-effect, incomplete block crossover study was completed in 16 healthy male subjects. All subjects received a 10 mg IV infusion of BMS-187745, and a single oral dose of either BMS-187745 (PO1) or BMS-188494 (PO2). A model is proposed to calculate the oral bioavailability of BMS-187745 which has a long half-life; incomplete data points were available to characterize its elimination phase. The plasma concentration-time data obtained following IV infusion of parent drug, and after administration of either PO1 or PO2 treatment were fitted simultaneously with systemic pharmacokinetic parameters shared by both the oral and IV routes of administration. Results. The best simultaneous fittings of the plasma concentration-time data were obtained by using a biexponential pharmacokinetic model with a first-order absorption rate constant. The mean bioavailability (F) values of BMS-187745 estimated by the proposed model were 26.5% and 2.6% when given as oral solution of its prodrug and as the parent drug. The coefficient of variation (CV) of these F values are reasonable, ranging from 38–40%. In contrast, F calculated by the model-independent AUC method exhibited high CV, ranging from 111–120%. Conclusions. The oral bioavailability values estimated by the proposed model were more reasonable compared to those calculated by the model-independent AUC method. The proposed approach may be useful for estimating bioavailability of long half-life drugs when incomplete data points are available to characterize their elimination phase.     

Transsynovial Drug Distribution: Synovial Mean Transit Time of Diclofenac and Other Nonsteroidal Antiinflammatory Drugs

The synovial mean transit time of diclofenac was determined by two methods from existing plasma and synovial fluid concentration-time data. These data were obtained from single- and multiple-dosing regimens of diclofenac in patients with osteoarthritis and rheumatoid arthritis. Plasma and synovial fluid concentration-time data taken from the literature for four other nonsteroidal antiinflammatory drugs (etodolac, ibuprofen, indomethacin, and tenoxicam) were also analyzed. The two methods of data analysis rely on the determination of the ratio of the area under the synovial fluid concentration-time curve to the area under the plasma concentration-time curve. Both methods can be considered noncompartmental because in determining the first-order exit rate constant for the synovial fluid (the inverse of the synovial mean transit time), an analysis of the overall distribution and elimination characteristics of the drug is unnecessary. Method 1 makes use of the information contained in the postdistributional synovial fluid to plasma concentration ratio whereas method 2 is a linear pharmacokinetic model using a partial-areas analysis. The single dose mean ± S.D. synovial fluid exit rate constant for diclofenac was 0.39 ± 0.33 hr^–1 (n = 6), which was not significantly different from that determined by method 2; which was 0.49 ± 0.52 hr^–1. The steady state mean ± S.D. diclofenac synovial fluid exit rate constants for methods 1 and 2 were 0.43 ± 0.18 and 0.54 ± 0.71 hr^–1 (n = 8), respectively, which were not significantly different. These values of synovial fluid exit rate constants result in a synovial mean transit time for diclofenac that is approximately 2 to 2.5 hours. The synovial mean transit time calculated using method 1 from literature data for etodolac, ibuprofen, indomethacin, and tenoxicam were 6.8, 2.2, 4.8, and 3.5 hours, respectively. The synovial mean transit times calculated by method 2 for the same drugs were 5.3, 3.4, 4.7, and 4.0 hours, respectively. Similar values of the synovial mean transit time of nonsteroidal antiinflammatory drugs were achieved by using either of these two methods, both of which avoid complex equation fitting which is statistically problematic in the frequently data-sparse environment of extravascular sampling.     

A novel simultaneous modeling approach to estimate linearity of pharmacokinetic parameters, including saturation of intestinal efflux, in the rat

INTRODUCTION: Various independent methods exist for the estimation of linearity of pharmacokinetic parameters in vivo. A novel simultaneous modeling approach has been developed in the rat that in combination allows estimation of the rate and extent of duodenal absorption, hepatic first pass extraction and saturation of potential dose-dependent duodenal bioavailability (saturation of intestinal efflux). METHODS: Simultaneous modeling of plasma concentrations of a Pfizer compound in the rat were conducted using NONMEM after (1) accelerated intravenous, intraduodenal, and intraportal infusions over 5 h and (2) 5-min intravenous infusions of 0.28 and 1.4 mg doses. RESULTS: The data was best described by a two-compartment linear pharmacokinetic model with good agreement between observed and model predicted plasma concentrations following the various routes of administration. Clearance was estimated to be linear up to plasma concentrations of 1200 ng/ml. The estimated rate constants (+/-asymptotic errors) for intraduodenal absorption (KA), movement of drug from plasma to tissue (K23) and movement of drug from tissue to plasma (K32) were 0.645+/-0.107, 18.0+/-2.98, and 2.02+/-0.209 h(-1), respectively. The rate constants for drug elimination from the central compartment (K20) after 5-min intravenous infusion or accelerated infusion were 3.24+/-0.6 or 6.26+/-1.64 h(-1). The estimated maximal extent of first pass extraction was 17%. The model (including increasing duodenal bioavailability as the amount in the duodenum increases, from a minimum of 5% to a maximum estimated intraportal bioavailability value-83%) indicated a saturable intestinal efflux process. DISCUSSION: This novel study design and the proposed method for data analysis provides a robust and efficient means for assessing the linearity of multiple pharmacokinetic processes while accounting for the multi-compartmental distribution characteristics of the test compound.     

Plasma and tonsillar tissue pharmacokinetics of teicoplanin following intramuscular administration to children

The population pharmacokinetics of teicoplanin in plasma and tonsillar tissue in children was determined following intramuscular administration. Thirty seven patients in all received either a single 5 mg/kg dose; 2 doses of 5 mg/kg, 12 h apart; 3 doses of 5 mg/kg, 12 h apart; or, a single 10 mg/kg dose. Limited data, comprising a maximum of 2 blood samples and 1 tonsillar sample were taken from each patient, with the maximum time being 48 h after the first dose of teicoplanin (in the 3×5 mg/kg dosing schedule). All plasma data were analyzed simultaneously by a maximum likelihood method employing a modified EM algorithm. A first-order absorption, one-compartment disposition model was fitted to the data. Mean parameter values (with lower and upper 95% confidence intervals) were: clearance/bioavailability, 0.024 L h⁻¹ kg⁻¹ (0.020–0.027); volume of distribution/bioavailability, 0.61 L kg⁻¹ (0.54–0.70); absorption rate constant, 0.43 h⁻¹ (0.31–0.61). A first-order transfer model for distribution of teicoplanin between plasma and tonsillar tissue was fitted to the tonsil data. The mean parameter values (95% confidence intervals) were: transfer rate constant between plasma and tonsils 0.49 h⁻¹ (0.35–0.67); transfer rate constant between tonsils and plasma 0.73 h⁻¹ (0.52–1.03). These rate constants correspond to a distribution half-life of 0.95 h and an equilibrium distribution concentration ratio between tonsillar tissue and plasma of 0.67. After normalising clearance and volume of distribution for body weight, there was no further influence of body weight on the pharmacokinetic parameters. Also, there was no effect of dose, and as two formulations were used, one for the 5 mg/kg dose and the other for the 10 mg/kg dose, no effect of formulation on the pharmacokinetics of teicoplanin after im (intramuscular) administration was found.     

A simple method for determining whether absorption and elimination rate constants are equal in the one-compartment open model with first-order processes

A simple method is presented by which one may determine if the absorption and the elimination rate constants are equal (in the one-compartment body model) using only plasma drug data. This method suggests the pertinent equation to calculate the relevent pharmacokinetic parameters.     

Measurement of sulfamethizole clearance rate by nonthrombogenic constant blood-withdrawal system.

A method for the measurement of the total body clearance rate (CR) of drugs is described. It involves a single intravenous injection of a known quantity of the drug (D) and automatic integration of the plasma concentration curve, using a portable, nonthrombogenic, constant blood-withdrawal system. When blood withdrawal is carried out until the concentration of the drug in the plasma approaches zero, the concentration of the drug in the collected pool, the integrated concentration (ICT) multiplied by the time of collection (T) yields the integral of the concentration curve: (see article). The method was tested by measuring the clearance rate of sulfamethizole in five dogs by the established constant infusion method. At three plasma levels (25, 75, and 200 mg/liter), the plasma concentration had no significant effect on the clearance rate. The clearance rate of sulfamethizole was subsequently measured in the same dogs by the new single-injection constant withdrawal method. Multiple blood samples were collected at 15-min intervals simultaneously with the constant withdrawal of blood. There was no significant difference between the clearance rate of sulfamethizole measured by the two methods. The initial peak mean concentration of the drug from the time of injection (t = 0) to the time of the first blood sampling (t = 15 min) was calculated from the difference between (see article) obtained by the constant withdrawal method and that obtained from the results of the multiple blood withdrawals by the trapezoidal rule. The integrated concentration IC15 was significantly higher than its estimation by the semilogarithmic linear regression method.     

General derivation of the ideal intravenous drug input required to achieve and maintain a constant plasma drug concentration. Theoretical application to lignocaine therapy

Summary A constant plasma drug concentration can be achieved and maintained by the intravenous administration of an initial bolus loading dose in conjunction with a constant rate and an exponential intravenous drug infusion. The drug input required to achieve a constant plasma drug concentration is derived without making any assumptions about the nature of drug distribution within the body or elimination from the body.     

A minimax approach to the single-point method of drug dosing

The single-point dose prediction method is based on the observation that for drugs obeying single compartment elimination kinetics there is a nearly constant reciprocal relation between the plasma level at a fixed time following a single loading dose and the dose that is required to maintain the desired steady state plasma level of the drug. This paper describes an improved method for choosing a plasma sampling time and a proportionality constant. It applies to either drugs administered intravenously or to drugs whose rates of absorption from the site of administration are very rapid compared to their rates of elimination from the body. The sampling time and proportionality constant chosen are those that minimize the maximum relative deviation of the maintenance dose estimated by the single-point method from the dose that would be estimated if the individual's true elimination rate constant were known. The paper also supplies a method to determine the maximum error that may be introduced into the estimation of the maintenance dose by using the single-point method.This investigation was supported in part by NIH National Research Service Award GM 09279-02 (M.M.B.), NIH grant R01 AM 25744-07, and NATO Collaborative Research Grant 85/0207 (E.M.L.). M.M.B. is a Daland Scholar of the American Philosophical Society.     

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 (k_m) 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 k_m to be averaged, but works best using data prior to the metabolite tax.This work was supported in part by National Institutes of Health grant 24211.     

An APL computer program for estimating rate constants of drug absorption

The algorithm of this program for estimating rate constants of drug absorption is mainly based on the Loo-Riegelman method. In order to improve the flexibility of the program, several options for the users were included: one-, two- as well as three-compartment open models with first-order elimination; two optional methods to calculate the area under the curve, i.e. the simple trapezoidal method and the Lagrange method combined with log-trapezoidal approximation and others. In addition to the estimation of the rate constant of drug absorption, this program can be applied for the design of optimal sampling schemes. For this purpose an extra subroutine for simulating plasma drug concentration-time courses is also included.     

Pharmacokinetics and bioavailability of theophylline following enema and suppository administration in man

The pharmacokinetics and bioavailability of theophylline from a commercial oral elixir of theophylline, a rectal suppository of aminophylline, and a rectal enema of theophylline monoethanolamine was compared in six normal subjects. Using a complete crossover design, the fasted subjects received a single dose of each dosage form. Blood and saliva samples were collected at frequent time intervals for 24 h, and the plasma assayed for theophylline by a specific thin-layer chromatography densitometric method. No statistically significant differences existed among the three dosage forms with respect to Cmax and AUC corrected for the elimination rate constant and the dose (mg kg-1). However, tmax was significantly larger for the suppository. While the rate of absorption was significantly slower for the suppository, no differences in the extent of absorption existed among the three dosage forms. A one-compartment open model with apparent first-order absorption adequately described the plasma concentration-time data for the elixir and enema, whereas the suppository data were best fitted by a one-compartment open model with apparent zero-order absorption and a lag time. A rate-limiting, concentration-independent release of drug from the base most likely accounts for the slow absorption of theophylline from the suppository. While the saliva:plasma ratio remained fairly constant for most of the study period, the large variability found during the absorption phase following drug administration limits the usefulness of this parameter as a monitor of theophylline plasma concentrations.