Bioavailability assessment: methods to estimate total area (AUC O to infinity) and total amount excreted (A infinity e) and importance of blood and urine sampling scheme with application to digoxin

The history and future of population pharmacokinetic analysis in drug development

The analysis of pharmacokinetic data has been in a constant state of evolution since the introduction of the term pharmacokinetics. Early work focused on mechanistic understanding of the absorption, distribution, metabolism and excretion of drug products.The introduction of non-linear mixed effects models to perform population pharmacokinetic analysis initiated a paradigm shift. The application of these models represented a major shift in evaluating variability in pharmacokinetic parameters across a population of subjects.While technological advancements in computing power have fueled the growth of population pharmacokinetics in drug development efforts, there remain many challenges in reducing the time required to incorporate these learnings into a model-informed development process. These challenges exist because of expanding datasets, increased number of diagnostics, and more complex mathematical models.New machine learning tools may be potential solutions for these challenges. These new methodologies include genetic algorithms for model selection, machine learning algorithms for covariate selection, and deep learning models for pharmacokinetic and pharmacodynamic data. These new methods promise the potential for less bias, faster analysis times, and the ability to integrate more data.While questions remain regarding the ability of these models to extrapolate accurately, continued research in this area is expected to address these questions.

Organophosphorus pesticide degradation product in vitro metabolic stability and time-course uptake and elimination in rats following oral and intravenous dosing

Levels of urinary dialkylphosphates (DAPs) are currently used as a biomarker of human exposure to organophosphorus insecticides (OPs). It is known that OPs degrade on food commodities to DAPs at levels that approach or exceed those of the parent OP. However, little has been reported on the extent of DAP absorption, distribution, metabolism and excretion. The metabolic stability of O,O-dimethylphosphate (DMP) was assessed using pooled human and rat hepatic microsomes. Time-course samples were collected over 2 h and analyzed by LC-MS/MS. It was found that DMP was not metabolized by rat or pooled human hepatic microsomes. Male Sprague-Dawley rats were administered DMP at 20 mg kg(-1) via oral gavage and i.v. injection. Time-course plasma and urine samples were collected and analyzed by LC-MS/MS. DMP oral bioavailability was found to be 107 ± 39% and the amount of orally administered dose recovered in the urine was 30 ± 9.9% by 48 h. The in vitro metabolic stability, high bioavailability and extent of DMP urinary excretion following oral exposure in a rat model suggests that measurement of DMP as a biomarker of OP exposure may lead to overestimation of human exposure.

Prediction of modified release pharmacokinetics and pharmacodynamics from in vitro, immediate release, and intravenous data

The aim of this study was to demonstrate the value of mechanistic simulations in gaining insight into the behaviors of modified release (MR) formulations in vivo and to use the properly calibrated models for prediction of pharmacokinetics (PK) and pharmacodynamics (PD). GastroPlus (Simulations Plus, Inc.) was used to fit mechanistic models for adinazolam and metoprolol that describe the absorption, PK, and PD after intravenous (i.v.) and immediate release (IR) oral (p.o.) administration. The fitted model for adinazolam was then used to predict the PD profile for a MR formulation and to design a new formulation with desired onset and duration of action. The fitted metoprolol model was used to gain insight and to explain the in vivo behaviors of MR formulations. For each drug, a single absorption/PK model was fitted that provided simulated plasma concentration-time profiles closely matching observed in vivo profiles across several different i.v. and p.o doses. Sedation score profiles of adinazolam were fitted with an indirect PD model. For metoprolol, the fitted absorption/PK model for IR p.o. doses was used to select in vitro dissolution conditions that best matched the in vivo release of MR doses. This model also explained differences in exposure after administration of MR formulations with different release rates. Mechanistic absorption/PK models allow for detailed descriptions of all processes affecting the two drugs' bioavailability, including release/dissolution, absorption, and intestinal and hepatic first pass extraction. The insights gained can be used to design formulations that more effectively overcome identified problems.

Digoxin: use pattern in Estonia and bioavailability of the local market leader

BACKGROUND

In comparison with neighbouring Scandinavian countries, the use of digoxin in Estonia is high. The present study was carried out to determine the use pattern of digoxin in Estonia and bioavailability of the local market leader preparation in comparison with Lanoxin.

METHOD

Drug use data were evaluated from the annual reports of wholesale companies. For the bioequivalence study, a single-blind cross-over randomised two-way single-dose comparative bioavailability study was performed using 14 healthy volunteers. Digoxin concentrations in serum samples and urine were measured by chemiluminescent competitive immunoassay.

RESULTS

The use of digoxin in Estonia has increased by 35% during the period 1994-97. The steady market leader was the local generic drug. No statistically significant differences were found in any pharmacokinetic parameter between the generic preparation and Lanoxin. All parameters showed considerable variability. The total amount of drug excreted was the parameter with lowest inter- individual variation.

CONCLUSION

The present study indicates that the generic digoxin preparation studied is bioequivalent to Lanoxin. The increasing use of digoxin in Estonia is not caused by low bioavailability of the local market leader but by therapeutic traditions.

Calculating confidence intervals for summary measures of individual curves via nonlinear regression models

In biomedical research data are often collected serially over time. Hence, the main outcome is represented by response curves. A suitable approach to analyse such data is given by summary measures describing the main features of the response curves. An important issue is the precision of the estimated summary measures, which can be represented by confidence intervals. However, since summary measures frequently cannot be obtained via linear relationships, the calculation of confidence intervals involves some special considerations. In this paper attention is focused on unimodal response curves. Important summary measures for this type of response curves are the curve maximum (Cmax), the time to curve maximum (tmax), and the area under the curve (AUC). These summary measures can be calculated from the parameters of nonlinear regression models fitted to the data. Since the summary measures are nonlinear functions of the regression coefficients the multivariate delta method is used to derive formulas for the standard errors and confidence intervals of the summary measures. The method is illustrated by application to pharmacodynamic data.

Optimal design allocations for estimating area under curves for studies employing destructive sampling

Optimal allocations of experimental resources for the estimation of integrals is considered for experiments that use destructive sampling. Given a set of sampling times, a minimum mean square error rule is given for the allotment of fixed experimental resources to the independent variable. The results are seen to be functionally dependent upon the pattern of underlying variability assumed in the model and upon the quadrature rule used to estimate the integral. Extensions to other optimality criteria, including a minimum mean absolute deviation criterion, and to cases involving multiple treatment groups, are also noted.

Steroid metabolism in isolated rat hepatocytes

In vivo predictability of results obtained from studies of drug metabolism using isolated rat hepatocytes is questionable, mainly because of modeling difficulties due to the simultaneously occurring substrate transferring processes. In the present study, an attempt was made at simplifying the models used to describe the kinetics of biotransformation by enzymes enclosed in a cellular environment. Viability assessment of the cell preparation indicated that the cell membrane was intact and functional. Six corticosteroids were used in these studies. Simplifying assumptions concerning uptake and protein binding were confirmed by running independent experiments. Progress curves of unchanged steroid disappearance from the cell suspending medium at different initial concentrations were used to either confirm applicability or detect deviations from simple Michaëlis-Menten behavior and were fitted to the appropriate kinetic models by means of nonlinear least-squares regression analysis. As an example, corticosterone extraction ratio obtained in this study compared well with literature values from intact rats. A linear correlation was found between the logarithm of the apparent first order rate constant (Vm/Km) obtained at low substrate concentrations and the logarithm of the oil/water partition coefficients of 17 alpha-hydroxyprogesterone, corticosterone and hydrocortisone.

A model describing the disposition of phenytoin in isolated rat hepatocytes

The use of isolated rat hepatocytes in studies of drug metabolism has become well documented in the past few years. However, in part because of modelling difficulties due to the simultaneously occurring substrate transferring processes, its predictability of in vivo situations has not been emphasized. Much controversy surrounds the metabolism of phenytoin (5,5-diphenylhydantoin), a widely used anticonvulsant, and an appropriate pharmacokinetic model to describe the disposition of this drug still lacks general acceptance. In the present study, metabolism of phenytoin in the isolated rat hepatocyte system was followed by assaying either the unchanged drug or the pooled metabolites in both the suspending medium and the cells. A model was developed which can describe the time course of the different species sampled. Inhibition of biotransformation by the major metabolic product [5-(p-hydroxyphenyl)-5-phenylhydantoin or p-HPPH] and the uptake and release of the latter were also studied, in order to elucidate the role of product inhibition in determining the dose-dependent pharmacokinetic behaviour of the drug. The results obtained strongly suggest that only concentrations of p-HPPH higher than the ones attained by phenytoin biotransformation alone can significantly inhibit the main enzymatic reaction.

Sampling strategies for noncompartmental estimation of mean residence time

An optimization procedure is presented for selecting sample times for estimating mean residence time using noncompartmental data analysis. Performance of this experimental design strategy is evaluated using Monte Carlo simulations of a model for digoxin kinetics. The contribution of measurement error to the overall expected error in MRT estimates is examined and its importance emphasized. Also, the sensitivity of the proposed experimental design strategy to required assumptions is investigated using the digoxin model, and the importance of accurate estimates of extrapolated areas is noted.

Absorption and bioavailability of oral erythromycin

1 Extent and rate of absorption of erythromycin were studied in 24 healthy volunteers whose disposition kinetics after i.v. injections had been previously documented. 2 Two clinically attractive oral dosage regimens were administered: erythromycin stearate tablets 1 h before meals (Regimen A), and erythromycin base capsules 30 min after start of meals (Regimen B), each equivalent to erythromycin 250 mg, 6 h apart for 9 doses. 3 Serum concentrations of erythromycin measured during the 1st and 9th (steady-state) dosing intervals resulted in higher maximum serum concentrations for Regimen A (median 1.1, range 0-3.3 and 2.7, 0.6-7.3 mg/l for Doses 1 and 9, respectively) compared with Regimen B (0.4, 0-2.2 and 1.4, 0.2-4.9 mg/l). 4 Absorption occurred earlier with Regimen A with times to maximum concentrations (median, range) being 128, 60-greater than 360 and 118, 75-210 min for doses 1 and 9 respectively, (lag times 75, 15- greater than 360 and 73, 10-110 min) compared with 303, 130-greater than 360 and 173, 45-greater than 360 min (lag times 183, 70-greater than 360 and 190, 20-330 min) for Regimen B. 5 Where it could be assessed, absolute bioavailability for Regimen A was approximately 30% (Dose 1) and 65% (Dose 9) and 40% for both doses of Regimen B. 6 Whereas individual serum concentration-time curves were accurately predicted by the mean for Regimen A, predictability for Regimen B was impossible due to prolonged and variable lag time. 7 The large intersubject variability in erythromycin serum concentration after oral administration, has been shown conclusively to be related to variability in absorption kinetics and absolute bioavailability rather than to variability in disposition kinetics.

Evidence of nonlinearity in digoxin pharmacokinetics

Six normal male volunteers received 0.5 mg label doses of digoxin as (a) a bolus intravenous injection over 2 min, (b) a constant rate intravenous infusion over 1 hr, (c) a constant rate intravenous infusion over 3 h, and (d) a solution in 5% dextrose given orally. Plasma concentrations of digoxin were measured by radioimmunoassay for a 4 day period and urinary excretion for a 6 day period after the single doses. The mean (coefficient of variation) total areas under the plasma concentration-time curves per 0.5 mg of digoxin were (a) 35.55 (14.8%), (b) 30.20 (27.7%), (c) 25.80 (35.5%), and (d) 15.47 (49.9%); the means differed significantly (0.01 greater than p greater than 0.005). The mean (coefficient of variation) total amounts excreted in the urine as a fraction of the dose were (a) 0.689 (6.31%), (b) 0.517 (20.4%), (c) 0.588 (16.8%), and (d) 0.374 (23.4%); the means differed significantly (p less than 0.001). Both the total clearance and the nonrenal clearance of digoxin differed significantly with the method of intravenous administration. The slower the rate of input of digoxin to the body, the greater were both the total clearance and the nonrenal clearance of the drug, which strongly suggests nonlinear pharmacokinetics.

A standard approach to compiling clinical pharmacokinetic data

A standard format for a Clinical Pharmacokinetic Summary is proposed. It consists of a heading, tables, notes, and references for each drug reviewed. The table presents a unified and logical set of clinically useful population pharmacokinetic parameters. They concern four major areas: absorption, distribution, elimination, and the relationship of concentration to effect. Within each major group, parameters dealing with extents and rates of processes are given. Each such parameter is really two: a population mea value (for example, average volume of distribution) and the standard deviation of individual values about this mean. The first value allows individual predictions of dosage or drug level to be made; the second allows computation of the likely proximity of subsequently observed quantities to those predictions. The table presents single consensus values for each population parameter, rather than a list of values. A procedure for computing these consensus values, and for revising them in the light of new data, or reinterpreted old data, is given. Examples of Summaries are given. The method appears applicable to a variety of drugs. We suggest our approach as a standard one for preparing Clinical Pharmacokinetic Summaries, and urge our colleagues to consider it for that purpose.

The unsteady model. An alternative approach to nonlinear pharmacokinetics

In this paper an alternative approach to nonlinear pharmacokinetics modelling has been developed from first principles. This "Unsteady Model" is able to describe the situation whereby one or more independent drugs and their metabolites compete for free attachment sites in liver, tissue, red blood cells etc. The Unsteady model collapses to well-known existing models viz: Michaelis-Menten, Langmuir tissue binding and the linear compartment models, under certain well-defined, limiting conditions. The Unsteady model and its collapse to existing models is derived mathematically and illustrated with simulations. For several reasons the Unsteady model would appear to have many advantages and wide application.

Studies on the clinical pharmacokinetics of imidazopyrazole

Plasma decay kinetics were analyzed for seven patients (400-5700 mg) during a Phase I clinical trial of imidazopyrazole. A two-compartment open pharmacokinetic model was able to account for the data. The median alpha-phase half-life was found to be 0.65 hour, with a median beta-phase half-life of 23.1 hours. Twelve per cent of the administered drug was excreted unchanged in 72 hours, whereas the total amount of imidazopyrazole equivalents excreted in that period was 38.6%. The median plasma equivalent space was found to be 15.9 l./m2, and volume of distribution at steady state was 40.2 l./m2. Renal and plasma clearance for imidazopyrazole was found to be 0.2 and 1.7 l./m2/hr, respectively.

A determinant solution for infinity values of multi-exponential equations using equal time intervals

A determinant solution for the infinity values of multi-exponential equations using the Guggenheim method of equal time intervals is demonstrated. The resultant solution is independent of the rate constants and can be applied using data in the early non-log-linear phase of the process. The minimum number of data points needed for an nth exponential equation is (2N + 1).

A method to predict infinity values for biexponential processes

An equation is presented which allows infinity values for biexponential processes to be predicted in the early nonlinear phase when samples are taken at equal time intervals. This equation is independent of the value or ratio of the rate constants involved in the process. However, this method is very sensitive to noise normally associated with urine data.

Methods for evaluation of urinary excretion parameters of alclofenac after I.M. administration of its water soluble lysine salt in man

The urinary excretion data after I.M. administration of water soluble lysine salt of Alclofenac were analysed by the techniques suggested by Niebergall, Wagner, Martin and Cummings. All methods used give similar estimates of both DU infinity and Kel with exception of the "Sigma minus" method when DU infinity obtained by "Rate Method" was utilized. Niebergall's method is preferred on the basis that it provides an accurate estimation of both DU infinity and Kel. These parameters, evaluated after administration of Alclofenac-lysinate, resulted in agreement with previously reported data obtained after administration of different pharmaceuticals of acidic drug.

Sensitive radioimmunoassay for digoxin in plasma and urine

A reproducible and sensitive radioimmunoassay for digoxin in either serum, plasma or urine is described. Using 0.5 ml of serum or plasma, the assay sensitivity is 0.05 ng of digoxin/ml. The antiserum and tracer solutions employed are available in a kit sold in the United States. All other reagents were prepared in the laboratory. The assay allows measurement of digoxin in plasma or serum for 96 hours after single 0.5 mg doses of digoxin; this is necessary in human bioavailability studies to accurately estimate the total area under the digoxin concentration, time curve from zero to infinite time. In contrast, with the kit assay, employing 0.2 ml of plasma or serum, it has been reported that the 12 hr serum digoxin levels, after single 0.5 mg doses, are, in most subjects, below the sensitivity limit (about 0.5 ng/ml) of the assay.