A method for estimating within-individual variability in clearance and in volume of distribution from standard bioavailability studies

Proof of Concept in Assignment of Within-Subject Variability During Virtual Bioequivalence Studies: Propagation of Intra-Subject Variation in Gastrointestinal Physiology Using Physiologically Based Pharmacokinetic Modeling

While the concept of ‘Virtual Bioequivalence’ (VBE) using a combination of modelling, in vitro tests and integration of pre-existing data on systems and drugs is growing from its infancy, building confidence on VBE outcomes requires demonstration of its ability not only in predicting formulation-dependent systemic exposure but also the expected degree of population variability. The concept of variation influencing the outcome of BE, despite being hidden with the cross-over nature of common BE studies, becomes evident when dealing with the acceptance criteria that consider the 90% confidence interval (CI) around the relative bioavailability. Hence, clinical studies comparing a reference product against itself may fail due to within-subject variations associated with the two occasions that the individual receives the same formulation. In this proof-of-concept study, we offer strategies to capture the most realistic predictions of CI around the pharmacokinetic parameters by propagating physiological variations through physiologically based pharmacokinetic modelling. The exercise indicates feasibility of the approach based on comparisons made between the simulated and observed WSV of pharmacokinetic parameters tested for a clinical bioequivalence case study. However, it also indicates that capturing WSV of a large array of physiological parameters using backward translation modelling from repeated BE studies of reference products would require a diverse set of drugs and formulations. The current case study of delayed-release formulation of posaconazole was able to declare certain combinations of WSV of physiological parameters as ‘not plausible’. The eliminated sets of WSV values would be applicable to PBPK models of other drugs and formulations.

New mathematical implementation of generalized pharmacodynamic models: method and clinical evaluation

A new method and experimental design are presented to unambiguously estimate the transduction function (phi) and the conduction function (psi) of the generalized pharmacodynamic model: E = phi (psi * r), when measured pharmacokinetic response r is (i) drug plasma concentration and (ii) drug input rate into the systemic circulation. phi relates the observed pharmacologic effect E to the concentration at the effect site: ce = (psi * r), psi defines transfer of drug from plasma site to effect site or from input site to effect site, and * represents the convolution integral. The model functions psi and phi were expressed as cubic splines giving a very flexible description of those processes which is not biased by the structured assumptions of more conventional models, e.g., effect compartment models. The experimental design proposed addresses the problem of ambiguous identification of the model functions typical of these models; that is, there is more than one pair of very different functions describing the effect data collected after a single drug administration. We tested the hypothesis that the simultaneous fitting of at least two administrations allows the unambiguous identification of the model functions without the need for unlikely or cumbersome constraints. The performance of the mathematical implementation and the robustness of the methods with respect to measurement noise and possible failure of some assumptions, such as intraindividual variability, were tested by computer simulations. The method was then applied to the results of a clinical study of verapamil pharmacodynamics in 6 healthy subjects. Results of these studies demonstrated that the mathematical implementation does not introduce bias or artifact into the estimated functions and that the models and the proposed methods are suitable for application to clinical research. Two drug administrations were sufficient to unambiguously describe verapamil pharmacodynamics in the 6 human subjects studied.

Pharmacokinetic interactions between theophylline and other medication (Part II)

Part I of this article, which appeared in the previous issue of the Journal, covered the effects or lack of effects on theophylline clearance of sympathomimetics, corticosteroids, antihistamines and other antiallergy drugs, antimicrobial agents, phenytoin, carbamazepine, barbiturates, antacids and activated charcoal. In Part II, this discussion is extended to the effects of other agents. Overall summaries, both textual and tabular, appear in Part I.

Theophylline pharmacokinetics after intramuscular administration

This study was aimed at assessing the pharmacokinetics of a single dose of theophylline solution (aminophylline 480 mg) administered by intramuscular (i.m.) route to 16 subjects (age 28-61 years, body weight 52-75 kg). The same dose was given a week apart by oral route in fasting conditions. The intraindividual comparison shows that by i.m. route the rate, but not the extent, of absorption may be somewhat lower. From the first hour on, until hour 3-4 after i.m. dosing, all subjects achieved a safe and effective serum theophylline concentration (9-17 mg/liter). This suggests that, although usually not recommended, self-administration of a single dose of aminophylline by i.m. route may temporarily help theophylline-responsive patients in distress, when other routes of administration are not available and facilities for intensive conventional treatment are lacking.

Lack of effect of ponsinomycin on the plasma pharmacokinetics of theophylline

The influence of ponsinomycin on the pharmacokinetics of theophylline has been studied in 12 young healthy volunteers. They received 10 doses of theophylline 200 mg every 8 h p.o., successively in the absence and then in the presence of ponsinomycin. This new macrolide, structurally related to midecamycin, was given in the therapeutic dose of 800 mg b.d. for 5 days, starting 2 days before the second phase of treatment with theophylline. The pharmacokinetic parameters of theophylline, calculated from its plasma concentration at steady-state, were not affected by the co-treatment. In particular, there was no significant difference between the peak and trough plasma levels, apparent clearance or apparent elimination half-life of theophylline in the absence and the presence of ponsinomycin. Only renal clearance was slightly (27%) but significantly increased by the co-treatment. The results suggest that ponsinomycin would be a good choice if a macrolide antibiotic were needed in patients being treated with theophylline.

Inter- and intrasubject variation of digoxin renal clearance in normal adult males

Three methods of estimating inter- and intrasubject variances and coefficients of variation of digoxin renal clearance are discussed and illustrated. All three methods gave essentially the same values for intrasubject variation; two of the methods (II and III), based on two-factor and one-factor analyses of variance, respectively, gave the same estimates of intersubject variation. The preferred method I involves directly calculating variances from the rows and columns of the tabular data, where the rows are repetitive treatments in the same subject and the mean variance represents intrasubject variance; a column represents different subjects' results on a given treatment and the mean of the column variances represents intersubject variance. Problems in attempting to use components of variance are discussed. Intrasubject coefficients of variation of digoxin renal clearance averaged 23.8 percent by method I and ranged from 15.2 to 28.6 percent. Intersubject coefficients of variation averaged 30.5 percent with a range of 17.5-41.8 percent by method I and averaged 42.1 percent with a range of 19.2-49.7 percent by methods II and III.

Interindividual and intraindividual variability in labetalol pharmacokinetics

The between-subject and within-subject variability in the pharmacokinetics of labetalol at steady state were determined. Sixteen nonobese normal volunteers (mean age, 27 years) received five different formulations of labetalol orally on five different occasions every 12 hours for five doses. A 7-day washout separated each administration phase. Plasma concentration-time data for labetalol were obtained over the 24-hour period after the fifth dose in each phase. Labetalol concentrations in plasma were measured using high-performance liquid chromatography (HPLC). Pharmacokinetic parameters for each subject after each study phase were estimated. The mean V beta/F, Vdss/F, TBC/F, t1/2 beta, and AUC tau 0 for each subject ranged between 18.1 and 161.9 L/kg, 7.1 and 53.9 L/kg, 1.3 and 5.72 L/hr/kg, 6.9 and 11.0 hours, and 154 and 520 micrograms.hr/L, respectively, indicating large interindividual variability. Considerable intraindividual variability in each of the pharmacokinetic parameters was also observed. These data indicate that a larger number of subjects will be required to detect "significant" differences in the disposition of labetalol.

Use of simultaneous computer fitting to estimate the apparent absorption rate constant

In this study we explored an alternative approach to specifically determine the apparent absorption rate constant (ka) and the initial disposition macro-rate constant (alpha) without intravenous dose data. Data sets were simulated with ka values in a range of +/- 70% of alpha. A 10%, uniformly distributed, random error was added to all the simulation parameters and to the concentration values. The data sets were fit individually (one data set) and simultaneously (all possible combinations of two, four, or six data sets) using NONLIN. The parameters alpha, beta (the terminal disposition rate constant), and k21 (the exit rate constant from the peripheral compartment) were assumed to be common parameters between the data sets. If a single data set was used in fitting the equation, large deviations in the estimates for ka and alpha occurred as ka became less than alpha. However, when multiple data sets were fit simultaneously, correct values for ka and alpha were consistently predicted regardless of the relative magnitude of the initial estimates.

Individualizing theophylline dosage: evaluation of a single-point maintenance dose prediction method

A dosage prediction method to estimate theophylline clearance and dose requirement was evaluated in 22 outpatients with partly reversible obstructive airways disease. The steady state theophylline dose required to achieve a target concentration (Css) was predicted using a single serum theophylline determination 8 h after a single oral test dose. In 17 nonsmoking patients a mean absolute deviation of 8.2% (range 0.0-21.7%) between predicted and observed Css was found, and in 5 smoking patients the mean deviation was 34.0% (range 2.2-53.8%). In 17 healthy smokers the single-point method was found to predict theophylline clearance at a sampling time of 8 h with a prediction error of 11.3 (range 0.8-25.3%) compared to the clearance determination using the area under the curve. In addition, a numerical simulation program to assess the influence of absorption, elimination and sampling time on predictive accuracy showed that the method could be successfully applied to a patient population with elimination rate constants between 0.07 1/h and 0.25 1/h, allowing a mean prediction error of 15%.

Estimation of absolute bioavailability assuming steady state apparent volume of distribution remains constant

The limitations of using estimates of extent of bioavailability (F) based on the assumption that either clearance (CL) or Varea remain, constant are discussed in relation to the situation where CL changes between doses. When estimates of F assume CL to remain constant, the extent of the error is the same for all drugs where the percentage change in CL is the same. Assuming Varea to remain constant, the error in F will vary between drugs for similar percentage changes in CL and is related to the extent to which the kinetics of the disposition process deviate from a one compartment body model. A noncompartmental method is described where, provided the reference dose is given intravenously, F can be estimated based on the assumption that Vss remains constant between doses. This method is more accurate than those based on the assumption that either CL or Varea remain, constant when CL changes between doses, but is subject to error when the terminal log-linear slope of Cp vs. time better reflects the process of absorption rather than elimination.

Urine flow-dependence of theophylline renal clearance in man

Theophylline renal clearance is highly dependent on urine flow rate and is neither concentration nor dose related. To examine the flow dependency, theophylline was administered in single doses (4.3 mg/kg to 8.6 mg/kg) to 14 volunteers. Seven of these volunteers participated in studies in which theophylline and metabolite concentrations were held constant at six different levels. Due to the diuretic effect of theophylline, its renal clearance contributed up to 70% of the time-averaged total clearance, dose/total area, in the first hour after a single dose. The contribution then dropped to 5% of the time-averaged total clearance when the normal urine flow rate was restored. As a consequence of extensive tubular reabsorption, the urine/plasma concentration ratio of theophylline varied with urine flow rate and approached the value of the unbound fraction in plasma. On assumption that the reabsorption is passive, a mathematical model was used to explain the urine flow dependence of reabsorption and, therefore, the renal clearance of theophylline.