Sidney Riegelman

Statistical estimations in pharmacokinetics

Several important statistical aspects of pharmacokinetic analyses by digital computer are discussed. These include selection of appropriate equations, weighting of data, precision of parameter estimates, comparisons of parameters, analysis of weighted residuals, and criteria useful in the selection of particular models. Data obtained after administration of isoniazid and isonicotinuric acid to man are analyzed to illustrate the usefulness of the discussed methods.

The application of statistical moment theory to the evaluation of in vivo dissolution time and absorption time

Moments analysis has been applied to the calculation of mean (in vivo)dissolution time (MDT) and mean absorption time (MAT) from plasma level of drug versus time data. Methods for accurately estimating the MDT under varying conditions, limitations of the methods, and interpretation of the data are presented. The importance of accurate estimates of the terminal rate constant (λz) and the drug concentration at the time of withdrawing the final plasma sample (Ĉz)is emphasized in connection with extrapolation to t=∞.The appropriate use of a logarithmic trapezoidal equation for calculating the area under the moments curve (AUMC) is shown to increase the accuracy of estimating MDT.

Nonlinear theophylline elimination.

Elimination kinetics of theophylline and its major metabolites were investigated in 14 healthy adults in single‐dose studies and in a multiple‐plateau study. The plasma concentrations of theophylline and the metabolites 3‐methylxanthine (3‐MX), 1‐methyluric acid (1‐MU), and 1,3‐dimethyluric acid (13‐MU) were monitored to about 0.020 mg/l and became convex descending at concentrations below 1 mg/l after single theophylline doses. Renal clearance values of 3‐MX, 1‐MU, and 13‐MU were 12.0 ± 1.3 l/hr, 22.5 ± 1.5 l/hr, and 22.6 ±1.6 l/hr. Metabolite formation of the three metabolites followed Michaelis‐Menten kinetics and became capacity limited within the therapeutic range of theophylline. The apparent Michaelis‐Menten parameters for each metabolite formation step were obtained by computer fitting. For the formation of 3‐MX, 1‐MU, and 13‐MU, the approximate mean maximal rate of formation of metabolite (Vmax) values were 5 mg/hr, 13 mg/hr, and 34 mg/hr and the apparent concentration of theophylline at which metabolite formation rate is half of Vmax values were 2.7 mg/l, 9.3 mg/l, and 14.2 mg/l. The elimination of each of the metabolites was rate limited by the elimination of theophylline. Concomitant measurement of theophylline urinary excretion rate showed the renal clearance of the drug to be highly dependent on urine flow. The initial renal clearance, elevated due to diuresis, and the distribution phase tended to counterbalance the saturable metabolic formation clearance after a single therapeutic dose. Therefore, plasma theophylline concentration decayed roughly in a log‐linear fashion and the convex‐descending curve, characterized by capacity‐limited elimination kinetics, was observed only at lower concentrations.

The clinical pharmacokinetics of phenytoin

Procedures for estimating the variability in dosage requirements of phenytoin to achieve steadystate plasma concentrations of 10–20 mg/liter and for estimating the plasma concentrations produced on a fixed dose are given. Further, a method is proposed for estimating the dosage required to achieve a desired steady-state plasma phenytoin concentration when a steady-state value on a known daily dose has been measured, A method is also described for estimating dosage requirements when two or more plasma concentrations have been measured. These methods are derived from data obtained on administering phenytoin in four to five different dosage regimens until steady state was achieved in each of nine volunteers. The drug was administered orally as a suspension every 8 hr, starting with about 100mg/day. The daily dose was increased in steps, and maintained at each daily dose rate for 6–14 days, or longer. Blood samples were drawn 4 and 8 hr after the last dose on 2 successive days at the end of each step and analyzed for phenytoin concentration. The average of these values was used to estimate the steady-state plasma concentration, Cpss. For each subject the Cpss values were fitted to a rearranged Michaelis-Menten equation Cpss =KmR/(Vm-R). In this equation R is the dosing rate, Vm is the maximum rate of metabolism, and Km is a constant equal to the plasma concentration at which the metabolism rate is one-half maximum. The average values found for Vm and Km were 10.3 mg/kg/day and 11.54 mg/liter, respectively. The individual values of Vm and Km appear to be constant over time, but there is considerable interindividual variability: coefficients of variation are 25% and 50%, respectively.

Convenient and sensitive high-performance liquid chromatography assay for ketoprofen, naproxen and other allied drugs in plasma or urine.

A new high-performance liquid chromatography technique enables convenient and rapid assay of ketoprofen and naproxen in biological samples at a sensitivity (10 and 2 ng/ml, respectively in plasma; 20 and 50 ng/ml in urine) far greater than previously available. Superior sensitivity is attributable to the buffered neutral eluent employed, which yields improved separation from material of biological origin. There is no interference from the major ketoprofen and naproxen metabolites tested and excellent reproducibility and accuracy can be maintained. Moreover, the same system can be used to assay probenecid and also shows promise of applicability to ibuprofen, fenoprofen and other members of the aryl-alkanoic acid class of non-steroidal anti-inflammatory agents.

Simultaneous determination of theophylline and its major metabolites in urine by reversed-phase ion-pair high-performance liquid chromatography

A new, highly slective high-performance liquid-chromatographic (HPLC) assay for theophylline and its major metabolites in urine is described. The method utilizes an ion-pair extraction followed by separation and quantitation by reversed-phase ion-pair gradient-elution HPLC. Comparison with several other methods showed that interferences were present in too many blank urine samples to allow for the accurate quantitation of the metabolites of theophylline by direct injection--isocratic HPLC assays. Sample processing involving ion-pair complexing and extraction together with gradient-elution systems is recommended for accurate pharmacokinetic studies.

Intraindividual variability in theophylline pharmacokinetics: Statistical verification in 39 of 60 healthy young adults

After administering a single 300 mg dose of theophylline in oral solution to 12 healthy adults, the dose-normalized area under the plasma concentration-time curve was 97.2±20.1 % (mean±SD) of that after giving a 500 mg dose and statistically indistinguishable. Similarly, these areas multiplied by the individuals terminal disposition rate constant (β) were statistically indistinguishable between 300 and 500mg doses (99.1±10.3%), giving no evidence of dose-dependence for theophylline kinetics at the levels below 15 μg/ml observed in these individuals. After an intravenous dose, a shortlived distribution phase (t1/2α) is sometimes seen. An a phase, however, is hardly discernible in over 250 profiles arising from oral doses administered during five single dose bioavailability studies. Almost all such profiles appear to follow single-compartment model predictions. With precautions to avoid a potential a phase, a terminal log-linear slope can be fitted by least squares analysis with a relative standard error in the slope determination almost always less than 6%. Covariance analysis confirms statistically that 39 of the 60 participating individuals varied in their β on the different occasions each was required to take a dose during the course of a crossover bioavailability trial. In one study, even though each individual was observed on only two occasions, 9 out of 12 showed statistically identifiable variation in β. Fluctuations in β of 60% can be seen. Changes of 30% or greater are common and can occur within 3 or 4 days. Thus real, large, and potentially frequent changes in β of theophylline have been identified in a majority of normal subjects. These changes do not appear to be confined to either sex, to smokers or nonsmokers, or to heavier or lighter individuals. No chronological pattern has, as yet, been recognized in the intraindividual variability in β.

Evaluation of the absorption from 15 commercial theophylline products indicating deficiencies in currently applied bioavailability criteria.

The biovailability of theophylline from alcoholic and aqueous oral solutions was compared to that from an intravenous dose in 12 normal adults. The alcoholic elixir surprisingly gave rise to a significantly greater (114 ±14%, mean±sd amount absorbed than did the intravenous dose. The aqueous solution (99±8%) and intravenous dose were statistically indistinguishable in this respect, and, furthermore, the extent of absorption from a 300-mg dose of the aqueous solution was 99±10% of that from a 500-mg dose, and not statistically different. The aqueous solution was thus employed in three subsequent studies as a standard with which to compare 13 different types of theophylline tablets, all marketed in the United States. Of the 13 tablets, eight showed bioavailability statistically distinguishable from that of the standard. Nevertheless, for only two tablets could it be claimed with 95% confidence that the bioavailability was less than 95%. For none can it be stated at this confidence level that the bioavailability is less than 90%. Bioavailability studies should include criteria of clinical significance in addition to criteria of statistical significance. Contrary to the usual rationale behind choice of a bioavailability standard, nine of the 12 uncoated tablets appeared to allow more rapid absorption of theophylline than did the standard oral solution, an aqueous syrup. Increasing the dose of syrup decreased the rate of theophylline absorption. Orally administered drug solutions may have properties more absorption rate limiting than the disintegration of many brands of tablet.

Pharmacokinetics; Pharmacokinetic factors affecting epidermal penetration and percutaneous absorption

Dermal pharmacokinetics has to do with the rate processes involved in dissolution, diffusion, and/or release of the drug substance from its vehicle, transit to the absorption site, penetration through the limiting barrier to the site of action, and subsequent elimination of that compound. Dermatology is almost exclusively interested in the pharmacologic and therapeutic effects of drugs within the skin. Emphasis will be primarily made in this presentation to the epidermal penetration of drugs so as to induce no local responses. However, comments will be made later related to percutaneous absorption with the intent to elicit systemic response.

Effect of route of administration on drug disposition

While the first-pass effect is a fairly generally understood phenomenon in the gross sense, it is not commonly appreciated that the rate at which the drug is delivered to the liver can influence the fraction of the administered dose which reaches the fluids of distribution. The drug molecules being absorbed via the hepatic portal vein intermix with previously absorbed drug recycling in the hepatic artery. The concentration of the drug returning via the hepatic artery is affected by the volume of distribution of the drug into body tissues (and the relative partition of the drug between the blood and the tissues). If one presumes that liver uptake is controlled by a Michaelis-Menten process of metabolism, it can be readily shown that the extent of extraction of the drug by the liver is controlled not only by the Michaelis-Menten constants, but also by the concentration of the drug transitting the liver per unit time. The effects of dose, rate of absorption, partitioning, and tissue distribution characteristics are systematically discussed and referred to in relation to selected examples of drugs in common use.