Without extrapolation, Cmax/AUC is an effective metric in investigations of bioequivalence.
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Kinetics↗
Biomedical subjects
L Endrenyi
Publications and source records attributed to L Endrenyi.
Comparative efficiencies of randomized concentration- and dose-controlled clinical trials.
OBJECTIVE: To compare efficiencies of randomized dose- and concentration-controlled trials (RDCT and RCCT) for estimating the parameters of concentration-effect relationships. RATIONALE: In 1991 Sanathanan and Peck (Controlled Clin Trials 1991;12:780-94) suggested that estimation by RDCT is biased and much less efficient than analysis by RCCT. Their conclusion was based on a pharmacodynamic model that characterizes the effect of theophylline in subjects with asthma, in which the response was related linearly to a limited range of concentrations and independent of concentration otherwise. Therefore it was intended to explore whether the conclusion of Sanathanan and Peck applied to other pharmacodynamic models. RESULTS: The results of Sanathanan and Peck were confirmed for the restricted linear, baseline-plateau model: with large pharmacokinetic and no pharmacodynamic variability, RCCT was 3.1 times more efficient than RDCT. However, under the same conditions, the efficiency of RCCT exceeded that of RDCT only 1.5 and 1.2 times when response was related, without restrictions, to concentration and log concentration, respectively. Moreover, in the presence of even moderate pharmacodynamic variability, the ratio of RCCT/RDCT efficiencies did not exceed 1.30 and 1.08, respectively. The parameters estimated by RDCT with these two models were not biased. Finally, in the presence of interindividual variability of the median effective concentration (EC50), pharmacokinetic variability did not affect the observed variation of the parameters in the log-linear pharmacodynamic relationship. CONCLUSIONS: RCCT generally estimates pharmacodynamic parameters with an efficiency that is not much higher than, or even similar to, those yielded by RDCT. Therefore statistical benefits often do not call for the application of RCCT. However, sometimes its use should be seriously considered, particularly for drugs having small therapeutic indexes or when the baseline and plateau of the response occur near the therapeutic region of concentrations.
Dose-Response Relationship, Drug↗
Pharmacokinetics of inhaled pyrene in rats.
Male Wistar rats were exposed to micronized aerosol concentrations of a 14C-labeled model polycyclic aromatic hydrocarbon (pyrene) at 200, 500, and 800 mg/m3 for a period of 95 min. Both the 14C label and free pyrene were monitored in the blood, urine, and feces. At the termination of the blood sampling, three of the six rats per dose group were killed and the distribution of [14C]pyrene to eight major tissues was analyzed. The analysis of blood concentration data using a one-compartment pharmacokinetic model revealed that the uptake and elimination kinetic parameters were dose dependent, for both total radioactivity (pyrene plus metabolites) and for pyrene per se, over the range of exposures used in this study. The ratio of the percent excreted via the urinary and fecal routes, collected over a 5-d period postexposure was about 1.0 at each exposure level.
Absorption↗
A method for the evaluation of individual bioequivalence.
A method is presented for the evaluation of individual bioequivalence. The approach is simple and effective. It considers two drugs to be inequivalent in individuals if their contrast shows larger variation than that observed within formulations, which are repeatedly administered to the subjects. The necessary information can be obtained in 3- or 4-period crossover trials, in which individuals receive not only both drug products but also the replicate application of at least one of them. In the implementation of the procedure, it is suggested that two drug products could be considered to show individual bioequivalence if the upper, one-sided confidence limit for the ratio of intraindividual variances estimated between and within formulations does not exceed a preset critical value, Fcr. For initial considerations, a confidence level of 90% and Fcr = 4.0 are recommended. The intraindividual variances between and within formulations can be estimated either by simple, direct calculations or by an analysis of variance (ANOVA). The structure of the latter is different from that of the ANOVA applied for the assessment of average bioequivalence. Another approach assessing individual bioequivalence from an estimated variance component is less favoured. Graphical, exploratory analysis of the multiperiod crossover trials is recommended and illustrated. The suggested procedures are demonstrated on an example evaluating the individual (and average) bioequivalence of olsalazine tablets and capsules.
Analysis of Variance↗
Percutaneous uptake, distribution, and excretion of pyrene in rats.
Groups of 12 male Wistar rats, of about 400 g body weight, were dosed with 2, 6, or 15 mg/kg of 14C-labeled pyrene, dissolved in acetone, applied to 4 cm2 of a shaved area of the mid back. Three animals in each dose group were killed at 1, 2, 4, and 6 d post-dosing, and their principal organs were removed and analyzed for pyrene and [14C]pyrene equivalents. Urine and feces, as well as the area of skin to which the dose was applied, were also analyzed for [14C]pyrene equivalents. The rate of uptake from the skin was rapid (t1/2 0.5-0.8 d) relative to rate processes for the other organs, and about 50% of the applied dose was excreted over the 6 d of the study. The significant decrease in the fraction of the dose excreted and in the normalized amounts distributed to the various organs and tissues, as the dose increased for all chemical species measured, was strongly suggestive of nonlinear kinetics, as has been observed in previous studies. Levels of pyrene were highest in the liver, kidneys, and fat. Levels of metabolites were also high in the lung. It was evident that the dermal route of uptake was not insignificant for this model polycyclic aromatic hydrocarbon and may represent a significant exposure route for exposed humans.
Adipose Tissue↗
A computationally efficient approach for the design of population pharmacokinetic studies.
A computationally efficient procedure was devised for designing experiments in which population pharmacokinetic parameters are estimated. The method, referred to as the large-sample approach, evaluates the variances of parameter estimates for a population pharmacostatistical model. The procedure utilizes the NONMEM program and requires a single simulation that assumes many, say 1000, subjects. The approach reduced CPU time by about a factor of 50 when compared with the evaluation of the same variances by the direct simulation of experiments. The large-sample and simulation approaches yielded generally similar values for the variances of parameter estimates. The variances calculated by the large-sample approach were, in the case of a simple model, close to the expected variances. The proposed method identified correctly the imprecise parameter estimates but somewhat underestimated their variances.
Computer Simulation↗
Vasodepressor reaction induced by inferior vena caval occlusion and isoproterenol.
UNLABELLED: Testing for the susceptibility for vasodepressor reaction in humans involves the combination of restriction of venous return by passive upright tilting and the administration of isoproterenol. To explore the basis of the vasodepressor test in humans, the present experiment examined whether a reduced cardiac volume coupled with adrenergic stimulation causes a vasodepressor reaction in rats. Vasodepressor reaction was defined as paradoxical heart rate slowing in conjunction with hypotension during inferior vena caval occlusion. Inferior vena caval occlusion was performed for 60 s and the maximum changes in R-R were measured during seven states as follows. (A) Under control conditions inferior vena caval occlusion alone accelerated the rate in 32 of 32 rats (delta R-R, -13.9 +/- 1.7 ms, p less than 0.001). (B) When inferior vena caval occlusion was performed during an infusion of isoproterenol (0.5-1.0 micrograms.min-1), a vasodepressor reaction was observed in all rats as the heart rate slowed (delta R-R, +138.1 +/- 14.8 ms, p less than 0.001). The vasodepressor reaction was further examined during isoproterenol and inferior vena caval occlusion under five additional states. (C) After atropine the vasodepressor reaction was unchanged (delta R-R, +132.7 +/- 24.8 ms, p less than 0.001). (D) After bilateral vagotomy the paradoxical slowing was eliminated. (E) After intrapericardial lidocaine the paradoxic slowing was eliminated. (F) After bilateral stellectomy nonsignificant slowing was still present, but this was markedly reduced when compared with B (p less than 0.001). (G) Following chronic chemical sympathetic denervation with 6-hydroxydopamine the paradoxic bradycardia was eliminated. CONCLUSIONS: (1) Reduced cardiac volume combined with adrenergic stimulation can stimulate a vasodepressor reaction; (2) the vasodepressor reaction requires signalling by the afferent but not efferent vagal fibers; (3) the bradycardia is mainly due to withdrawal of sympathetic efferent tone.
Animals↗
The effects of sympathetic denervation on spontaneous ventricular defibrillation in the rat.
Ventricular tachycardia or ventricular fibrillation was electrically induced in 38 normal rats (group 1) and 24 sympathetically denervated rats (6-hydroxydopamine) (group 2). The time for spontaneous reversion to sinus rhythm was measured during (1) control, (2) isoproterenol, and (3) the combination of isoproterenol and phenylephrine. The time for spontaneous reversion was the same in both groups in the three states. The reversion time was prolonged threefold by isoproterenol, and restored to control values when phenylephrine was added to the infusion of isoproterenol. The tachycardia duration and the refractory period were inversely related: log10 (tachycardia duration) = 3.466-0.091 (refractory period). Ventricular tachycardia/fibrillation induction was examined as follows: (i) Ventricular tachycardia/fibrillation was induced in 100% of normal rats (group 1), but only 42% of the denervated rats (group 2, p less than 0.001); (ii) during isoproterenol, ventricular tachycardia/fibrillation was induced in 100% of rats of both groups; and (iii) when phenylephrine was added to isoproterenol, ventricular tachycardia/fibrillation was induced in 100% of group 1 rats versus 82% of group 2 rats, (p = NS). These observations suggest (1) the induction of ventricular tachycardia/fibrillation is highly dependent on intact sympathetic innervation, and (2) exogenous adrenergic agonists modulate the duration of ventricular fibrillation through their effects on ventricular refractory period, independent of sympathetic innervation.
Animals↗
Evaluation of two assumptions: single straight line, and single normal distribution.
Using graphical and statistical approaches, Laszlo Endrenyi and Mayank Patel describe methods that answer two frequently asked questions: 'Can the data be characterized by a single straight line, or should a more complex model be invoked?' and 'Do the observations follow a single normal distribution, or is there evidence for deviations from this assumption, including the possibility of bimodality?" These methods complement those addressed in a recent Principles article by Dick Barlow.
Research Design↗
Pharmacokinetics and bioavailability of pyrene in the rat.
Groups of 6 male Wistar rats, of about 400 g body weight, were dosed with 14C-labeled pyrene, dissolved in an Emulphor/water solvent vehicle, at 5 different dose levels by the intravenous or oral routes. Appropriate mathematical models were fitted to blood concentration-time data for [14C]pyrene and pyrene per se and dose-trend analyses were carried out. Areas under these curves were used to assess the bioavailability of the orally administered doses. Tissue concentrations, measured at the termination of the blood sampling period, gave a quantitative measure of the distribution of the administered dose. Attempts to repeat these studies with similar doses of tritium-labeled benzo[a]pyrene were frustrated by the lack of meaningful blood-level data. Dose trends for the derived pharmacokinetic parameters for pyrene revealed that the kinetics were nonlinear and strongly suggestive of enterohepatic recycling. Biliary excretion, measured in a separate experiment, gave support to this hypothesis. The bioavailability of the orally administered doses was between 50 and 60%. Over a 6-d period postdosing, some 45 and 40% of the administered dose was excreted via the urine and feces, respectively, irrespective of the route of administration. Distribution to the tissues of the 14C-label was highest in the perirenal fat, intermediate in the liver, kidneys, and lungs, and lowest in the heart, testes, spleen, and brain.
Administration, Oral↗
A new, sensitive graphical method for detecting deviations from the normal distribution of drug responses: the NTV plot.
1. A new graphical method was developed for the detection of deviations from the normal distribution. The approach took advantage of the similarity of graphical features of a graded dose-response relationship and a cumulative normal distribution. 2. The behaviour of the new normal test variable (NTV) plot was evaluated, in comparison with that of the probit plot and probability density functions (the generalization of histograms), for various assumed distributions. These included skewed distributions and composites of normal distributions with a variety of separations, ratios of peak sizes and widths. 3. The NTV approach generally detected deviations from the normal distribution more sensitively than the probit plot. 4. The NTV and probit plots may be able to identify biomadality by complementary approaches. 5. The characteristics of the three graphical representations were illustrated by a simulated sample from a composite of normal distributions and by an example of sparteine metabolism in 142 Cuna Amerindians.
Dose-Response Relationship, Drug↗
Cmax/AUC is a clearer measure than Cmax for absorption rates in investigations of bioequivalence.
In bioequivalence studies, the maximum concentration (Cmax) is shown to reflect not only the rate but also the extent of absorption. Cmax is highly correlated with the area under the curve (AUC) contrasting blood concentration with time. Therefore, use of the Cmax/AUC ratio is recommended for assessing the equivalence of absorption rates. The ratio is independent of both intrasubject variations and possible differences in the extent of absorption and reflects only the contrast between the absorption and disposition rate constants (ka/k).
Absorption↗
Forskolin-resistant Y1 mutants harbor defects associated with the guanyl nucleotide-binding regulatory protein, Gs.
The properties of the adenylate cyclase from forskolin-resistant mutants of Y1 adrenocortical tumor cells was compared with the properties of the enzyme from parental Y1 cells in order to localize the site of mutation. In parental Y1 cells, forskolin stimulated adenylate cyclase activity with kinetics suggestive of an interaction at two sites; in mutant cells, forskolin resistance was characterized by a decrease in enzymatic activity at both sites. Forskolin potentiated the enzyme's responses to NaF and guanyl-5'-yl imidodiphosphate (Gpp(NH)p) in parent and mutant clones, and the mutant enzyme showed the same requirements for Mg2+ and Mn2+ as did the parent enzyme. The adenylate cyclase associated with forskolin-resistant mutants was insensitive to ACTH and was less responsive to Gpp(NH)p than was the parent enzyme. In parental Y1 cells and in the forskolin-resistant mutants, cholera toxin catalyzed the transfer of [32P]ADP-ribose from [32P]NAD+ into three membrane proteins associated with the alpha subunit of Gs; however, the amount of labeled ADP-ribose incorporated into mutant membranes was reduced by as much as 70%. Both parent and mutant membranes were labeled by pertussis toxin to the same extent. The insensitivity of the mutant adenylate cyclase to ACTH and Gpp(NH)p and the selective resistance of the mutant membranes to cholera toxin-catalyzed ADP-ribosylation suggest that a specific defect associated with Gs is involved in the mutation to forskolin resistance in Y1 cells.
Adenosine Diphosphate Ribose↗
Decompression of the spinal cord improves recovery after acute experimental spinal cord compression injury.
The value of decompression after spinal cord injury in patients is still an unresolved issue. It has previously been shown in our laboratory that functional recovery in rats after cord compression varied with both the force and time until decompression. However, the longest duration studied was only 15 minutes, which is far less than that usually encountered in clinical practice, and therefore, the present study was undertaken to determine the value of decompression after more prolonged periods of compression. A factorially designed experiment with five rats per cell was used with the clip compression injury model. Forces of 2.3, 16.9 or 53.0 gms were applied at C7-T1 until decompression was performed after 15, 60, 120, or 240 minutes of compression. Functional recovery was assessed weekly for 8 weeks using the inclined plane technique. Maximum and minimum performance limits were established in normal rats and rats with cord transection, respectively. Univariate analysis and multiple comparison tests were used to analyse the data. The major determinant of recovery was the force of the injury. For example, the animals injured by the 2.3 gm clip performed significantly better than those injured at higher forces for all times until decompression (p less than 0.0001), and there was a significant difference in recovery between the groups injured by the 16.9 and 53.0 gm clips, although only for the 15 minutes until decompression group (p less than 0.05). The time until decompression also affected recovery, but only for the lighter compression forces (2.3 and 16.9 gm). For example, animals decompressed after 60 minutes of 2.3 gm compression recovered significantly better than those decompressed after 240 minutes (p less than 0.05). Thus, if the initial injury force is small, decompression is beneficial even after prolonged injury.
Animals↗
Design of experiments for the precise estimation of dose-response parameters: the Hill equation.
Optimal experimental designs were evaluated for the precise estimation of parameters of the Hill model. The optimally effective designs were obtained by using the criterion of D-optimization. For the Hill model, optimal designs replicate 3 sampling points. These points were shown to be quite sensitive to the behavior of the experimental error. Since an investigator is often uncertain about error conditions in biological studies, a practical approach would use the sampling scheme calculated for an intermediate error condition. Thus, if the behavior of error variances is not known, precise parameters of the Hill model are obtained by choosing concentrations which yield fractional responses (responses divided by their asymptotic, maximum value) of 0.086, 0.581 and 1.0. When experimental constraints limit the maximum attainable concentration and response, all design points are lowered. Appropriate designs can be constructed based on the design which is optimal when constraints result in a maximum attainable fractional response of 0.5. The optimal designs were found to be robust when the parameter values assumed by the investigator did not equal their true values. The estimating efficiencies obtained by using two frequently applied designs were assessed. Uniformly spaced concentrations yielded imprecise parameters. Six-point, geometrically spaced designs gave generally good results. However, their estimating efficiency was generally exceeded by the recommended sampling schemes even in the presence of uncertainty about error conditions. The method exemplified in this paper can be used for other models.
Dose-Response Relationship, Drug↗
Robust regression of enzyme kinetic data.
A method described previously [Cornish-Bowden & Endrenyi (1981) Biochem. J. 193, 1005-1008] for fitting theoretical equations to enzyme kinetic data without prior knowledge of weights or error distribution has been tested by computer simulation. With the equations for various kinds of linear inhibition as an example, the method performed well under all of the conditions examined, giving results that were often much better than those given by widely used least-squares alternatives, and were never appreciably worse. Although equations for two-substrate kinetics were not explicitly tested, the results for inhibition equations can be generalized to include two-substrate equations because the two are formally equivalent for simulation purposes. As a check on the results with inhibition equations the method was also tested for fitting bell-shaped pH-activity profiles and gave correspondingly good results.
Computers↗
An enzyme-distributed system for lidocaine metabolism in the perfused rat liver preparation.
The influence of enzymic distribution on lidocaine metabolism was investigated in the once-through perfused rat liver preparation. Low input concentrations of 14C-lidocaine (1-2 microM) and preformed monoethylglycine xylidide (MEGX; 2.3-2.8 microM) were delivered by normal and retrograde flow directions to the liver preparations at 10 ml/min per liver. Upon reversal of normal to retrograde delivery of lidocaine, the rates at which lidocaine, MEGX, and glycine xylidide (GX) left the liver almost doubled, whereas the rates of appearance of (total) hydroxylated lidocaine and MEGX in bile and perfusate increased to lesser extents. Upon reversal of normal to retrograde delivery of preformed MEGX, the rates of appearance of MEGX and GX were virtually unchanged. Computer simulations on lidocaine and preformed MEGX metabolism were performed on both evenly distributed ("parallel tube" model) and enzyme-distributed systems. An even or parallel distribution of N-deethylation and hydroxylation activities for lidocaine metabolism failed to predict the observed increased hepatic availability of lidocaine. Rather, the distribution of a low-affinity, high-capacity N-deethylation system anterior to a high-affinity, low-capacity hydroxylation system for lidocaine metabolism adequately predicted the increased hepatic availability of lidocaine. Further extension of these consistent enzyme-distributed models on the metabolism of lidocaine metabolites suggests that the N-deethylation and hydroxylation activities for the metabolism of lidocaine, MEGX, 3-hydroxyidocaine, and 3-hydroxy MEGX are not identically distributed. When these enzyme-distributed models were appraised with reference to the "parallel tube" and "well-stirred" models of hepatic drug clearance, predictions from these enzyme-distributed models proved to be superior to the "parallel tube" and "well-stirred" models for the present data on lidocaine metabolites with normal and retrograde perfusions. Previously published data on lidocaine and MEGX metabolism after inputting 4 micrograms/ml (17 microM) lidocaine at flow rates of 10, 12, 14, and 16 ml/min were reexamined with respect to the adequacy of these enzyme-distributed models. They were found to be superior to the evenly-distributed or "parallel tube" model in predicting hepatic availability of lidocaine and the rate of appearance of MEGX. However, the enzyme-distributed systems were not as consistent as the "well-stirred" model in predicting lidocaine hepatic availability in these flow experiments.
Animals↗
Plasma concentration-response relationships of two formulations of propranolol.
The time-course of beta blockade induced by two formulations of propranolol was compared to their plasma concentration-time curves. Graded infusions of isoproterenol were used to assess the degree of beta blockade at different times after oral administration of 80 mg of propranolol to 11 healthy volunteers. The time-course of drug effect was measured as the decline of the systolic pressor dose 20 (SPD 20) and the chronotropic dose 20 (CD 20). Variability of plasma propranolol concentration was small, varying within subjects from 27% to 36% and between subjects from 19% to 28% at the various sampling times. Pharmacodynamic effects showed a similar reproducibility: intra-individual variation was 15% to 28% for CD 20 and 17% to 32% for SPD 20; interindividual variation was 10% to 24% for CD 20 and 13% to 23% for SPD 20. Pooling of the data of all subjects indicated a parallel decline of drug concentration and effect. However, three of the 11 subjects showed drug effects declining at a faster rate than drug levels. This dissociation between serum concentrations and effects points out the clinical relevance of complementing kinetic studies of propranolol with pharmacodynamic studies. The good reproducibility within subjects and the small interindividual variation suggests that isoproterenol dose-response curves may be a useful tool for such studies.
Adult↗