Area-dose relationships in nonlinear models

Confidence interval criteria for assessment of dose proportionality

PURPOSE

The aim of this work was a pragmatic, statistically sound and clinically relevant approach to dose-proportionality analyses that is compatible with common study designs.

METHODS

Statistical estimation is used to derive a (1-alpha)% confidence interval (CI) for the ratio of dose-normalized, geometric mean values (Rdnm) of a pharmacokinetic variable (PK). An acceptance interval for Rdnm defining the clinically relevant, dose-proportional region is established a priori. Proportionality is declared if the CI for Rdnm is completely contained within the critical region. The approach is illustrated with mixed-effects models based on a power function of the form PK = beta0 x Dose(beta1); however, the logic holds for other functional forms.

RESULTS

It was observed that the dose-proportional region delineated by a power model depends only on the dose ratio. Furthermore, a dose ratio (rho1) can be calculated such that the CI lies entirely within the pre-specified critical region. A larger ratio (rho2) may exist such that the CI lies completely outside that region. The approach supports inferences about the PK response that are not constrained to the exact dose levels studied.

CONCLUSION

The proposed method enhances the information from a clinical dose-proportionality study and helps to standardize decision rules.

Nonlinear pharmacokinetics of DQ-2556, a new 3-quaternary ammonium cephalosporin antibiotic, in rats caused by non-Michaelis-Menten type, dose-dependent renal clearance

The pharmacokinetics and its dose dependency of a new cephalosporin, DQ-2556, were studied in the rat and rabbit. The pharmacokinetics of the compound in the rat was linear up to a dose of 300 mg/kg; however, at a dose of 1200 mg/kg, renal clearance decreased dramatically and the normalized area under the blood concentration-time curve increased remarkably. On the other hand, there were no dose-dependent changes in tissue/serum concentration ratios, serum protein binding, red cell binding, and the distribution of DQ-2556. In the rabbit, the pharmacokinetics of DQ-2556 was linear even up to a dose of 1200 mg/kg and no unusual pharmacokinetic behavior was observed. The renal clearance experiments demonstrated that DQ-2556 is excreted by glomerular filtration. It was also shown that the glomerular filtration rate (GFR) remained constant up to a dose of 1000 mg/kg of DQ-2556 in the rat, whereas the GFR decreased by 95.1% at a dose of 1200 mg/kg. The coincidence of dose relationship and species difference in the disorder of GFR and renal toxicity suggests that the change of pharmacokinetics of DQ-2556 was caused by its renal toxic effects at very high dose.

Dose-dependent pharmacokinetics of benzoic acid following oral administration of sodium benzoate to humans

Plasma concentration-time data for benzoic and hippuric acids and urinary excretion-time data for hippuric acid were analyzed simultaneously after oral doses of 40, 80 or 160 mg/kg sodium benzoate administered at least one week apart to 6 healthy subjects. The mean AUCs of benzoic acid after the doses of 80 and 160 mg/kg of sodium benzoate were 3.7- and 12.0-times greater, respectively, than after 40 mg/kg. However, the mean AUC of hippuric acid was roughly proportional to the benzoate doses. The observed data were explained by a one-compartment model with first-order rate absorption and Michaelis-Menten elimination of benzoic acid, together with a one-compartment model with first-order elimination for hippuric acid. Although the maximum rate of biotransformation of benzoic acid to hippuric acid varied between 17.2 and 28.8 mg.kg-1.h-1 among the six individuals, the mean value (23.0 mg.kg-1.h-1) was fairly close to that provided by daily maximum dose (0.5 g.kg-1.day-1) recommended in the treatment of hyperammonaemia in patients with inborn errors of ureagenesis. The individual maximum rate of metabolism can be estimated from the urinary excretion rate of hippuric acid 1.5 to 3 h after the single oral dose of 80 to 160 mg.kg-1 sodium benzoate. The justification of this concept requires further studies in patients with inborn errors of urea synthesis.

Michaelis-Menten metabolite formation kinetics: equations relating area under the curve and metabolite recovery to the administered dose

A computational approach which concomitantly determines the capacity-limited rate constants of parent drug elimination and metabolite formation is presented. The approach applies both the presently derived total excretory recovery versus dose relationships of the metabolite and the AUC versus dose relationships of the parent drug to identify the parameters. Three parent drug elimination conditions were assessed: pooled first-order, pooled Michaelis-Menten, and parallel first-order and pooled Michaelis-Menten kinetics. Model and parameter identification criteria are discussed. Literature data for theophylline and two of its metabolites in rats were examined to reveal pooled Michaelis-Menten elimination kinetics of theophylline and capacity-limited formation of the metabolites. The proposed technique is useful for quantitating commonly obtained nonlinear drug disposition data such as AUC and amount of metabolites excreted.

Michaelis-Menten elimination kinetics: areas under curves, steady-state concentrations, and clearances for compartment models with different types of input

For single bolus administration, intermittent bolus administrations to steady-state, a single dose as a zero order input, intermittent zero order inputs to steady-state, and continuous zero order input to steady-state, and for both simple Michaelis-Menten elimination and parallel Michaelis-Menten and first order elimination, the appropriate equations are given for the areas, AUC 0-oo or AUC 0-tau, steady-state concentrations, and clearances. Some 20 new equations have been derived. For the case of first order input and Michaelis-Menten elimination, no solution is given but the effect of input rate on systemic availability is reported following some numerical integrations. The effect of slow input in reducing systemic bioavailability when Michaelis-Menten elimination kinetics are operative is stressed and the implications of this in the field of sustained-release medication mentioned.

In vitro binding of 14C-labeled acidic compounds to serum albumin and their tissue distribution in the rat

The acidic compounds, such as phenoxyacetic acids, substituted benzoic acids, or acetylsalicylic acid, were found to bind to bovine serum albumin (BSA). Among phenoxyacetic acids, the binding affinity to BSA was highest for 2,4,5-trichlorophenoxyacetic acid (2,4,5-T), which was approximately 4-, 24-, and 160-fold greater than those for 2,4-dichlorophenoxyacetic acid (2,4-D), o-chlorophenoxyacetic acid (CPA), and phenoxyacetic acid (PAA), respectively. There were two bound to serum albumins of other mammalian species. The binding affinity varied among species and also depended on the chemicals. However, the order of binding affinity in the albumin of each species remained the same as observed in BSA with few exceptions. Blood/tissue ratios of 14C from rats dosed with these 14C-labeled acids were highly correlated with the logarithm of the binding affinity constantsaffinity constants.

Pharmacokinetics of fenclofenac following single and multiple doses

The plasma concentration of the anti-inflammatory drug fenclofenac was investigated in volunteers following single oral doses of 200, 500 and 600 mg, as well as multiple doses of 600mg b.i.d. over five days, using gas chromatography with electron capture detection. The pharmacokinetic parameters derived were independent of dose, and the terminal half-life, t1/2, varied independently of dose between 20 and 38 hours (27.23 +/- 1.8 at 600mg). The apparent volume of distribution (Vd area) had similar values at doses of 200, 500 and 600mg of 15.2 +/- 2.6, 18.2 +/- 1.5 and 14.7 +/- 1.7 litres respectively. These small volumes of distribution indicate that fenclofenac distributes mainly into extracellular space. A mean peak plasma concentration of 63.5 +/- 4.6microgram/ml developed after 3 to4 hours following a single 600mg dose whilst a mean steady state plasma concentration (600mg b.i.d.) of 86.9 +/- 5.7 microgram/ml was achieved within four days, and this decayed with a mean terminal half-life of 25.9 +/- 4.2 hours.

The influence of protein binding on the pharmacokinetics of sulphadimethoxine in rabbits

The pharmacokinetics of sulphadimethoxine was investigated in rabbits at five dose levels. A significant nonlinearity of dose dependent pharmacokinetics was demonstrated. A large dose dependent change in per cent of sulphadimethoxine bound to plasma proteins was shown. It is concluded that the nonlinearity of the pharmacokinetics of sulphadimethoxine is mainly caused by the dose dependent changes in per cent of drug bound to plasma proteins.