Davide Verotta

Building population pharmacokinetic--pharmacodynamic models. I. Models for covariate effects.

One major task in clinical pharmacology is to determine the pharmacokinetic-pharmacodynamic (PK-PD) parameters of a drug in a patient population. NONMEM is a program commonly used to build population PK-PD models, that is, models that characterize the relationship between a patients PK-PD parameters and other patient specific covariates such as the patients (patho)physiological condition, concomitant drug therapy, etc. This paper extends a previously described approach to efficiently find the relationships between the PK-PD parameters and covariates. In a first step, individual estimates of the PK-PD parameters are obtained as empirical Bayes estimates, based on a prior NONMEM fit using no covariates. In a second step, the individual PK-PD parameter estimates are regressed on the covariates using a generalized additive model. In a third and final step, NONMEM is used to optimize and finalize the population model. Four real-data examples are used to demonstrate the effectiveness of the approach. The examples show that the generalized additive model for the individual parameter estimates is a good initial guess for the NONMEM population model. In all four examples, the approach successfully selects the most important covariates and their functional representation. The great advantage of this approach is speed. The time required to derive a population model is markedly reduced because the number of necessary NONMEM runs is reduced. Furthermore, the approach provides a nice graphical representation of the relationships between the PK-PD parameters and covariates.

Pharmacokinetic-pharmacodynamic modelling: history and perspectives.

A major goal in clinical pharmacology is the quantitative prediction of drug effects. The field of pharmacokinetic–pharmacodynamic (PK/PD) modelling has made many advances from the basic concept of the dose–response relationship to extended mechanism-based models. The purpose of this article is to review, from a historical perspective, the progression of the modelling of the concentration–response relationship from the first classic models developed in the mid-1960s to some of the more sophisticated current approaches. The emphasis is on general models describing key PD relationships, such as: simple models relating drug dose or concentration in plasma to effect, biophase distribution models and in particular effect compartment models, models for indirect mechanism of action that involve primarily the modulation of endogenous factors, models for cell trafficking and transduction systems. We show the evolution of tolerance and time-variant models, non- and semi-parametric models, and briefly discuss population PK/PD modelling, together with some example of more recent and complex pharmacodynamic models for control system and nonlinear HIV-1 dynamics. We also discuss some future possible directions for PK/PD modelling, report equations for general classes of novel semi-parametric models, as well as describing two new classes, additive or set-point, of regulatory, additive feedback models in their direct and indirect action variants

Pharmacodynamic modeling of the EEG effects of ketamine and its enantiomers in man

The pharmacodynamics of a racemic mixture of ketamine R,S (±)-ketamine and of each enantiomer, S(+)-ketamine and R(−)-ketamine, were studied in five volunteers. The median frequency of the electroencephalogram (EEG) power spectrum, a continuous noninvasive measure of the degree of central nervous system (CNS) depression (pharmacodynamics), was related to measured serum concentrations of drug (pharmacokinetics). The concentration-effect relationship was described by an inhibitory sigmoid Emax pharmacodynamic model, yielding estimates of both maximal effect (Emax) and sensitivity (IC50) to the racemic and enantiomeric forms of ketamine. R(−)-ketamine was not as effective as R,S(±)-ketamine or S(+)-ketamine in causing EEG slowing. The maximal decrease (mean±SD) of the median frequency (Emax)for R(−)-ketamine was 4.4±0.5 Hz and was significantly different fromR,S (±)-ketamine (7.6 ±1.7 Hz) and S(+)-ketamine (8.3±1.9Hz). The ketamine serum concentration that caused one-half of the maximal median frequency decrease (IC50) was 1.8±0.5Μg/mL for R(−)-ketamine; 2.0±0.5 Μg/mL for R,S(±)-ketamine; and 0.8±0.4 Μg/mL for S(+)-ketamine. Because the maximal effect (Emax) of the R(−)-ketamine was different from that of S(+)-ketamine and R,S(±)-ketamine, it was not possible to directly compare the potency (i.e., IC50) of these compounds. Accordingly, a classical agonist/partial-agonist interaction model was examined, using the separate enantiomer results to predict racemate results. Although the model did not predict racemate results well, its failure was not so great as to provide clear evidence of synergism (or excess antagonism) of the enantiomers.

Input Characteristics and Bioavailability after Administration of Immediate and a New Extended-release Formulation of Hydromorphone in Healthy Volunteers

Background To compare the pharmacokinetics of intravenous, oral immediate-release (IR), and oral extended-release (OROS®) formulations of hydromorphone. Methods In this randomized, six-session, crossover-design study, 12 subjects received hydromorphone 8-mg intravenous, 8-mg IR oral, and 8-, 16-, and 32-mg OROS® formulations or placebo orally followed by plasma sampling for hydromorphone determination. Pharmacokinetic analysis was performed using NONMEM. Using the disposition of hydromorphone from the intravenous administration, deconvolution was used to estimate the input rate function (release rate from the gut to the blood) for the IR and OROS® formulations. A linear spline was used to describe the drug input rate function. Results The deconvolution using linear splines described the in vivo release characteristics of both the IR and OROS® formulations. The mean absolute bioavailability for the 8-mg OROS® formulation was significantly larger (P = 0.025) than for the 8-mg IR formulation: 0.24 (SD 0.059) versus 0.19 (SD 0.054), respectively. The bioavailability was the same for the three doses of the OROS® formulation. Predicted degree of fluctuation of plasma concentrations would be expected to be 130% and 39% for the IR and OROS® 8-mg doses, respectively. Conclusions The OROS® formulation of hydromorphone produced continued release of medication over 24 h, which should allow for once-daily oral dosing. The extended release of hydromorphone will produce less fluctuation of plasma concentrations compared with IR formulations, which should provide for more constant pain control. The in vivo release of hydromorphone from both IR and OROS® formulations were adequately described using a linear spline deconvolution approach. The increased bioavailability from the OROS® formulation may be related to decreased metabolism by a first-pass effect or enterohepatic recycling of hydromorphone.

Comparative tissue concentration profiles of fentanyl and alfentanil in humans predicted from tissue/blood partition data obtained in rats.

The steady-state tissue/blood partition coefficients of fentanyl and alfentanil were determined in 13 organs and tissues in the rat. A 6-h infusion of both drugs was used in order to achieve steady-state. Blood and tissue concentrations of drugs were measured by gas-liquid chromatography. The partition coefficients of fentanyl were two- to 30-fold higher than those of alfentanil. These data were then used in a physiologic pharmacokinetic model describing the disposition of the two opioids in humans. The model predicted the plasma pharmacokinetics of these drugs in humans reasonably well. However, simulation beyond 24 h after a bolus administration showed a terminal half-life of 20 h for fentanyl, i.e., an elimination phase that has not yet been described in actual pharmacokinetic studies. In keeping with this, the volume of distribution of fentanyl in the model was also larger than expected. The simulated tissue concentration curves of fentanyl and alfentanil in humans could be used to explain the propensity of fentanyl to give secondary peaks in plasma concentration curves and the difference in effect kinetics between the two opioids. Physiologic pharmacokinetic modeling, based on measured data in small animals, can generate information that is not obtainable by empirical methods in humans.

An inequality-constrained least-squares deconvolution method

The output-function (Y) of a linear system is the convolution of the input function (I) to the system with the disposition-function (H) of the system. Given Y and H deconvolution yields I. A non-parametric method for numerical deconvolution is described. The method is based on an inequality-constrained least-squares criterion and approximates I by a discontinuous function. No assumptions are made about the form of H or Y. Numerical stability and physical realism are obtained by constraining the estimated I to be nonnegative and piecewise-monotonic (nonincreasing, nondecreasing, or alternating segments of both). When I is constrained to be monotonic, the deconvolution yields a staircase function. The method can be used to calculate drug input rates. It is compared to previously published deconvolution methods for this purpose, using simulated data and real theophylline and pentobarbital data.

Additive Inhibition of Nicotinic Acetylcholine Receptors by Corticosteroids and the Neuromuscular Blocking Drug Vecuronium

Background: Neuromuscular disorders associated with muscular weakness and prolonged paralysis are common in critically ill patients. Acute myopathy has been described in patients receiving a combination therapy of corticosteroids and nondepolarizing neuromuscular blocking drugs for treatment of acute bronchospasm. The cause of this myopathy is not fully established and may involve drug interactions that perturb neuromuscular transmission. To investigate the interaction of corticosteroids with neuromuscular blocking drugs, the authors determined the effects of methylprednisolone and hydrocortisone alone and in combination with vecuronium on fetal (&ggr;-subunit containing) and adult (&egr;-subunit containing) subtypes of the muscle-type nicotinic acetylcholine receptor. Methods: Functional channels were expressed in Xenopus laevis oocytes and activated with 1 &mgr;M acetylcholine. The resulting currents were recorded using a whole cell two-electrode voltage clamp technique. Results: Both forms of the muscle-type acetylcholine receptor were potently inhibited by methylprednisolone and hydrocortisone, with concentrations producing 50% inhibition in the range of 400–600 &mgr;M and 1–2 mM, respectively. The corticosteroids produced noncompetitive antagonism of the muscle-type nicotinic acetylcholine receptor at clinical concentrations. Both receptor forms were also inhibited, even more potently, by vecuronium, with a concentration producing 50% inhibition in the range of 1–2 nM. Combined application of vecuronium and methylprednisolone showed additive effects on both receptor forms, which were best described by a two-site model, with each site independent. Conclusions: The enhanced neuromuscular blockade produced when corticosteroids are combined with vecuronium may augment pharmacologic denervation and contribute to the pathophysiology of prolonged weakness observed in some critically ill patients.

The pharmacokinetics and pharmacodynamics of diltiazem and its metabolites in healthy adults after a single oral dose

A potential complicating factor in the characterization of the pharmacokinetics and pharmacodynamics of diltiazem after an oral dose is the presence of two metabolites, N‐demethyldiltiazem and desacetyldiltiazem, in plasma. Both N‐demethyldiltiazem and desacetyldiltiazem have been shown to have pharmacologic activity in animal tissues. It is therefore possible that these metabolites contribute to the pharmacologic effect of diltiazem, but this possibility has not been explored. The purpose of this study was to investigate the pharmacokinetics and pharmacodynamics of diltiazem, N‐demethyldiltiazem, and desacetyldiltiazem. Particular attention was paid to the effect of diltiazem on atrioventricular conduction. Six healthy men received a 120 mg oral dose of diltiazem. Concentrations of diltiazem, N‐demethyldiltiazem, and desacetyldiltiazem in plasma and urine were measured by a sensitive HPLC method. Measures of pharmacologic response (heart rate, blood pressure, and PR interval) were obtained at each blood sampling time. Mean (± SD) peak plasma concentrations of diltiazem, N‐demethyldiltiazem, and desacetyldiltiazem were 174.3 ± 72.7, 42.6 ± 10.0, and 14.9 ± 3.3 ng/ml, respectively. The apparent half‐lives of diltiazem, N‐demethyldiltiazem, and desacetyldiltiazem were 6.5 ± 1.4 hours, 9.4 ± 2.2 hours, and 18 ± 6.2 hours, respectively. Both N‐demethyldiltiazem and diltiazem were eliminated by net renal secretion, whereas the renal clearance of desacetyldiltiazem did not exceed clearance by filtration. Both N‐demethyldiltiazem and desacetyldiltiazem are bound to plasma proteins, with unbound fractions of 0.323 ± 0.035 and 0.230 ± 0.021. These values are similar to the unbound fraction of diltiazem (0.254 ± 0.027). No significant effect of diltiazem on blood pressure or heart rate was noted. However, a prolongation of the PR interval was observed in all six subjects. Furthermore, an apparent clockwise hysteresis in the concentration‐effect relationship was found in four of the six subjects. These findings suggest that some form of acute tolerance to the electrophysiologic effect of diltiazem develops, but the results of pharmacodynamic modeling suggest that this is not caused by the antagonistic effects the metabolites.

Population analyses of sustained-release verapamil in patients: Effects of sex, race, and smoking

Our objective was to determine the effects of age, sex, and sustained‐release formulation on apparent oral clearance of sustained‐release racemic verapamil in patient populations.

Simultaneous modeling of pharmacokinetics and pharmacodynamics: an improved algorithm

An algorithm and computer program is presented that fits a largely non-parametric model to pharmacokinetic (PK) and pharmacodynamic (PD) data; it is an extension of a recently proposed approach. A PK model relates dose to plasma concentrations (Cp), a link model relates plasma concentrations to the concentration in the effect site (Ce), a PD model relates Ce to the effect. Both the PK and the PD model are non-parametric, but the link model is parametric. The extension presented here allows modeling of PK/PD data arising from non-steady-state experiments after arbitrary dosage. In addition, several data sets from the same individual (or from different individuals) can now be analyzed simultaneously, assuming the same link model for all, but allowing either all the PD models to be the same, or all to be different.