Philippe Jacqmin

Modelling Response Time Profiles in the Absence of Drug Concentrations: Definition and Performance Evaluation of the K–PD Model

The plasma concentration–time profile of a drug is essential to explain the relationship between the administered dose and the kinetics of drug action. However, in some cases such as in pre-clinical pharmacology or phase-III clinical studies where it is not always possible to collect all the required PK information, this relationship can be difficult to establish. In these circumstances several authors have proposed simple models that can analyse and simulate the kinetics of the drug action in the absence of PK data. The present work further develops and evaluates the performance of such an approach. A virtual compartment representing the biophase in which the concentration is in equilibrium with the observed effect is used to extract the (pharmaco)kinetic component from the pharmacodynamic data alone. Parameters of this model are the elimination rate constant from the virtual compartment (KDE), which describes the equilibrium between the rate of dose administration and the observed effect, and the second parameter, named EDK50 which is the apparent in vivo potency of the drug at steady state, analogous to the product of EC50, the pharmacodynamic potency, and clearance, the PK “potency” at steady state. Using population simulation and subsequent (blinded) analysis to evaluate this approach, it is demonstrated that the proposed model usually performs well and can be used for predictive simulations in drug development. However, there are several important limitations to this approach. For example, the investigated doses should extend from those producing responses well below the EC50 to those producing ones close to the maximum response, optimally reach steady state response and followed until the response returns to baseline. It is shown that large inter-individual variability on PK–PD parameters will produce biases as well as large imprecision on parameter estimates. It is also clear that extrapolations to dosage routes or schedules other than those used to estimate the parameters should be undertaken with great caution (e.g., in case of non-linearity or complex drug distribution). Consequently, it is advised to apply this approach only when the underlying structural PD and PK are well understood. In any case, K–PD model should definitively not be substituted for the gold standard PK–PD model when correct full model can and should be identified.

Population pharmacokinetics meta-analysis of recombinant human erythropoietin in healthy subjects.

ObjectiveThe aim of this analysis was to develop a population pharmacokinetic model to describe the pharmacokinetics of recombinant human erythropoietin (rHuEPO) in healthy subjects, after intravenous and subcutaneous administration over a wide dose range, and to examine the influence of demographic characteristics and other covariates on the pharmacokinetic parameters of rHuEPO.MethodsErythropoietin serum concentration data were available from 16 studies comprising 49 healthy subjects who received rHuEPO intravenous doses from 10 to 300 IU/kg, 427 healthy subjects who received rHuEPO subcutaneous doses from 1 to 2400 IU/kg, and 57 healthy subjects who received placebo and where endogenous erythropoietin concentrations were measured. Different pharmacokinetic models were fitted to the dataset using nonlinear mixed-effects modeling software (NONMEM, Version V, Level 1). Several patient covariates were tested in order to quantify the effect on rHuEPO pharmacokinetic parameters. Model evaluation was examined using a posterior predictive check.ResultsErythropoietin showed a diurnal baseline variation of ±20%, described with a dual cosine model. Disposition was described with a two-compartment model with a small volume of distribution (6L) and parallel linear and nonlinear clearance. Total clearance varied between 0.3 and 0.9 L/h over the concentration range studied. A dual absorption model was used to characterise the rHuEPO absorption from the subcutaneous formulation and consisted of a faster pathway described as a sequential zero- and first-order absorption process and a parallel slower pathway characterised as a zero-order process. The bioavailability of subcutaneous rHuEPO increased from 30% at low doses to 71% at the highest dose of 160 kIU and was described using a hyperbolic model. The most important covariate effects were a decrease in the first-order absorption rate constant (ka) with increasing age, an increase in subcutaneous bioavailability with increasing baseline haemoglobin, and a decrease in bioavailability with increasing bodyweight. A posterior predictive check showed no systematic deviation of the simulated data from the observed values.ConclusionThe population pharmacokinetic model developed is suitable to describe the pharmacokinetic behaviour of rHuEPO after intravenous and subcutaneous administration in healthy subjects, over a wide dose range.

Retrospective Population Pharmacokinetic Analysis of Levetiracetam in Children and Adolescents with Epilepsy : Dosing Recommendations

AbstractObjective: To characterize levetiracetam pharmacokinetics, identify significant covariate relationships and identify doses in children that achieve blood concentrations similar to those observed in adults. Methods: Nonlinear mixed-effects modelling was used to analyse pooled data collected from 228 children with epilepsy aged 3 months to 18 years in five trials of adjunctive levetiracetam therapy. Simulations were used to identify dosing regimens achieving levetiracetam steady-state peak and trough plasma concentrations similar to those attained in adults receiving the recommended starting dose for adjunctive therapy (500 mg twice daily). The covariates considered for inclusion in the base model were age, bodyweight, gender, race, body surface area (BSA), body mass index (BMI), creatinine clearance (CLCR), levetiracetam dose, concomitant antiepileptic drug (AED) by category (neutral, enzyme inducer, inhibitor, combination of inducer and inhibitor), and benzodiazepines. Results: A one-compartment model with first-order absorption and elimination best characterized the data. The following significant covariates were identified: (i) age on the absorption rate constant (ka); (ii) bodyweight, dose, CLCR and concomitant enzyme-inducing AED on plasma oral clearance (CL/F); and (iii) bodyweight on the apparent volume of distribution after oral administration (Vd/F). The main explanatory covariates were age on ka, bodyweight on CL/F and Vd/F, and enzyme-inducing AED on CL/F, of which bodyweight was the most influential covariate. Dosing can be carried out with either 10 mg/kg of oral solution twice daily in children weighing <50 kg and a 500-mg tablet twice daily in those weighing >50 kg or, when patients favour a solid formulation, 10 mg/kg of oral solution twice daily in children weighing <20 kg, a 250-mg tablet twice daily in those weighing 20–40 kg, and a 500-mg tablet twice daily in those weighing >40 kg. All of these doses achieved steady-state peak and trough plasma concentrations similar to those observed in adults following the recommended starting dose for adjunctive therapy (500 mg twice daily). Conclusions: The most influential covariate of levetiracetam pharmacokinetics in children is bodyweight. A starting dose of levetiracetam 10 mg/kg twice daily ensures the same exposure in children as does 500 mg twice daily in adults.

The use of the SAEM algorithm in MONOLIX software for estimation of population pharmacokinetic-pharmacodynamic-viral dynamics parameters of maraviroc in asymptomatic HIV subjects

Using simulated viral load data for a given maraviroc monotherapy study design, the feasibility of different algorithms to perform parameter estimation for a pharmacokinetic-pharmacodynamic-viral dynamics (PKPD-VD) model was assessed. The assessed algorithms are the first-order conditional estimation method with interaction (FOCEI) implemented in NONMEM VI and the SAEM algorithm implemented in MONOLIX version 2.4. Simulated data were also used to test if an effect compartment and/or a lag time could be distinguished to describe an observed delay in onset of viral inhibition using SAEM. The preferred model was then used to describe the observed maraviroc monotherapy plasma concentration and viral load data using SAEM. In this last step, three modelling approaches were compared; (i) sequential PKPD-VD with fixed individual Empirical Bayesian Estimates (EBE) for PK, (ii) sequential PKPD-VD with fixed population PK parameters and including concentrations, and (iii) simultaneous PKPD-VD. Using FOCEI, many convergence problems (56%) were experienced with fitting the sequential PKPD-VD model to the simulated data. For the sequential modelling approach, SAEM (with default settings) took less time to generate population and individual estimates including diagnostics than with FOCEI without diagnostics. For the given maraviroc monotherapy sampling design, it was difficult to separate the viral dynamics system delay from a pharmacokinetic distributional delay or delay due to receptor binding and subsequent cellular signalling. The preferred model included a viral load lag time without inter-individual variability. Parameter estimates from the SAEM analysis of observed data were comparable among the three modelling approaches. For the sequential methods, computation time is approximately 25% less when fixing individual EBE of PK parameters with omission of the concentration data compared with fixed population PK parameters and retention of concentration data in the PD-VD estimation step. Computation times were similar for the sequential method with fixed population PK parameters and the simultaneous PKPD-VD modelling approach. The current analysis demonstrated that the SAEM algorithm in MONOLIX is useful for fitting complex mechanistic models requiring multiple differential equations. The SAEM algorithm allowed simultaneous estimation of PKPD and viral dynamics parameters, as well as investigation of different model sub-components during the model building process. This was not possible with the FOCEI method (NONMEM version VI or below). SAEM provides a more feasible alternative to FOCEI when facing lengthy computation times and convergence problems with complex models.

Population pharmacokinetic/ pharmacodynamic analysis of CCR5 receptor occupancy by maraviroc in healthy subjects and HIV-positive patients

BACKGROUND Maraviroc, a noncompetitive antagonist of the CCR5 coreceptor, was recently approved in the USA as a treatment of HIV infection. For antiretroviral agents that target the virus, antiviral effect can be related to some extent to plasma drug concentrations. For CCR5 antagonists that target the host cells, receptor occupancy in vivo might be a better predictor of efficacy. AIMS To develop a population pharmacokinetic (PK)-pharmacodynamic (PD) model that describes CCR5 receptor occupancy by maraviroc after oral administration at different doses in healthy volunteers and HIV-positive patients and to assess the relevance of receptor occupancy in predicting the decrease in viral load (HIV-1 RNA copies ml(-1)) in HIV-positive patients. METHODS Receptor occupancy data from 88 individuals enrolled in two multiple dose trials were included in the population PK-receptor binding model. Out of the 88 individuals, 25 were HIV-1-infected patients and had viral load measurements, whereas the remaining 63 were healthy volunteers. Doses ranged from 3 mg b.i.d. to 600 mg q.d. A previously published PK-PD disease model describing the effect of maraviroc on the viral load was updated by replacing its PD module by the receptor occupancy model. Simulated viral load-time profiles with the updated model were compared with the profiles observed in patients. RESULTS The majority of measured plasma concentrations were associated with receptor occupancy > or = 50% even at the lowest dose of 3 mg b.i.d. A simple direct E(max) model appeared to describe satisfactorily the PK-receptor occupancy relationship. The estimated K(D) was around 0.0894 ng ml(-1), far below the operational in vivo antiviral IC(50) of 8 ng ml(-1). Accordingly, simulations led to marked overprediction of the decrease in viral load-time profiles. CONCLUSIONS Maraviroc receptor occupancy close to the maximum is required to induce a significant decrease in viral load, indicating that in vivo CCR5 receptor occupancy by maraviroc is not a direct measure of drug inhibitory activity. Considering the imprecision of the measurement in the upper flat part of the maraviroc concentration vs. percent CCR5 occupancy curve, it can reasonably be concluded that routine monitoring of receptor occupancy as a biomarker for maraviroc efficacy will not be helpful. Based on this analysis, it was decided not to use receptor occupancy as a biomarker of viral load inhibition during the development of CCR5 antagonist compounds.

Population pharmacokinetics of levetiracetam in Japanese and Western adults.

ObjectiveTo assess the population pharmacokinetics of levetiracetam, a second-generation antiepileptic drug, in adult Japanese and Western populations.MethodsData were pooled from ten matched clinical trials conducted in Japan and in Europe and the USA, in which levetiracetam was administered orally to healthy subjects and subjects with epilepsy. Overall, 5408 plasma concentrations were available from 524 subjects in six clinical pharmacology studies and two confirmatory and two long-term safety studies of add-on treatment for partial epilepsy. A one-compartment open model with first-order absorption and elimination was fitted to the plasma concentrations using nonlinear mixed-effects modelling with first-order estimation.ResultsEthnicity had no statistically significant effect on the pharmacokinetics of levetiracetam in the presence of the other covariates. Bodyweight, sex, creatinine clearance and concomitant intake of enzyme inducers or valproic acid had a statistically significant effect on apparent plasma clearance of levetiracetam. Bodyweight, disease and valproic acid had a statistically significant effect on the volume of distribution. Levetiracetam exposure (the area under the plasma concentration-time curve over the 12-hour dosing interval at steady state) was 12% higher in females than in males. Decreasing bodyweight from 70kg to 40kg was predicted to increase exposure by 16%, while halving creatinine clearance was predicted to increase exposure by 10%. Enzyme inducers reduced exposure by 8%, while valproic acid resulted in a 23% increase in exposure. The latter effect was assumed to arise from the known association between valproic acid and increased body fat, since levetiracetam is negligibly metabolised by cytochrome P450 enzymes.ConclusionsPopulation pharmacokinetic analysis points to the absence of ethnic differences in the pharmacokinetics of levetiracetam between Japanese and Western populations, other than those arising from bodyweight differences. Small, clinically non-relevant differences between individual demographic characteristics suggest that dose adjustment is usually not necessary.

Pharmacokinetic/pharmacodynamic Modeling of Psychomotor Impairment Induced by Oral Clonazepam in Healthy Volunteers

This study was undertaken to model the relationship between clonazepam plasma concentrations and a central nervous system adverse effect (impairment of the psychomotor performance) following the oral administration of immediate-release tablets of clonazepam in healthy volunteers. Such a (P)pharmacokinetic/(P)pharmacodynamic (PK/PD) study is important to interpret properly the consequences of determined levels of plasma concentrations of psychoactive therapeutic drugs reported to be involved in road-traffic accidents. Twenty-three male subjects received a single oral dose of 4 mg clonazepam. Plasma concentration, determined by on-line solid phase extraction coupled with high-performance liquid chromatography tandem mass spectrometry, and psychomotor performance, quantified through the Digit Symbol Substitution Test, were monitored for 72 hours. A 2-compartment open model with first order absorption and lag-time better fitted the plasma clonazepam concentrations. Clonazepam decreased the psychomotor performance by 72 ± 3.7% (observed maximum effect), 1.5 to 4 hours (25th-75th percentile) after drug administration. A simultaneous population PK/PD model based on a sigmoid Emax model with time-dependent tolerance described well the time course of effect. Such acute tolerance could minimize the risk of accident as a result of impairment of motor skill after a single dose of clonazepam. However, an individual analysis of the data revealed a great interindividual variation in the relationship between clonazepam effect and plasma concentration, indicating that the phenomenon of acute tolerance can be predicted at a population, but not individual, level.

A receptor theory-based semimechanistic PD model for the CCR5 noncompetitive antagonist maraviroc

AIM To develop a novel combined viral dynamics/operational model of (ant-)agonism that describes the pharmacodynamic effects of maraviroc, a noncompetitive CCR5 inhibitor, on viral load. METHODS A common theoretical framework based on receptor theory and the operational model of (ant-)agonism has been developed to describe the binding of maraviroc to the CCR5 receptor and the subsequent decrease in viral load. The anchor point of the operational model in the differential equations of the viral dynamic model is the infection rate constant; this is assumed to be dependent on the number of free activated receptors on each target cell. RESULTS The new model provides one explanation for the apparent discrepancy between the in vivo binding of maraviroc to the CCR5 receptor (K(D) = 0.089 ng ml(-1)) and the estimated in vivo inhibition (IC(50) = 8 ng ml(-1)) of the infection rate. The estimated K(E) value of the operational model indicates that only 1.2% of free activated receptors are utilized to elicit 50% of the maximum infection rate. CONCLUSIONS The developed model suggests that the target cells, when activated, express more receptors (spare receptors) than needed. In the presence of maraviroc these spare receptors first require blocking before any decrease in the infection rate, and consequently in the viral load at equilibrium, can be detected. The model allows the simultaneous simulation of the binding of maraviroc to the CCR5 receptor and the change in viral load after both short- and long-term treatment.

Modeling and simulation of intravenous levetiracetam pharmacokinetic profiles in children to evaluate dose adaptation rules

PURPOSE To develop a pharmacokinetic model for intravenous levetiracetam in children, based on adult intravenous data and pediatric oral data. METHODS Data from two adult Phase-I studies in which levetiracetam was given intravenously were utilized to develop the adult population pharmacokinetic two-compartment intravenous model. After model qualification, combination with an existing pediatric one-compartment oral population pharmacokinetic model enabled simulation of twice-daily intravenous infusions of levetiracetam in children. Median and 90% confidence intervals for C(trough), C(max) (end of infusion) and AUC(tau) were simulated for 2000 children and compared to the values observed in adults. RESULTS The population pharmacokinetic two-compartment model successfully described intravenous levetiracetam pharmacokinetics in healthy adults. After combination with the oral pediatric population model, steady-state concentrations at the end of 15-, 30- and 60 min b.i.d. levetiracetam intravenous infusions in children were predicted to be 29-41, 17-24 and 6-13% higher than those observed after oral dosing of 30 mg/kg b.i.d. Concentrations returned to the range of oral exposures within 1h after the infusion peak. The combined model predicted that steady-state peak plasma concentrations and AUC(tau) in children receiving 30 mg/kg twice daily as 15 min intravenous infusions were within the range of predicted and observed C(max,ss) and AUC(tau )values of adults receiving 15 min intravenous infusions of 1500 mg levetiracetam. CONCLUSIONS The simulations suggest that levetiracetam may be administered intravenously in children as 15 min infusions.

A Combined Specific Target Site Binding and Pharmacokinetic Model to Explore the Non-linear Disposition of Draflazine

AbstractThe capacity-limited high-affinity target site binding ofdraflazine to the nucleoside transporters located on the erythrocytes isa source of nonlinearity in the pharmacokinetics of the drug. Anattractive feature of draflazine is that the specific target sitebinding characteristics can be determined easily by simultaneouslymeasuring plasma and whole blood concentrations of the drug. Measureddrug concentrations following various infusion rates and infusiondurations were used to develop a model in which the interrelatedblood–plasma distribution, elimination, and specific target sitebinding of draflazine were incorporated simultaneously. The estimatedbinding (dissociation) constant Kdwas0.57 ng/ml plasma and the maximal specific erythrocyte bindingcapacity