An Identifiability Analysis of a Parent–Metabolite Pharmacokinetic Model for Ivabradine

The paper considers the structural identifiability of a parent–metabolite pharmacokinetic model for ivabradine and one of its metabolites. The model, which is linear, is considered initially for intravenous administration of ivabradine, and then for a combined intravenous and oral administration. In both cases, the model is shown to be unidentifiable. Simplification of the model (for both forms of administration) to that proposed by Duffull et al. (1) results in a globally structurally identifiable model. The analysis could be applied to the modeling of any drug undergoing first-pass metabolism, with plasma concentrations available from drug and metabolite.     

Population Pharmacokinetic–Pharmacodynamic Modeling of Subcutaneous and Pulmonary Insulin in Rats

Purpose: To develop a population pharmacokinetic–pharmacodynamic (PKPD) model for insulin in rats. Methods: Rats were administered insulin either subcutaneously (s.c) (0.26,1.3,2.6 U/kg) or by pulmonary route (spray-instillation (s.i)) (0.26,1.3,2.6,13,26 U/kg). Insulin (0.26,1.3,2.6 U/kg) combined with different combinations of hydroxy methyl amino propionic acid (HMAP: 5,10,16,25 mg/kg) was also administered by spray-instillation. Plasma insulin and glucose concentrations at pre-determined time points were measured. Population pharmacokinetic–pharmacodynamic modeling was performed using NONMEM. Results: Insulin exhibited dose-disproportional PK across formulations and routes of administration. The kinetic model suggested monoexponential disposition with simultaneous first order (64%-dimeric form of insulin) – zero order (36%-hexameric form of insulin) absorption. Maximum relative bioavailability (relative to s.c – 0.26 U/kg) of spray-instilled insulin was 46%. Addition of HMAP increased the relative bioavailability of insulin administered via spray-instilled route by 40%. The insulin–glucose relationship was characterized using an indirect response model, wherein, insulin stimulation of glucose uptake into muscle cells was assumed. The basal zero order production rate of glucose (k_{G, prod}) was estimated as 0.98 mg/dl/min. The SC₅₀ was fixed at 80 μ U/ml based on literature reports and the S_max was estimated to be 6. Conclusions: The proposed PKPD model satisfactorily describes insulin disposition and glucose concentrations across range of doses with and without HMAP.     

Pharmacokinetic–Pharmacodynamic Modeling of the Effectiveness and Safety of Buprenorphine and Fentanyl in Rats

Objective Respiratory depression is a serious and potentially life-threatening side-effect of opioid therapy. The objective of this investigation was to characterize the relationship between buprenorphine or fentanyl exposure and the effectiveness and safety outcome in rats. Methods Data on the time course of the antinociceptive and respiratory depressant effect were analyzed on the basis of population logistic regression PK–PD models using non-linear mixed effects modeling software (NONMEM). The pharmacokinetics of buprenorphine and fentanyl were described by a three- and two-compartment model, respectively. A logistic regression model (linear logit model) was used to characterize the relationship between drug exposure and the binary effectiveness and safety outcome. Results For buprenorphine, the odds ratios (OR) were 28.5 (95% CI, 6.9–50.1) and 2.10 (95% CI, 0.71–3.49) for the antinociceptive and respiratory depressant effect, respectively. For fentanyl these odds ratios were 3.03 (95% CI, 1.87–4.21) and 2.54 (95% CI, 1.26–3.82), respectively. Conclusion The calculated safety index (OR_{antinociception}/OR_{respiratory depression}) for fentanyl of 1.20 suggests that fentanyl has a low safety margin, implicating that fentanyl needs to be titrated with caution. For buprenorphine the safety index is 13.54 suggesting that buprenorphine is a relatively safe opioid.     

Pharmacokinetic–Pharmacodynamic Modeling of Doxacurium: Effect of Input Rate

One of the basic assumptions in pharmacokinetic–pharmacodynamic modeling (PK–PD) is that drug equilibration rate constant between plasma concentration and effect (K_e0 ) is not changed by input rate. To test this assumption in a clinical setting, a 25 g/kg iv dose of doxacurium was administered either by bolus injection or 10-min infusion to 15 anesthetized patients. Neuromuscular function was monitored using train-of-four stimulation of the ulnar nerve. For the short infusion dose, arterial concentrations were measured at 1-min intervals during infusion and at frequent intervals thereafter. Following the iv bolus dose, the early PK profile of doxacurium was investigated by measuring doxacurium arterial concentrations every 10 sec during the first 2 min and at frequent intervals thereafter. PK–PD modeling was performed using nonparametric approach with and without including a finite receptor concentration (R_tot ) in the effect compartment. Kinetic parameters were unchanged. For the bolus and the infusion, K_e0 values were 0.053±0.006 and 0.056±0.009 min ^–1 , respectively. Using the R_tot model, corresponding K_e0 values were 0.148±0.016 and 0.150±0.024, respectively. The relatively faster K_e0 obtained with the R_tot model is compatible with the high potency of doxacurium. Our results show that PK–PD parameters derived with either a bolus or an infusion mode of administration are equally reliable.     

Pharmacokinetic–Pharmacodynamic Modeling of Tolmetin Antinociceptive Effect in the Rat Using an Indirect Response Model: A Population Approach

The relationship between the pharmacokinetics and the antinociceptive effect of tolmetin was characterized by an indirect model using a population approach. Animals received an intra-articular injection of uric acid in the right hindlimb to induce its dysfunction. Once dysfunction was complete, rats received an oral tolmetin dose of 1, 3.2, 10, 31.6, 56.2, or 100mg/kg and antinociceptive effect and blood tolmetin concentration were simultaneously evaluated. Tolmetin produced a dose-dependent recovery of functionality, which was not directly related to blood concentration. An inhibitory indirect response model was used based on these response patterns and the fact that tolmetin reduced nociception by inhibiting prostaglandin synthesis. Pharmacokinetic (PK) and pharmacodynamic (PD) data were simultaneously fitted using nonlinear mixed effects modeling (NONMEM) to the one-compartment model and indirect response model. The individual time courses of the response were described using Bayesian analysis with population parameters as a priori estimates. There was good agreement between the predicted and observed data. Population analysis yielded a maximal inhibition of the nociceptive response of 76% and an IC₅₀ of 9.22 g/ml. This IC₅₀ is similar to that for tolmetin-induced prostaglandin synthesis inhibition in vitro (3.0 g/ml). The present results demonstrate that mechanism-based PK-PD analysis using a population approach is useful for quantitating individual responses as well as reflecting the actual mechanism of action of a given drug in vivo.     

Unified Pharmacogenetics-Based Parent–Metabolite Pharmacokinetic Model Incorporating Acetylation Polymorphism for Talampanel in Humans

The N-acetylation of the noncompetitive AMPA antagonist talampanel (TLP) represents a route of varying significance in various species. For a detailed analysis in humans, plasma concentrations of TLP and its N-acetyl metabolite (NAc–TLP) were measured for up to 48 h after administration of a single oral dose of 75 mg in 28 healthy volunteers following genotyping for the N-acetyltansferase NAT2 isozymes (alleles NAT2*4, *5, *6, and *7). Unified parent–metabolite pharmacokinetic (PK) models that allowed three different rates of acetylation were used to simultaneously fit plasma levels for both the parent drug and its metabolite following genotype-based classification as slow, intermediate, or fast acetylator. A perfect correspondence was found between the phenotype inferred from genotyping and the phenotype determined by using plasma metabolite-to-parent molar ratios indicating that this route of metabolism is indeed mediated by NAT2. Linear parent-metabolite PK models (first-order input, first-order elimination through two parallel routes one of which is through a metabolite with polymorphic rate of formation) gave adequate and sufficiently consistent fit. Parameters obtained suggest that for TLP in humans, N-acetylation represents only about 1/4th of the total elimination even in true (*4/*4 homozygous) fast acetylators, acetylation is about 8–12 times faster in fast and 3–6 times faster in intermediate acetylators than in slow acetylators, and the N-acetyl metabolite is eliminated faster than the parent drug. Such PK models can provide quantitative estimates of relative in vivo metabolism rates for routes catalyzed by functionally polymorphic enzymes.     

Population Pharmacokinetic–Pharmacodynamic Modeling of Filgrastim (r-metHuG-CSF) in Healthy Volunteers

The pharmacokinetic–pharmacodynamic (PK–PD) relationship of the granulopoietic effects of Filgrastim in healthy volunteers was characterized via a population approach. Healthy male volunteers were enrolled into a four-way crossover clinical trial. Subjects received four single doses of Filgrastim (375 and 750 g iv and sc) with an intervening washout period of 7 days. Serum concentrations of Filgrastim were determined using an enzyme-linked immunosorbent assay. Absolute neutrophil count (ANC) was determined. Data analysis was performed using mixed-effects modeling as implemented in the NONMEM software package. The final PKPD model incorporates a two-compartment PK model with bisegmental absorption from the sc site, first-order and saturable elimination pathways, and an indirect PD model. A sigmoidal E_max model for the stimulation of ANC input rate k_in) was superior to the conventional E_max model ( ±SE: E_max=12.7 ± 1.7; EC50=4.72 ± 0.72 ng/ml; Hill=1.34 ± 0.19). In addition, a time-variant scaling factor for ANC observations was introduced to account for the early transient depression of ANC after Filgrastim administration. The absolute bioavailability of subcutaneously administered Filgrastim was estimated to be 0.619±0.058 and 0.717±0.028 for 375 g and 750 g sc doses, respectively. The time profiles of concentration and ANC, as well as the concentrationANC relationship of Filgrastim in healthy volunteers were well described by the developed population PK–PD model.     

Mechanism-Based Pharmacokinetic–Pharmacodynamic Modeling of the Dopamine D<Subscript>2</Subscript> Receptor Occupancy of Olanzapine in Rats

Purpose  

A mechanism-based PK-PD model was developed to predict the time course of dopamine D₂ receptor occupancy (D₂RO) in rat striatum following administration of olanzapine, an atypical antipsychotic drug.     

Predicting Plutonium Decorporation Efficacy after Intravenous Administration of DTPA Formulations: Study of Pharmacokinetic–Pharmacodynamic Relationships in Rats

Purpose The objectives of this study were: 1) to assess the relationship between plutonium decorporation (increased excretion and reduced retention in main organs of deposition) induced by intravenous liposome formulations of the chelating agent diethylene triamine pentaacetic acid (DTPA) and its pharmacokinetics, and 2) to model the renal excretion of plutonium after treatment with liposome-encapsulated DTPA in order to predict its efficacy and to optimise treatment schedules.Materials and Methods Pharmacokinetic parameters from plasma or urinary data (days 0–16 sample collections) were modelled versus decorporation efficacy, and best correlations were selected for their goodness of fit.Results The plutonium decorporation enhancement by DTPA liposomal formulations was well described by logistic models and the best correlation was observed with the area under the DTPA concentration curve of each formulation. The plutonium urinary excretion rates decreased mono-exponentially as a function of time after a single dose and the proposed model allowed a simple determination of the elimination half-life of the Pu–DTPA complex, a reasonably good approximation of the long-term efficacy of the treatments from truncated urinary data.Conclusions Both liposomal formulations of chelating agents and pharmacokinetic approaches to plutonium decorporation should be helpful in optimising treatment protocols.     

Impact of Pharmacokinetic–Pharmacodynamic Model Linearization on the Accuracy of Population Information Matrix and Optimal Design

Influence of experimental design on hyperparameter estimates precision when performing a population pharmacokinetic–pharmacodynamic (PK–PD) analysis has been shown by several studies and various approaches have been proposed for optimizing or evaluating such designs. Some of these methods rely on the optimization of a suitable scalar function of the population information matrix. Unfortunately for the nonlinear models encountered in pharmacokinetics or pharmacodynamics the latter is particularly difficult to evaluate. Under some assumptions and after a linearization of the PK–PD model a closed form of this matrix can be obtained which considerably simplifies its calculation but leads to an approximation. The aim of this paper is to evaluate the quality of the latter and its potential impact, when comparing or optimizing population designs and to relate it to Bates and Watts curvature measures. Two models commonly used in PK–PD were considered and nominal hyperparameter values where chosen for each one. Several population designs were studied and the associated population information matrix was computed for each using the approximate procedure and also using a reference method. Design optimizations were calculated under constraints for each model from the reference and approximate population information matrix. Nonlinearity curvatures were also computed for every model and design. The impact of model linearization when calculating the population information matrix was then examined in terms of lower bound accuracies on the hyperparameter estimates, design criterion variation, as well as D-optimal population designs, these results being related to nonlinearity curvature measures. Our results emphasize the influence of the parameter effects curvature when deriving the lower bounds of the hyperparameter estimates precision for a given design from the approximate population information matrix especially for hyperparameters quantifying the PK–PD interindividual variability. No discrepancies were detected between the population D-optimal designs obtained from the approximate and reference matrix despite some minor differences in criterion variation with respect to the design. More pronounced differences were, however, observed when comparing the amplitudes of criterion variation which can lead to errors when calculating design efficiencies. From a practical point of view, a strategy easily applicable by the pharmacokineticist for avoiding such problems in the context of population design optimization or comparison is then proposed.     

Peripheral Link Model as an Alternative for Pharmacokinetic–Pharmacodynamic Modeling of Drugs Having a Very Short Elimination Half-Life

Attempts to obtain estimates of pharmacokinetic–pharmacodynamic (PK–PD) parameters for mivacurium with traditional central link models were unsuccessful in many patients. We hypothesized that a link model with the peripheral compartment would be more appropriate for mivacurium in view of its extremely rapid plasma clearance and its potential elimination by tissue pseudocholinesterases. For validation purposes, the peripheral link model was applied to other neuromuscular blocking agents (NMBA), i.e., atracurium and doxacurium which have respectively an intermediate and a long elimination half-life. Assuming peripheral elimination in PK–PD modeling was investigated but found to have no impact on the estimation of PK–PD parameters. Our results indicate that, for drugs having intermediate and long elimination half-lives, EC50 values are similar with either the central or peripheral link model. For mivacurium, a peripheral link model enables PK–PD modeling in all subjects, with more precision in the PK–PD parameter estimates and a better fitting of the effect data when compared to the central link model. For these reasons, a peripheral link model should be preferred for mivacurium.     

Oxymorphone Active Uptake at the Blood–Brain Barrier and Population Modeling of its Pharmacokinetic–Pharmacodynamic Relationship

The aim of this study was to characterize the blood–brain barrier (BBB) transport and pharmacokinetics–pharmacodynamics (PKPD) relationship of oxymorphone and to further elucidate its possible contribution to oxycodone analgesia. The BBB transport of oxymorphone was studied using microdialysis in male Sprague–Dawley rats. Samples from microdialysis blood and brain probes, brain tissue, and plasma were analyzed by liquid chromatography with tandem mass spectrometry. The effect was measured as tail-flick latency. The study consisted of a PKPD experiment with combined microdialysis and antinociceptive measurements (n = 8), and another antinociceptive effect experiment (n = 9) using a 10 times lower dose. The combined data were analyzed with an integrated PKPD model in nonlinear mixed effect modeling utilizing a specific method (M3) for handling missing PD observations. The concentration of unbound oxymorphone was higher in brain than in blood, with a ratio of 1.9 (RSE, 9.7%), indicating active uptake at the BBB. The integrated PKPD model described the oxymorphone BBB transport and PKPD relationship successfully, with an EC₅₀ in the brain of 63 ng/mL, and the M3 method was able to address the issue of censored observations. Oxymorphone has active uptake transport at the BBB in rats, with moderate uptake clearance to the brain. Its contribution to analgesia after oxycodone administration is not significant.     

A Population Pharmacokinetic–Pharmacodynamic Analysis of Repeated Measures Time-to-Event Pharmacodynamic Responses: The Antiemetic Effect of Ondansetron

This paper presents and illustrates methodology for specifying, estimating, and evaluating a predictive model for repeated measures time-to-event responses. The illustrative example specifies a model of the antiemetic effect vs. concentration relationship for the 5-HT ₃ antagonist ondansetron in the human ipecac model for emesis. A key part of this model is a time-dependent log hazard function for emesis that is increased by ipecac administration and decreased by ondansetron concentration. The model is fit using an approximate maximum likelihood method. The data consist of the time free of emeses and, for those individuals with emetic episodes, the time(s) of the episode(s). Model evaluation is accomplished using residual plots adapted to time-to-event data and a posterior predictive check wherein observed data statistics are compared to those obtained from data simulated from the fitted model. The ondansetron concentration required to obtain a 50% reduction in the hazard of emesis is estimated to be 1.4±0.2 ng/ml, and the rate constant for elimination of ipecac-induced hazard is 1.5±0.2hr ^–1 .     

Pharmacokinetic–Pharmacodynamic–Efficacy Analysis of Efalizumab in Patients with Moderate to Severe Psoriasis

Purpose Efalizumab is a humanized anti-CD11a monoclonal antibody that demonstrated efficacy in the treatment of patients with psoriasis. The objective of this study was to perform a pharmacokinetic (PK)–pharmacodynamic (PD)–efficacy (E) modeling analysis with intersubject variability assessment to increase our understanding of the interaction of efalizumab with CD11a on T cells and consequent reduction in severity of disease in psoriasis patients.Methods A total of 6,329 samples from 240 patients in five Phase I and II clinical studies were used in the analysis. For the analysis, plasma efalizumab concentration was used as the PK measurement, the percent of predose CD11a was used as the PD measurement, and the psoriasis area and severity index was used as the measure of efficacy. A receptor-mediated PK/PD model was developed that describes the dynamic interaction of efalizumab binding with CD11a. In the efficacy model, the rate of psoriasis skin production is directly proportional to the amount of free surface CD11a on T cells, which is offset by the rate of skin healing. An additional CD11a-independent component to psoriasis skin production accounted for incomplete response to efalizumab therapy. A Monte Carlo parametric expectation maximization method implemented in the ADAPT II program was used to obtain the estimate of population parameters and inter- and intrasubject variability.Results and Conclusions The final model described the PK/PD/E data in psoriasis patients reasonably well. In addition, simulations using the final model suggested that efalizumab administered less frequently could possibly be more convenient with similar efficacy.     

Integrated Population Pharmacokinetic Model of Both Cyclophosphamide and Thiotepa Suggesting a Mutual Drug–Drug Interaction

PURPOSE/AIMS: Cyclophosphamide (CP) and thiotepa (TT) are frequently administered simultaneously in high-dose chemotherapy regimens. The prodrug CP shows strong autoinduction resulting in increased formation of its activated metabolite 4-hydroxycyclophosphamide (4OHCP). TT inhibits this bioactivation of CP. Previously, we successfully modelled CP bioactivation and the effect of TT on the autoinduction. Recently we suggested that CP may also induce the conversion of TT in to its metabolite tepa (T). The aim of the current study was to investigate whether the influence of CP on TT metabolism can be described with a population pharmacokinetic model and whether this interaction can be incorporated in an integrated model describing both CP and TT pharmacokinetics. METHODS: Plasma samples were collected from 49 patients receiving 86 courses of a combination of high-dose CP (4000 or 6000 mg/m2), TT (320 or 480 mg/m2) and carboplatin (1067 or 1600 mg/m2) given in short infusions during four consecutive days. For each patient, approximately 20 plasma samples were available per course. Concentrations of CP, 4OHCP, TT and T were determined using GC and HPLC. Kinetic data were processed using NONMEM. RESULTS: The pharmacokinetics of TT and T were described with a two-compartment model. TT was eliminated through a non-inducible and an inducible pathway, the latter resulting information of T (ClindTT = 12.4 l/hr, ClnonindTT = 17.0 l/hr). Induction of TT metabolism was mediated by a hypothetical amount of enzyme, different from that involved in CP induction, whose amount increased with time in the presence of CP. The amount of enzyme followed a zero-order formation and a decrease with a first-order elimination rate constant of 0.0343 hr(-1) (t1/2 = 20 hr). This model was significantly better than a model lacking the induction by CP. The model was successfully incorporated into the previously published pharmacokinetic model for CP, and resulted in comparable parameter estimates for this compound and its metabolite 4OHCP. CONCLUSION: The pharmacokinetics of TT, when administered in combination with CP, were successfully described. The model confirms induction of TT metabolism with time and it appears likely that CP is responsible for this phenomenon. The existence of a mutual pharmacokinetic interaction between CP and TT, as described in our integrated model, may be relevant in clinical practice.