Population pharmacokinetic/pharmacodynamic (PK/PD) modelling of the hypothalamic-pituitary-gonadal axis following treatment with GnRH analogues.

AIMS: To develop a population pharmacokinetic/pharmacodynamic (PK/PD) model of the hypothalamic-pituitary-gonadal (HPG) axis describing the changes in luteinizing hormone (LH) and testosterone concentrations following treatment with the gonadotropin-releasing hormone (GnRH) agonist triptorelin and the GnRH receptor blocker degarelix. METHODS: Fifty-eight healthy subjects received single subcutaneous or intramuscular injections of 3.75 mg of triptorelin and 170 prostate cancer patients received multiple subcutaneous doses of degarelix of between 120 and 320 mg. All subjects were pooled for the population PK/PD data analysis. A systematic population PK/PD model-building framework using stochastic differential equations was applied to the data to identify nonlinear dynamic dependencies and to deconvolve the functional feedback interactions of the HPG axis. RESULTS: In our final PK/PD model of the HPG axis, the half-life of LH was estimated to be 1.3 h and that of testosterone 7.69 h, which corresponds well with literature values. The estimated potency of LH with respect to testosterone secretion was 5.18 IU l(-1), with a maximal stimulation of 77.5 times basal testosterone production. The estimated maximal triptorelin stimulation of the basal LH pool release was 1330 times above basal concentrations, with a potency of 0.047 ng ml(-1). The LH pool release was decreased by a maximum of 94.2% by degarelix with an estimated potency of 1.49 ng ml(-1). CONCLUSIONS: Our model of the HPG axis was able to account for the different dynamic responses observed after administration of both GnRH agonists and GnRH receptor blockers, suggesting that the model adequately characterizes the underlying physiology of the endocrine system.

Stochastic differential equations in NONMEM: implementation, application, and comparison with ordinary differential equations.

PURPOSE: The objective of the present analysis was to explore the use of stochastic differential equations (SDEs) in population pharmacokinetic/pharmacodynamic (PK/PD) modeling. METHODS: The intra-individual variability in nonlinear mixed-effects models based on SDEs is decomposed into two types of noise: a measurement and a system noise term. The measurement noise represents uncorrelated error due to, for example, assay error while the system noise accounts for structural misspecifications, approximations of the dynamical model, and true random physiological fluctuations. Since the system noise accounts for model misspecifications, the SDEs provide a diagnostic tool for model appropriateness. The focus of the article is on the implementation of the Extended Kalman Filter (EKF) in NONMEM for parameter estimation in SDE models. RESULTS: Various applications of SDEs in population PK/PD modeling are illustrated through a systematic model development example using clinical PK data of the gonadotropin releasing hormone (GnRH) antagonist degarelix. The dynamic noise estimates were used to track variations in model parameters and systematically build an absorption model for subcutaneously administered degarelix. CONCLUSIONS: The EKF-based algorithm was successfully implemented in NONMEM for parameter estimation in population PK/PD models described by systems of SDEs. The example indicated that it was possible to pinpoint structural model deficiencies, and that valuable information may be obtained by tracking unexplained variations in parameters.

Non-linear mixed-effects pharmacokinetic/pharmacodynamic modelling in NLME using differential equations.

The standard software for non-linear mixed-effect analysis of pharmacokinetic/pharmacodynamic (PK/PD) data is NONMEM while the non-linear mixed-effects package NLME is an alternative as long as the models are fairly simple. We present the nlmeODE package which combines the ordinary differential equation (ODE) solver package odesolve and the non-linear mixed effects package NLME thereby enabling the analysis of complicated systems of ODEs by non-linear mixed-effects modelling. The pharmacokinetics of the anti-asthmatic drug theophylline is used to illustrate the applicability of the nlmeODE package for population PK/PD analysis using the available data analysis tools in R for model inspection and validation. The nlmeODE package is numerically stable and provides accurate parameter estimates which are consistent with NONMEM estimates.

Population pharmacokinetic modeling of a subcutaneous depot for GnRH antagonist degarelix.

PURPOSE: The objective of this study is to develop a population pharmacokinetic (PK) model that describes the subcutaneous (SC) depot formation of gonadotropin-releasing hormone (GnRH) antagonist degarelix, which is being developed for treatment of prostate cancer, exhibiting dose-volume and dose-concentration dependent absorption. METHODS: The PK analysis is made in NONMEM through joint analysis of data from two phase I clinical studies; an intravenous infusion study and a single SC dose escalation study. The SC absorption is modeled using an approximation to Ficks' second law of diffusion out of a spherical depot. The dose-volume effect on the SC release is estimated using a B-spline basis whereas the bioavailability is modeled as a function of the dose-concentration. RESULTS: The SC depot model is approximated by using two concentric spherical compartments for the SC absorption combined with a two-compartment disposition model. The results indicate that the volume effect is most apparent at low injection volumes whereas the effect is diminishing at higher injection volumes. The dose-concentration effect on the bioavailability is estimated to decrease at increasing dose-concentrations. CONCLUSIONS: The presented SC depot model describes the PK profile of GnRH antagonist degarelix. This modeling approach might also be applicable for other depot-formulated drugs exhibiting complex PK profiles.

Pharmacokinetic/pharmacodynamic modelling of GnRH antagonist degarelix: a comparison of the non-linear mixed-effects programs NONMEM and NLME.

In this paper, the two non-linear mixed-effects programs NONMEM and NLME were compared for their use in population pharmacokinetic/pharmacodynamic (PK/PD) modelling. We have described the first-order conditional estimation (FOCE) method as implemented in NONMEM and the alternating algorithm in NLME proposed by Lindstrom and Bates. The two programs were tested using clinical PK/PD data of a new gonadotropin-releasing hormone (GnRH) antagonist degarelix currently being developed for prostate cancer treatment. The pharmacokinetics of intravenous administered degarelix was analysed using a three compartment model while the pharmacodynamics was analysed using a turnover model with a pool compartment. The results indicated that the two algorithms produce consistent parameter estimates. The bias and precision of the two algorithms were further investigated using a parametric bootstrap procedure which showed that NONMEM produced more accurate results than NLME together with the nlmeODE package for this specific study.