Biomedical subjects

Henrik Madsen

Publications and source records attributed to Henrik Madsen.

16 recordsLinked to original sources

PubMed2006

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.

Dose-Response Relationship, Drug↗

PubMed2006

PKPD model of interleukin-21 effects on thermoregulation in monkeys--application and evaluation of stochastic differential equations.

PURPOSE: To describe the pharmacodynamic effects of recombinant human interleukin-21 (IL-21) on core body temperature in cynomolgus monkeys using basic mechanisms of heat regulation. A major effort was devoted to compare the use of ordinary differential equations (ODEs) with stochastic differential equations (SDEs) in pharmacokinetic pharmacodynamic (PKPD) modelling. METHODS: A temperature model was formulated including circadian rhythm, metabolism, heat loss, and a thermoregulatory set-point. This model was formulated as a mixed-effects model based on SDEs using NONMEM. RESULTS: The effects of IL-21 were on the set-point and the circadian rhythm of metabolism. The model was able to describe a complex set of IL-21 induced phenomena, including 1) disappearance of the circadian rhythm, 2) no effect after first dose, and 3) high variability after second dose. SDEs provided a more realistic description with improved simulation properties, and further changed the model into one that could not be falsified by the autocorrelation function. CONCLUSIONS: The IL-21 induced effects on thermoregulation in cynomolgus monkeys are explained by a biologically plausible model. The quality of the model was improved by the use of SDEs.

Algorithms↗

PubMed2006

Mathematical beta cell model for insulin secretion following IVGTT and OGTT.

Evaluation of beta cell function is conducted by a variety of glucose tolerance tests and evaluated by a number of different models with less than perfect consistency among results obtained from different tests. We formulated a new approximation of the distributed threshold model for insulin secretion in order to approach a model for quantifying beta cell function, not only for one, but for several different experiments. Data was obtained from 40 subjects that had both an oral glucose tolerance test (OGTT) and an intravenous tolerance test (IVGTT) performed. Parameter estimates from the two experimental protocols demonstrate similarity, reproducibility, and indications of prognostic relevance. Useful first phase indexes comprise the steady state amount of ready releasable insulin A0 and the rate of redistribution krd, where both yield a considerable correlation (both r=0.67) between IVGTT and OGTT estimates. For the IVGTT, A0 correlates well (r=0.96) with the 10 min area under the curve of insulin above baseline, whereas krd represents a new and possibly more fundamental first phase index. For the useful second phase index gamma, a correlation of 0.75 was found between IVGTT and OGTT estimates.

Adult↗

PubMed2005

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.

Algorithms↗

PubMed2005

Non-linear mixed-effects models with stochastic differential equations: implementation of an estimation algorithm.

Pharmacokinetic/pharmacodynamic modelling is most often performed using non-linear mixed-effects models based on ordinary differential equations with uncorrelated intra-individual residuals. More sophisticated residual error models as e.g. stochastic differential equations (SDEs) with measurement noise can in many cases provide a better description of the variations, which could be useful in various aspects of modelling. This general approach enables a decomposition of the intra-individual residual variation epsilon into system noise w and measurement noise e. The present work describes implementation of SDEs in a non-linear mixed-effects model, where parameter estimation was performed by a novel approximation of the likelihood function. This approximation is constructed by combining the First-Order Conditional Estimation (FOCE) method used in non-linear mixed-effects modelling with the Extended Kalman Filter used in models with SDEs. Fundamental issues concerning the proposed model and estimation algorithm are addressed by simulation studies, concluding that system noise can successfully be separated from measurement noise and inter-individual variability.

Algorithms↗

PubMed2005

Using stochastic differential equations for PK/PD model development.

A method for PK/PD model development based on stochastic differential equation models is proposed. The new method has a number of advantages compared to conventional methods. In particular, the new method avoids the exhaustive trial-and-error based search often conducted to determine the most appropriate model structure, because it allows information about the appropriate model structure to be extracted directly from data. This is accomplished through quantification of the uncertainty of the individual parts of an initial model, by means of which tools for performing model diagnostics can be constructed and guidelines for model improvement provided. Furthermore, the new method allows time-variations in key parameters to be tracked and visualized graphically, which allows important functional relationships to be revealed. Using simulated data, the performance of the new method is demonstrated by means of two examples. The first example shows how, starting from a simple assumption of linear PK, the method can be used to determine the correct nonlinear model for describing the PK of a drug following an oral dose. The second example shows how, starting from a simple assumption of no drug effect, the method can be used to determine the correct model for the nonlinear effect of a drug with known PK in an indirect response model.

Algorithms↗

PubMed2004

Analysis of a Kalman filter based method for on-line estimation of atmospheric dispersion parameters using radiation monitoring data.

A Kalman filter method is discussed for on-line estimation of radioactive release and atmospheric dispersion from a time series of off-site radiation monitoring data. The method is based on a state space approach, where a stochastic system equation describes the dynamics of the plume model parameters, and the observables are linked to the state variables through a static measurement equation. The method is analysed for three simple state space models using experimental data obtained at a nuclear research reactor. Compared to direct measurements of the atmospheric dispersion, the Kalman filter estimates are found to agree well with the measured parameters, provided that the radiation measurements are spread out in the cross-wind direction. For less optimal detector placement it proves difficult to distinguish variations in the source term and plume height; yet the Kalman filter yields consistent parameter estimates with large associated uncertainties. Improved source term assessment results, when independent estimates of the plume height can be used. Perspectives for using the method in the context of nuclear emergency management are discussed, and possible extensions to the present modelling scheme are outlined, to account for realistic accident scenarios.

Air Pollutants, Radioactive↗

PubMed2004

Kalman filtration of radiation monitoring data from atmospheric dispersion of radioactive materials.

A Kalman filter method using off-site radiation monitoring data is proposed as a tool for on-line estimation of the source term for short-range atmospheric dispersion of radioactive materials. The method is based on the Gaussian plume model, in which the plume parameters including the source term exhibit a 'random walk' process. The embedded parameters of the Kalman filter are determined through maximum-likelihood estimation making the filter essentially free of external parameters. The method is tested using both real and simulated radiation monitoring data. For simulated data, the method is shown to retrieve the embedded parameters employed in generating the data and to reconstruct the plume model parameters, including the source term. When tested against experimental radiation monitoring data the method is found accurately to uncover the known source term.

Air Movements↗

PubMed2004

Grey-box modelling of pharmacokinetic/pharmacodynamic systems.

Grey-box pharmacokinetic/pharmacodynamic (PK/PD) modelling is presented as a promising way of modelling PK/PD systems. The concept behind grey-box modelling is based on combining physiological knowledge along with information from data in the estimation of model parameters. Grey-box modelling consists of using stochastic differential equations (SDEs) where the stochastic term in the differential equations represents unknown or incorrectly modelled dynamics of the system. The methodology behind the grey-box PK/PD modelling framework for systematic model improvement is illustrated using simulated data and furthermore applied to Bergman's minimal model of glucose kinetics using clinical data from an intravenous glucose tolerance test (IVGTT). The grey-box estimates of the stochastic system noise parameters indicate that the glucose minimal model is too simple and should preferably be revised in order to describe the complicated in vivo system of insulin and glucose following an IVGTT.

Blood Glucose↗

PubMed2004

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.

Algorithms↗

PubMed2004

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.

Algorithms↗

PubMed2004

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.

Delayed-Action Preparations↗

PubMed2004

Effects of climate on incidence of Campylobacter spp. in humans and prevalence in broiler flocks in Denmark.

Campylobacter infections are increasing and pose a serious public health problem in Denmark. Infections in humans and broiler flocks show similar seasonality, suggesting that climate may play a role in infection. We examined the effects of temperature, precipitation, relative humidity, and hours of sunlight on Campylobacter incidence in humans and broiler flocks by using lag dependence functions, locally fitted linear models, and cross validation methods. For humans, the best model included average temperature and sunlight 4 weeks prior to infection; the maximum temperature lagged at 4 weeks was the best single predictor. For broilers, the average and maximum temperatures 3 weeks prior to slaughter gave the best estimate; the average temperature lagged at 3 weeks was the best single predictor. The combined effects of temperature and sunlight or the combined effects of temperature and relative humidity predicted the incidence in humans equally well. For broiler flock incidence these factors explained considerably less. Future research should focus on elements within the broiler environment that may be affected by climate, as well as the interaction of microclimatic factors on and around broiler farms. There is a need to quantify the contribution of broilers as a source of campylobacteriosis in humans and to further examine the effect of temperature on human incidence after this contribution is accounted for. Investigations should be conducted into food consumption and preparation practices and poultry sales that may vary by season.

Animals↗

PubMed2003

Grey-box pharmacokinetic/pharmacodynamic modelling of a euglycaemic clamp study.

Grey-box pharmacokinetic/pharmacodynamic (PK/PD) modelling is presented as a promising way of modelling the pharmacokinetics and pharmacodynamics of the in vivo system of insulin and glucose and to estimate model and derived PK/PD parameters. The concept behind grey-box modelling consists in using a priori physiological knowledge along with information from data in the estimation of model parameters. The PK/PD properties of two types of insulin are investigated in a euglycaemic clamp study where a single bolus of insulin is injected subcutaneously. The effect of insulin on the glucose disappearance is investigated by artificially maintaining a blood glucose concentration close to the normal fasting level. The infused glucose needed to maintain the clamped blood glucose concentration can therefore be used as a measure for the glucose utilization. The PK and PD parameters are successfully estimated simultaneously thereby describing the uptake, distribution, and effect of the two different types of insulin.

Adolescent↗

PubMed2003

Flavor release measurement by atmospheric pressure chemical ionization ion trap mass spectrometry, construction of interface and mathematical modeling of release profiles.

An instrumental on-line retronasal flavor analysis was developed to obtain information about the release of flavor compounds in expired air from humans during eating. The volatile flavor compounds were measured by ion trap mass spectrometry with an atmospheric pressure chemical ionization source (APCI). An interface was designed to sample the breath directly from the nose. The repeatability in vitro for seven different flavor compounds came out with relative standard derivation less than 10% in most cases, which is acceptable. In vitro quantification was carried out by a determination of the concentration in the gas phase over a flavor solution by GC/MS, followed by measurements of intensities by the APCI ion trap. Ion suppression by acetone in the breath was negligible at concentration levels relevant in these experiments. The instrumental limits of detection for menthone and menthol coincide with that of the flavor detection threshold. An application study on the release of menthone and menthol from chewing gum by a group of six test persons was performed. Flavored chewing gum was used as a model matrix because of the long chewing periods and the simplicity of the system. It is concluded that the interface and the method can be used to measure breath from the nose. A mathematical model of the data was developed to give a quantitative method for description and characterization of the release of flavor compounds. The release profiles consisted of two sequences, one for a chewing period, and one for a phasing out process. The proposed method for modeling provided a reasonable description of the release process. In addition to flavor compounds, this new interface and mathematical application could provide information on chemicals in the human breath, which could be interesting, for example, within medical diagnosis.

Journal Article↗

PubMed2002

Grey-box modelling of aeration tank settling.

A model of the concentrations of suspended solids (SS) in the aeration tanks and in the effluent from these during Aeration tank settling (ATS) operation is established. The model is based on simple SS mass balances, a model of the sludge settling and a simple model of how the SS concentration in the effluent from the aeration tanks depends on the actual concentrations in the tanks and the sludge blanket depth. The model is formulated in continuous time by means of stochastic differential equations with discrete-time observations. The parameters of the model are estimated using a maximum likelihood method from data from an alternating BioDenipho waste water treatment plant (WWTP). The model is an important tool for analyzing ATS operation and for selecting the appropriate control actions during ATS, as the model can be used to predict the SS amounts in the aeration tanks as well as in the effluent from the aeration tanks.

Air↗