Population Pharmacodynamic Modeling Using the Sigmoid Emax Model: Influence of Inter-individual Variability on the Steepness of the Concentration-Effect Relationship. a Simulation Study.

The relationship between the concentration of a drug and its pharmacological effect is often described by empirical mathematical models. We investigated the relationship between the steepness of the concentration-effect relationship and inter-individual variability (IIV) of the parameters of the sigmoid Emax model, using the similarity between the sigmoid Emax model and the cumulative log-normal distribution. In addition, it is investigated whether IIV in the model parameters can be estimated accurately by population modeling. Multiple data sets, consisting of 40 individuals with 4 binary observations in each individual, were simulated with varying values for the model parameters and their IIV. The data sets were analyzed using Excel Solver and NONMEM. An empirical equation (Eq. (11)) was derived describing the steepness of the population-predicted concentration-effect profile (γ*) as a function of γ and IIV in C50 and γ, and was validated for both binary and continuous data. The tested study design is not suited to estimate the IIV in C50 and γ with reasonable precision. Using a naive pooling procedure, the population estimates γ* are significantly lower than the value of γ used for simulation. The steepness of the population-predicted concentration-effect relationship (γ*) is less than that of the individuals (γ). Using γ*, the population-predicted drug effect represents the drug effect, for binary data the probability of drug effect, at a given concentration for an arbitrary individual.

Expert Discussion of the Role of Rate Constant Versus Clearance Approaches to Define Drug Pharmacokinetics: Theoretical and Clinical Considerations.

This article provides a dialogue covering an ongoing controversy on the use of clearance versus rate constant approaches for model parameterization when assessing pharmacokinetic (PK) data. It reflects the differences in opinions that can exist among PK experts. Importantly, this discussion extends beyond theoretical arguments to demonstrate how these different approaches impact the analysis and interpretation of data acquired in clinical situations. By not shying away from such dialogues, this article showcases how dissimilarity in well-grounded perspectives can influence how one applies PK and mathematical principles.

Vancomycin pharmacokinetic model development in patients on intermittent online hemodiafiltration.

BACKGROUND: Vancomycin is frequently used in hemodialysis (HD) and in hemodiafiltration (HDF) patients and is usually administered in the last 30 or 60 minutes of a dialysis session. Vancomycin pharmacokinetics are not well described in HDF patients. The aim of this study is to develop a population pharmacokinetic (PPK) model and dosing regimen for vancomycin in HDF patients and to evaluate its applicability in low-flux (LF-HD) patients. METHODS: Two-compartment PPK models were developed using data from HDF patients (n = 17), and was parameterized as follows: non-renal clearance (CLm), renal clearance as a fraction of creatinine clearance (fr), central volume of distribution (V1), intercompartmental clearance (CL12), peripheral volume of distribution (V2) and extracorporeal extraction ratio (Eec). We evaluated the final model in a cohort of LF-HD patients (n = 21). Dosing schemes were developed for a vancomycin 24-h AUC of 400 mg*h/L. RESULTS: Model parameters (± SD) were: CLm = 0.473 (0.271) L/h, fr = 0.1 (fixed value), V1 = 0.278 (0.092) L/kgLBMc, CL12 = 9.96 L/h (fixed value), V2 = 0.686 (0.335) L/kgLBMc and Eec = 0.212 (0.069). The model reliably predicted serum levels of vancomycin in both HDF and LF-HD patients during and between dialysis sessions. The median of the prediction error (MDPE) as a measure of bias is -0.7% (95% CI: -3.4%-1.7%) and the median of the absolute values of the prediction errors (MDAPE) as a measure of precision is 7.9% (95% CI: 6.0%-9.8%). In both HDF and LF-HD, the optimal vancomycin loading dose for a typical patient weighing 70 kg is 1700 mg when administered during the last 60 minutes of the hemodialysis session. Maintenance dose is 700 mg if administered during the last 30 or 60 minutes of the hemodialysis session. CONCLUSION: The developed PPK model for HDF is also capable of predicting serum levels of vancomycin in patients on LF-HD. A dosing regimen was developed for the use of vancomycin in HDF and LF-HD.

Darunavir Population Pharmacokinetic Model Based on HIV Outpatient Data.

BACKGROUND: Darunavir is a second-generation protease inhibitor and is registered for the treatment of HIV-1 infection. The aim of this study was to develop and validate a darunavir population pharmacokinetic model based on data from daily practice. METHODS: Data sets were obtained from 2 hospitals: ASST Fatebenefratelli Sacco University Hospital, Italy (hospital A), and University Medical Center Groningen, the Netherlands (hospital B). A pharmacokinetic model was developed using data from the largest data set using the iterative two-stage Bayesian procedure within the MWPharm software package. External validation was conducted using data from the smaller data set with Passing-Bablok regression and Bland-Altman analyses. RESULTS: In total, data from 198 patients from hospital A and 170 patients from hospital B were eligible for inclusion. A 1-compartment model with first-order absorption and elimination resulted in the best model. The Passing-Bablok analysis demonstrated a linear correlation between measured concentration and predicted concentration with r = 0.97 (P < 0.05). The predicted values correlated well with the measured values as determined by a Bland-Altman analysis and were overestimated by a mean value of 0.12 mg/L (range 0.23-0.94 mg/L). A total of 98.2% of the predicted values were within the limits of agreement. CONCLUSIONS: A robust population pharmacokinetic model was developed, which can support therapeutic drug monitoring of darunavir in daily outpatient settings.

Development of a mechanistic biokinetic model for hepatic bile acid handling to predict possible cholestatic effects of drugs.

Drug-induced liver injury (DILI) is a common reason for drug withdrawal from the market. An important cause of DILI is drug-induced cholestasis. One of the major players involved in drug-induced cholestasis is the bile salt efflux pump (BSEP; ABCB11). Inhibition of BSEP by drugs potentially leads to cholestasis due to increased (toxic) intrahepatic concentrations of bile acids with subsequent cell injury. In order to investigate the possibilities for in silico prediction of cholestatic effects of drugs, we developed a mechanistic biokinetic model for human liver bile acid handling populated with human in vitro data. For this purpose we considered nine groups of bile acids in the human bile acid pool, i.e. chenodeoxycholic acid, deoxycholic acid, the remaining unconjugated bile acids and the glycine and taurine conjugates of each of the three groups. Michaelis-Menten kinetics of the human uptake transporter Na+-taurocholate cotransporting polypeptide (NTCP; SLC10A1) and BSEP were measured using NTCP-transduced HEK293 cells and membrane vesicles from BSEP-overexpressing HEK293 cells. For in vitro-in vivo scaling, transporter abundance was determined by LC-MS/MS in these HEK293 cells and vesicles as well as in human liver tissue. Other relevant human kinetic parameters were collected from literature, such as portal bile acid levels and composition, bile acid synthesis and amidation rate. Additional empirical scaling was applied by increasing the excretion rate with a factor 2.4 to reach near physiological steady-state intracellular bile acid concentrations (80µM) after exposure to portal vein bile acid levels. Simulations showed that intracellular bile acid concentrations increase 1.7 fold in the presence of the BSEP inhibitors and cholestatic drugs cyclosporin A or glibenclamide, at intrahepatic concentrations of 6.6 and 20µM, respectively. This simplified model provides a tool for a first indication whether drugs at therapeutic concentrations might cause cholestasis by inhibiting BSEP.

Prediction of human CNS pharmacokinetics using a physiologically-based pharmacokinetic modeling approach.

Knowledge of drug concentration-time profiles at the central nervous system (CNS) target-site is critically important for rational development of CNS targeted drugs. Our aim was to translate a recently published comprehensive CNS physiologically-based pharmacokinetic (PBPK) model from rat to human, and to predict drug concentration-time profiles in multiple CNS compartments on available human data of four drugs (acetaminophen, oxycodone, morphine and phenytoin). Values of the system-specific parameters in the rat CNS PBPK model were replaced by corresponding human values. The contribution of active transporters for the four selected drugs was scaled based on differences in expression of the pertinent transporters in both species. Model predictions were evaluated with available pharmacokinetic (PK) data in human brain extracellular fluid and/or cerebrospinal fluid, obtained under physiologically healthy CNS conditions (acetaminophen, oxycodone, and morphine) and under pathophysiological CNS conditions where CNS physiology could be affected (acetaminophen, morphine and phenytoin). The human CNS PBPK model could successfully predict their concentration-time profiles in multiple human CNS compartments in physiological CNS conditions within a 1.6-fold error. Furthermore, the model allowed investigation of the potential underlying mechanisms that can explain differences in CNS PK associated with pathophysiological changes. This analysis supports the relevance of the developed model to allow more effective selection of CNS drug candidates since it enables the prediction of CNS target-site concentrations in humans, which are essential for drug development and patient treatment.

Modeling of prolactin response following dopamine D2 receptor antagonists in rats: can it be translated to clinical dosing?

Prolactin release is a side effect of antipsychotic therapy with dopamine antagonists, observed in rats as well as humans. We examined whether two semimechanistic models could describe prolactin response in rats and subsequently be translated to predict pituitary dopamine D2 receptor occupancy and plasma prolactin concentrations in humans following administration of paliperidone or remoxipride. Data on male Wistar rats receiving single or multiple doses of risperidone, paliperidone, or remoxipride was described by two semimechanistic models, the precursor pool model and the agonist-antagonist interaction model. Using interspecies scaling approaches, human D2 receptor occupancy and plasma prolactin concentrations were predicted for a range of clinical paliperidone and remoxipride doses. The predictions were compared with corresponding observations described in literature as well as with predictions from published models developed on human data. The pool model could predict D2 receptor occupancy and prolactin response in humans following single doses of paliperidone and remoxipride. Tolerance of prolactin release was predicted following multiple doses. The interaction model underpredicted both D2 receptor occupancy and prolactin response. Prolactin elevation may be deployed as a suitable biomarker for interspecies translation and can inform the clinical safe and effective dose range of antipsychotic drugs. While the pool model was more predictive than the interaction model, it overpredicted tolerance on multiple dosing. Shortcomings of the translations reflect the need for better mechanistic models.

Predicting Drug Concentration-Time Profiles in Multiple CNS Compartments Using a Comprehensive Physiologically-Based Pharmacokinetic Model.

Drug development targeting the central nervous system (CNS) is challenging due to poor predictability of drug concentrations in various CNS compartments. We developed a generic physiologically based pharmacokinetic (PBPK) model for prediction of drug concentrations in physiologically relevant CNS compartments. System-specific and drug-specific model parameters were derived from literature and in silico predictions. The model was validated using detailed concentration-time profiles from 10 drugs in rat plasma, brain extracellular fluid, 2 cerebrospinal fluid sites, and total brain tissue. These drugs, all small molecules, were selected to cover a wide range of physicochemical properties. The concentration-time profiles for these drugs were adequately predicted across the CNS compartments (symmetric mean absolute percentage error for the model prediction was <91%). In conclusion, the developed PBPK model can be used to predict temporal concentration profiles of drugs in multiple relevant CNS compartments, which we consider valuable information for efficient CNS drug development.

Combined proportional and additive residual error models in population pharmacokinetic modelling.

INTRODUCTION: In pharmacokinetic modelling, a combined proportional and additive residual error model is often preferred over a proportional or additive residual error model. Different approaches have been proposed, but a comparison between approaches is still lacking. METHODS: The theoretical background of the methods is described. Method VAR assumes that the variance of the residual error is the sum of the statistically independent proportional and additive components; this method can be coded in three ways. Method SD assumes that the standard deviation of the residual error is the sum of the proportional and additive components. Using datasets from literature and simulations based on these datasets, the methods are compared using NONMEM. RESULTS: The different coding of methods VAR yield identical results. Using method SD, the values of the parameters describing residual error are lower than for method VAR, but the values of the structural parameters and their inter-individual variability are hardly affected by the choice of the method. CONCLUSION: Both methods are valid approaches in combined proportional and additive residual error modelling, and selection may be based on OFV. When the result of an analysis is used for simulation purposes, it is essential that the simulation tool uses the same method as used during analysis.

An Allometric Model of Remifentanil Pharmacokinetics and Pharmacodynamics.

BACKGROUND: Pharmacokinetic and pharmacodynamic models are used to predict and explore drug infusion schemes and their resulting concentration profiles for clinical application. Our aim was to develop a pharmacokinetic-pharmacodynamic model for remifentanil that is accurate in patients with a wide range of age and weight. METHODS: Remifentanil pharmacokinetic data were obtained from three previously published studies of adults and children, one of which also contained pharmacodynamic data from adults. NONMEM was used to estimate allometrically scaled compartmental pharmacokinetic and pharmacodynamic models. Weight, age, height, sex, and body mass index were explored as covariates. Predictive performance was measured across young children, children, young adults, middle-aged, and elderly. RESULTS: Overall, 2,634 remifentanil arterial concentration and 3,989 spectral-edge frequency observations from 131 individuals (55 male, 76 female) were analyzed. Age range was 5 days to 85 yr, weight range was 2.5 to 106 kg, and height range was 49 to 193 cm. The final pharmacokinetic model uses age, weight, and sex as covariates. Parameter estimates for a 35-yr-old, 70-kg male (reference individual) are: V1, 5.81 l; V2, 8.82 l; V3, 5.03 l; CL, 2.58 l/min; Q2, 1.72 l/min; and Q3, 0.124 l/min. Parameters mostly increased with fat-free mass and decreased with age. The pharmacodynamic model effect compartment rate constant (ke0) was 1.09 per minute (reference individual), which decreased with age. CONCLUSIONS: We developed a pharmacokinetic-pharmacodynamic model to predict remifentanil concentration and effect for a wide range of patient ages and weights. Performance exceeded the Minto model over a wide age and weight range.

Pharmacokinetic modeling of gentamicin in treatment of infective endocarditis: Model development and validation of existing models.

Gentamicin shows large variations in half-life and volume of distribution (Vd) within and between individuals. Thus, monitoring and accurately predicting serum levels are required to optimize effectiveness and minimize toxicity. Currently, two population pharmacokinetic models are applied for predicting gentamicin doses in adults. For endocarditis patients the optimal model is unknown. We aimed at: 1) creating an optimal model for endocarditis patients; and 2) assessing whether the endocarditis and existing models can accurately predict serum levels. We performed a retrospective observational two-cohort study: one cohort to parameterize the endocarditis model by iterative two-stage Bayesian analysis, and a second cohort to validate and compare all three models. The Akaike Information Criterion and the weighted sum of squares of the residuals divided by the degrees of freedom were used to select the endocarditis model. Median Prediction Error (MDPE) and Median Absolute Prediction Error (MDAPE) were used to test all models with the validation dataset. We built the endocarditis model based on data from the modeling cohort (65 patients) with a fixed 0.277 L/h/70kg metabolic clearance, 0.698 (±0.358) renal clearance as fraction of creatinine clearance, and Vd 0.312 (±0.076) L/kg corrected lean body mass. External validation with data from 14 validation cohort patients showed a similar predictive power of the endocarditis model (MDPE -1.77%, MDAPE 4.68%) as compared to the intensive-care (MDPE -1.33%, MDAPE 4.37%) and standard (MDPE -0.90%, MDAPE 4.82%) models. All models acceptably predicted pharmacokinetic parameters for gentamicin in endocarditis patients. However, these patients appear to have an increased Vd, similar to intensive care patients. Vd mainly determines the height of peak serum levels, which in turn correlate with bactericidal activity. In order to maintain simplicity, we advise to use the existing intensive-care model in clinical practice to avoid potential underdosing of gentamicin in endocarditis patients.

A Generic Multi-Compartmental CNS Distribution Model Structure for 9 Drugs Allows Prediction of Human Brain Target Site Concentrations.

PURPOSE: Predicting target site drug concentration in the brain is of key importance for the successful development of drugs acting on the central nervous system. We propose a generic mathematical model to describe the pharmacokinetics in brain compartments, and apply this model to predict human brain disposition. METHODS: A mathematical model consisting of several physiological brain compartments in the rat was developed using rich concentration-time profiles from nine structurally diverse drugs in plasma, brain extracellular fluid, and two cerebrospinal fluid compartments. The effect of active drug transporters was also accounted for. Subsequently, the model was translated to predict human concentration-time profiles for acetaminophen and morphine, by scaling or replacing system- and drug-specific parameters in the model. RESULTS: A common model structure was identified that adequately described the rat pharmacokinetic profiles for each of the nine drugs across brain compartments, with good precision of structural model parameters (relative standard error <37.5%). The model predicted the human concentration-time profiles in different brain compartments well (symmetric mean absolute percentage error <90%). CONCLUSIONS: A multi-compartmental brain pharmacokinetic model was developed and its structure could adequately describe data across nine different drugs. The model could be successfully translated to predict human brain concentrations.

Summary data of potency and parameter information from semi-mechanistic PKPD modeling of prolactin release following administration of the dopamine D2 receptor antagonists risperidone, paliperidone and remoxipride in rats.

We provide the reader with relevant data related to our recently published paper, comparing two mathematical models to describe prolactin turnover in rats following one or two doses of the dopamine D2 receptor antagonists risperidone, paliperidone and remoxipride, "A comparison of two semi-mechanistic models for prolactin release and prediction of receptor occupancy following administration of dopamine D2 receptor antagonists in rats" (Taneja et al., 2016) [1]. All information is tabulated. Summary level data on the in vitro potencies and the physicochemical properties is presented in Table 1. Model parameters required to explore the precursor pool model are presented in Table 2. In Table 3, estimated parameter comparisons for both models are presented, when separate potencies are estimated for risperidone and paliperidone, as compared to a common potency for both drugs. In Table 4, parameter estimates are compared when the drug effect is parameterized in terms of drug concentration or receptor occupancy.

A comparison of two semi-mechanistic models for prolactin release and prediction of receptor occupancy following administration of dopamine D2 receptor antagonists in rats.

We compared the model performance of two semi-mechanistic pharmacokinetic-pharmacodynamic models, the precursor pool model and the agonist-antagonist interaction model, to describe prolactin response following the administration of the dopamine D2 receptor antagonists risperidone, paliperidone or remoxipride in rats. The time course of pituitary dopamine D2 receptor occupancy was also predicted. Male Wistar rats received a single dose (risperidone, paliperidone, remoxipride) or two consecutive doses (remoxipride). Population modeling was applied to fit the pool and interaction models to the prolactin data. The pool model was modified to predict the time course of pituitary D2 receptor occupancy. Unbound plasma concentrations of the D2 receptor antagonists were considered the drivers of the prolactin response. Both models were used to predict prolactin release following multiple doses of paliperidone. Both models described the data well and model performance was comparable. Estimated unbound EC50 for risperidone and paliperidone was 35.1nM (relative standard error 51%) and for remoxipride it was 94.8nM (31%). KI values for these compounds were 11.1nM (21%) and 113nM (27%), respectively. Estimated pituitary D2 receptor occupancies for risperidone and remoxipride were comparable to literature findings. The interaction model better predicted prolactin profiles following multiple paliperidone doses, while the pool model predicted tolerance better. The performance of both models in describing the prolactin profiles was comparable. The pool model could additionally describe the time course of pituitary D2 receptor occupancy. Prolactin response following multiple paliperidone doses was better predicted by the interaction model.

Translational Modeling in Schizophrenia: Predicting Human Dopamine D2 Receptor Occupancy.

OBJECTIVES: To assess the ability of a previously developed hybrid physiology-based pharmacokinetic-pharmacodynamic (PBPKPD) model in rats to predict the dopamine D2 receptor occupancy (D2RO) in human striatum following administration of antipsychotic drugs. METHODS: A hybrid PBPKPD model, previously developed using information on plasma concentrations, brain exposure and D2RO in rats, was used as the basis for the prediction of D2RO in human. The rat pharmacokinetic and brain physiology parameters were substituted with human population pharmacokinetic parameters and human physiological information. To predict the passive transport across the human blood-brain barrier, apparent permeability values were scaled based on rat and human brain endothelial surface area. Active efflux clearance in brain was scaled from rat to human using both human brain endothelial surface area and MDR1 expression. Binding constants at the D2 receptor were scaled based on the differences between in vitro and in vivo systems of the same species. The predictive power of this physiology-based approach was determined by comparing the D2RO predictions with the observed human D2RO of six antipsychotics at clinically relevant doses. RESULTS: Predicted human D2RO was in good agreement with clinically observed D2RO for five antipsychotics. Models using in vitro information predicted human D2RO well for most of the compounds evaluated in this analysis. However, human D2RO was under-predicted for haloperidol. CONCLUSIONS: The rat hybrid PBPKPD model structure, integrated with in vitro information and human pharmacokinetic and physiological information, constitutes a scientific basis to predict the time course of D2RO in man.

Development of an Optimized Pharmacokinetic Model of Dexmedetomidine Using Target-controlled Infusion in Healthy Volunteers.

BACKGROUND: Several pharmacokinetic models are available for dexmedetomidine, but these have been shown to underestimate plasma concentrations. Most were developed with data from patients during the postoperative phase and/or in intensive care, making them susceptible to errors due to drug interactions. The aim of this study is to improve on existing models using data from healthy volunteers. METHODS: After local ethics committee approval, the authors recruited 18 volunteers, who received a dexmedetomidine target-controlled infusion with increasing target concentrations: 1, 2, 3, 4, 6, and 8 ng/ml, repeated in two sessions, at least 1 week apart. Each level was maintained for 30 min. If one of the predefined safety criteria was breached, the infusion was terminated and the recovery period began. Arterial blood samples were collected at preset times, and NONMEM (Icon plc, Ireland) was used for model development. RESULTS: The age, weight, and body mass index ranges of the 18 volunteers (9 male and 9 female) were 20 to 70 yr, 51 to 110 kg, and 20.6 to 29.3 kg/m, respectively. A three-compartment allometric model was developed, with the following estimated parameters for an individual of 70 kg: V1 = 1.78 l, V2 = 30.3 l, V3 = 52.0 l, CL = 0.686 l/min, Q2 = 2.98 l/min, and Q3 = 0.602 l/min. The predictive performance as calculated by the median absolute performance error and median performance error was better than that of existing models. CONCLUSIONS: Using target-controlled infusion in healthy volunteers, the pharmacokinetics of dexmedetomidine were best described by a three-compartment allometric model. Apart from weight, no other covariates were identified.