Jan Freijer

Extensions to the Visual Predictive Check to facilitate model performance evaluation

The Visual Predictive Check (VPC) is a valuable and supportive instrument for evaluating model performance. However in its most commonly applied form, the method largely depends on a subjective comparison of the distribution of the simulated data with the observed data, without explicitly quantifying and relating the information in both. In recent adaptations to the VPC this drawback is taken into consideration by presenting the observed and predicted data as percentiles. In addition, in some of these adaptations the uncertainty in the predictions is represented visually. However, it is not assessed whether the expected random distribution of the observations around the predicted median trend is realised in relation to the number of observations. Moreover the influence of and the information residing in missing data at each time point is not taken into consideration. Therefore, in this investigation the VPC is extended with two methods to support a less subjective and thereby more adequate evaluation of model performance: (i) the Quantified Visual Predictive Check (QVPC) and (ii) the Bootstrap Visual Predictive Check (BVPC). The QVPC presents the distribution of the observations as a percentage, thus regardless the density of the data, above and below the predicted median at each time point, while also visualising the percentage of unavailable data. The BVPC weighs the predicted median against the 5th, 50th and 95th percentiles resulting from a bootstrap of the observed data median at each time point, while accounting for the number and the theoretical position of unavailable data. The proposed extensions to the VPC are illustrated by a pharmacokinetic simulation example and applied to a pharmacodynamic disease progression example.

Disease System Analysis: Basic Disease Progression Models in Degenerative Disease

PurposeTo describe the disease status of degenerative diseases (i.e., type 2 diabetes mellitus, Parkinson’s disease) as function of disease process and treatment effects, a family of disease progression models is introduced.MethodsDisease progression is described using a progression rate (Rdp) acting on the synthesis or elimination parameters of the indirect response model. Symptomatic effects act as disease-dependent or -independent effects on the synthesis or elimination parameters. Protective drug effects act as disease dependent or -independent effects on Rdp.ResultsSimulations with the ten disease models show distinctly different signature profiles of treatment effects on disease status. Symptomatic effects result in improvement of disease status with a subsequent deterioration. Treatment cessation results in a disease status equal to the situation where treatment had not been applied. Protective effects result in a lasting reduction, or even reversal, of the disease progression rate and the resulting disease status during the treatment period. After cessation of treatment the natural disease course will continue from the disease status at that point.ConclusionDisease system analysis constitutes a scientific basis for the distinction between symptomatic versus protective drug effects in relation to specific disease processes as well as the identification of the exposure-response relationship during the time-course of disease.

Population pharmacokinetic modelling of non-linear brain distribution of morphine: influence of active saturable influx and P-glycoprotein mediated efflux

Biophase equilibration must be considered to gain insight into the mechanisms underlying the pharmacokinetic‐pharmacodynamic (PK‐PD) correlations of opioids. The objective was to characterise in a quantitative manner the non‐linear distribution kinetics of morphine in brain.

Influence of biophase distribution and P‐glycoprotein interaction on pharmacokinetic‐pharmacodynamic modelling of the effects of morphine on the EEG

The aim was to investigate the influence of biophase distribution including P‐glycoprotein (Pgp) function on the pharmacokinetic‐pharmacodynamic correlations of morphines actions in rat brain.

Predicting the “First dose in children” of CYP3A‐metabolized drugs: Evaluation of scaling approaches and insights into the CYP3A7‐CYP3A4 switch at young ages

First‐dose‐in‐children relies on the prediction of clearance from adults for which little information is available on the accuracy of the scaling‐approaches applied. For CYP3A‐metabolized compounds, scaling of clearance is further challenged by different isoforms and by the CYP3A7 to CYP3A4 switch at young ages. This investigation aimed to evaluate the accuracy of two frequently used scaling approaches and to gain insights into the ontogeny of CYP3A. Hence, a literature database was compiled containing 203 clearance values from term‐neonates to adults for 18 CYP3A‐metabolized compounds. The clearances in adults were scaled to children using (i) allometric scaling plus maturation function and (ii) a mechanistic approach based on the well‐stirred model. Three maturation functions were separately evaluated. In children >3 months, all approaches were interchangeable heeding the maturation function applied and biases were mostly observed in children <3 months. The results from a sensitivity analysis indicate that these biases are possibly caused by disregarding the CYP3A7 activity which could account for up to 86% of the metabolism in term‐neonates. Only the mechanistic approach using an overall‐CYP3A maturation function led to unbiased predictions of clearances across all ages. The current investigation adds to the predictions of the first‐dose‐in‐children of compounds (partially) metabolized by CYP3A.

Pharmacokinetic-pharmacodynamic modelling of S(-)-atenolol in rats: reduction of isoprenaline-induced tachycardia as a continuous pharmacodynamic endpoint.

For development of mechanism‐based pharmacokinetic‐pharmacodynamic (PK‐PD) models, continuous recording of drug effects is essential. We therefore explored the use of isoprenaline in the continuous measurement of the cardiovascular effects of antagonists of β‐adrenoceptors (β‐blockers). The aim was to validate heart rate as a pharmacodynamic endpoint under continuous isoprenaline‐induced tachycardia by means of PK‐PD modelling of S(−)‐atenolol.

Pharmacokinetic/pharmacodynamic modelling of the EEG effects of opioids: the role of complex biophase distribution kinetics.

The objective of this investigation is to characterize the role of complex biophase distribution kinetics in the pharmacokinetic-pharmacodynamic correlation of a wide range of opioids. Following intravenous infusion of morphine, alfentanil, fentanyl, sufentanil, butorphanol and nalbuphine the time course of the EEG effect was determined in conjunction with blood concentrations. Different biophase distribution models were tested for their ability to describe hysteresis between blood concentration and effect. In addition, membrane transport characteristics of the opioids were investigated in vitro, using MDCK:MDR1 cells and in silico with QSAR analysis. For morphine, hysteresis was best described by an extended-catenary biophase distribution model with different values for k1e and keo of 0.038+/-0.003 and 0.043+/-0.003 min(-1), respectively. For the other opioids hysteresis was best described by a one-compartment biophase distribution model with identical values for k1e and keo. Between the different opioids, the values of k1e ranged from 0.04 to 0.47 min(-1). The correlation between concentration and EEG effect was successfully described by the sigmoidal Emax pharmacodynamic model. Between opioids significant differences in potency (EC50 range 1.2-451 ng/ml) and intrinsic activity (alpha range 18-109 microV) were observed. A statistically significant correlation was observed between the values of the in vivo k1e and the apparent passive permeability as determined in vitro in MDCK:MDR1 monolayers. It can be concluded that unlike other opioids, only morphine displays complex biophase distribution kinetics, which can be explained by its relatively low passive permeability and the interaction with active transporters at the blood-brain barrier.

Influence of Plasma Protein Binding on Pharmacodynamics: Estimation of In Vivo Receptor Affinities of β Blockers Using a New Mechanism-Based PK–PD Modelling Approach

The objective of this investigation was to examine in a systematic manner the influence of plasma protein binding on in vivo pharmacodynamics. Comparative pharmacokinetic-pharmacodynamic studies with four beta blockers were performed in conscious rats, using heart rate under isoprenaline-induced tachycardia as a pharmacodynamic endpoint. A recently proposed mechanism-based agonist-antagonist interaction model was used to obtain in vivo estimates of receptor affinities (K(B,vivo)). These values were compared with in vitro affinities (K(B,vitro)) on the basis of both total and free drug concentrations. For the total drug concentrations, the K(B,vivo) estimates were 26, 13, 6.5 and 0.89 nM for S(-)-atenolol, S(-)-propranolol, S(-)-metoprolol and timolol. The K(B,vivo) estimates on the basis of the free concentrations were 25, 2.0, 5.2 and 0.56 nM, respectively. The K(B,vivo)-K(B,vitro) correlation for total drug concentrations clearly deviated from the line of identity, especially for the most highly bound drug S(-)-propranolol (ratio K(B,vivo)/K(B,vitro) approximately 6.8). For the free drug, the correlation approximated the line of identity. Using this model, for beta-blockers the free plasma concentration appears to be the best predictor of in vivo pharmacodynamics.

A Semiphysiological Population Model for Prediction of the Pharmacokinetics of Drugs under Liver and Renal Disease Conditions

The application of model-based drug development in special populations becomes increasingly important for clinical trial optimization, mostly by providing a rationale for dose selection and thereby aiding risk-benefit assessment. In this article, a semiphysiological approach is presented, enabling the extrapolation of the pharmacokinetics from healthy subjects to patients with different disease conditions. This semiphysiological approach was applied to solifenacin, using clinical data on total and free plasma and urine concentrations in healthy subjects. The analysis was performed using nonlinear mixed-effects modeling and relied on the use of a general partitioning framework to account for binding to plasma proteins and to nonplasma tissues together with principles from physiology that apply to the main pharmacokinetic process, i.e., bioavailability, distribution, and elimination. Application of these physiology principles allowed quantification of the impact of key physiological parameters (i.e., body composition, glomerular function, liver enzyme capacity, and liver blood flow) on the pharmacokinetics of solifenacin. The prediction of the time course of the drug concentration in liver- and renal-impaired patients only required adjustment of the physiological parameters that are known to change upon liver and renal dysfunction without modifying the pharmacokinetic model structure and/or its respective parameter estimates. Visual predictive checks showed that the approach applied was able to adequately predict the pharmacokinetics of solifenacin in liver- and renal-impaired patients. In addition, better insight into the pharmacokinetic properties of solifenacin was obtained. In conclusion, the proposed semiphysiological approach is attractive for prediction of altered pharmacokinetics of compounds influenced by liver and renal disease conditions.

Mechanistic model for the acute effect of fluvoxamine on 5-HT and 5-HIAA concentrations in rat frontal cortex

A mechanistic model is proposed to predict the time course of the concentrations of 5-HT and its metabolite 5-hydroxyindolacetic acid (5-HIAA) in rat frontal cortex following acute administration of SSRIs. In the model, SSRIs increase synaptic 5-HT concentrations by reversible blockade of the SERT in a direct concentration-dependent manner, while the 5-HT response is attenuated by negative feedback via 5-HT autoreceptors. In principle, the model allows for the description of oscillatory patterns in the time course of 5-HT and 5-HIAA concentrations in brain extracellular fluid. The model was applied in a pharmacokinetic-pharmacodynamic (PK/PD) investigation on the time course of the microdialysate 5-HT and 5-HIAA response in rat frontal cortex following a 30-min intravenous infusion of 3.7 and 7.3mg/kg fluvoxamine. Directly after administration of fluvoxamine, concentrations of 5-HT were increased to approximately 450-600% of baseline values while 5-HIAA concentrations were decreased. Thereafter 5-HT and 5-HIAA concentrations gradually returned to baseline values in 6-10h, respectively. The PK/PD analysis revealed that inhibition of 5-HT reuptake was directly related to the fluvoxamine concentration in plasma, with 50% inhibition of 5-HT reuptake occurring at a plasma concentration of 1.1ng/ml (EC50). The levels of 5-HT at which 50% of the inhibition of the 5-HT response was reached (IC50) amounted to 272% of baseline. The model was unable to capture the oscillatory patterns in the individual concentration time curves, which appeared to occur randomly. The proposed mechanistic model is the first step in modeling of complex neurotransmission processes. The model constitutes a useful basis for prediction of the time course of median 5-HT and 5-HIAA concentrations in the frontal cortex in behavioral pharmacology studies in vivo.