Hypothetical Effect Compartment Research Articles

Development of a Subcellular Semimechanism-Based Pharmacokinetic/Pharmacodynamic Model to Characterize Paclitaxel Effects Delivered by Polymeric Micelles

A transit compartment model was widely and successfully applied to characterize the complex time course of cancer chemotherapeutic effects in vivo or in vitro. However, the underlying mechanisms were not quantitatively depicted. This study aimed to develop a semimechanism-based cellular pharmacokinetic/pharmacodynamic (PK/PD) model to characterize paclitaxel (PTX) effect delivered by PLGA-PEG micelles which was based on analysis of drug subcellular distribution, the tubulin assembly level, the cell cycle shift, and the resulting cytotoxicity. Human breast cancer cell line MCF-7 was exposed to PTX at the concentration of 20 and 40 ng/mL. The in vitro pharmacokinetics of micelle-entrapped PTX was described by a 3-compartment model composed of membrane/organelle, nucleus, and cytoskeleton. A hypothetical effect compartment was used to characterize the distribution delay. The time course of tubulin polymerization stimulation was fitted by the indirect response model. The relationship between tubulin polymerization and G2/M cell population was described by a linear model, and the promoting effect of G2/M arrest on the cytotoxicity was characterized by the Emax model. The proposed model captured the data successfully and described the cellular mechanism of antimitotic drug nanoparticles quantitatively. The methodology and the resulting model could be a supplement for traditional in vivo studies.

Population pharmacokinetic modeling of flurbiprofen, the active metabolite of flurbiprofen axetil, in Chinese patients with postoperative pain.

BackgroundFlurbiprofen axetil, a lipid-microsphere-carrier targeting preparation, is a non-steroidal anti-inflammatory drug indicated for the treatment of postoperative pain.AimThe aim of the study was to develop a population pharmacokinetic (PPK) model of flurbiprofen, the active metabolite of flurbiprofen axetil, and optimize the treatment of flurbiprofen axetil in Chinese patients.MethodsA total of 144 therapeutic drug-monitoring samples of flurbiprofen axetil from 72 patients were included in this study. The pharmacologically active metabolite flurbiprofen was used as the analytical target and determined 5–45 minutes after intravenous administration. The PPK model for flurbiprofen was developed using Phoenix NLME 1.3 with a nonlinear mixed-effect model. Bootstrap and visual predictive checks were used simultaneously to validate the final PPK model. Potential covariates of age, sex, body weight, height, and body-mass index were tested for PK parameters.ResultsThe PPK model of flurbiprofen was explained by a one-compartment model with first-order elimination, in which a hypothetical-effect compartment was linked to a PK compartment. Population mean values of PK parameters estimated in the final model were θKe=0.0015/h, θVd=7.91 L, and θCL=1.55 L/h. Analysis of covariates showed that height and weight influenced the Ke of flurbiprofen. The final model was proved to be robust.ConclusionThe final PPK model was demonstrated to be appropriate and effective, and can be used to assess the PK parameters of flurbiprofen in Chinese patients with postoperative pain.

Bridging the Gap Between In Vitro Dissolution and the Time Course of Ibuprofen-Mediating Pain Relief

In vitro–in vivo extrapolation techniques combined with physiologically based pharmacokinetic models represent a feasible approach to establishing links between critical quality attributes and the time course of drug concentrations in vivo. By further integrating the results with pharmacodynamic (PD) models, scientists can also explore the time course of drug effect. The aim of this study was to assess whether differences in dissolution rates would affect the onset, magnitude, and duration of the time course of ibuprofen-mediating pain relief. An integrated in vitro–in vivo extrapolation–physiologically based pharmacokinetic/PD model was used to simulate pharmacokinetic and PD profiles for ibuprofen free acid (IBU-H) and its salts. Two elements of the pharmacokinetic profile, the peak of exposure (Cmax) and the time to peak concentration (Tmax), were sensitive to dissolution rate, whereas only 1 element of the pharmacodynamic profile was affected, namely the onset of drug action. The Cmax differences between IBU-H and its salts seem to be mitigated in the (hypothetical) effect compartment because of the concurrent distribution and elimination processes. Furthermore, the predicted maximum concentration in the effect compartment exceeded the EC80 value, which marks the plateau phase of the PD concentration–response curve, regardless of whether IBU-H or its salts were administered. Understanding the target site distribution kinetics and the potential nonlinearities between exposure and response will assist in setting criteria that are more scientifically based for the demonstration of therapeutic equivalence.

Pharmacokinetic–Pharmacodynamic Modeling of the Antihypertensive Effect of Eprosartan in Black and White Hypertensive Patients

It is well recognized that many antihypertensive drugs exhibit large interindividual variability in effect and that this wide range of patient response to antihypertensive drugs is a major problem in achieving blood pressure (BP) control. Variability in both drug concentration and drug effect may cause the heterogeneity in antihypertensive drug response. However, for most antihypertensive drugs, no clear relationship between drug concentration and its effect on BP has been reported. This study aimed to describe the relationship between eprosartan exposure and its effect on the systolic blood pressure (SBP) using population pharmacokinetic-pharmacodynamic modeling. Interindividual variability in pharmacokinetics and pharmacodynamics was quantified and the influence of covariates on this relationship was evaluated. Eprosartan plasma concentrations and SBP measurements were determined in 86 mildly hypertensive patients from the ROTATE study aged 48.1±7.6years with different ethnic backgrounds (33 White Dutch, 41 Creole Surinamese, 12 Hindustani Surinamese). In 12 of these patients, pharmacokinetics were densely sampled and 24-h ambulatory BP measurements were obtained. Data were analyzed using nonlinear mixed effects modeling. Eprosartan concentration-time profiles were adequately described with a two-compartment pharmacokinetic model with zero-order absorption. A log-linear relationship was used to describe the relationship between concentration and the decrease in SBP. A hypothetical effect compartment was used to describe hysteresis in the drug effect. Approximately 80% of the maximum decrease in SBP was observed after 24days. Interindividual variability in drug response was 65% and decreased to 14% when ethnicity was added as covariate. Creole Surinamese exhibited no drug response in contrast to White Dutch and Hindustani Surinamese [-2.6mmHg per (ng/ml)]. The developed pharmacokinetic-pharmacodynamic model allows the quantification and explanation of variability in SBP between individuals with ethnicity as a useful determinant of responsiveness to eprosartan.

Enhanced Sensitivity to Drug‐Induced QT Interval Lengthening in Patients With Heart Failure Due to Left Ventricular Systolic Dysfunction

Patients with heart failure (HF) are at increased risk for drug-induced torsades de pointes (TdP) due to unknown mechanisms. Our objective was to determine if sensitivity to drug-induced QT interval lengthening is enhanced in patients with HF. In this multicenter, prospective study, 15 patients with atrial fibrillation or flutter requiring conversion to sinus rhythm were enrolled: 6 patients with New York Heart Association class II to III HF (mean ejection fraction [EF], 30% ± 9%), and 9 controls (mean EF, 53% ± 6%). Patients received ibutilide 1 mg intravenously. Blood samples and 12-lead electrocardiograms were obtained prior to and during 48 hours postinfusion. Serum ibutilide concentrations at 50% maximum effect on Fridericia-corrected QT (QT(F)) intervals (EC(50)) were determined, and areas under the effect (QT(F) interval vs time) curves (AUECs) were calculated. Ibutilide concentration-QT(F) relationships were best described by a sigmoidal E(max) model with a hypothetical effect compartment. Median [interquartile range] AUEC from 0 to 4 hours was larger in the HF group than in controls (1.86 [1.86-1.93] vs 1.82 [1.81-1.84] s·h; P = .04). Median EC(50) was lower in the HF group (0.48 [0.46-0.49] vs 1.85 [1.10-3.23] μg/L; P = .008). Sensitivity to drug-induced QT interval lengthening is enhanced in patients with systolic HF, which may contribute to the increased risk of drug-induced TdP.

Population pharmacokinetics and pharmacodynamics of escitalopram in overdose and the effect of activated charcoal

To describe the pharmacokinetics and pharmacodynamics (PKPD) of escitalopram in overdose and its effect on QT prolongation, including the effectiveness of single dose activated charcoal (SDAC). The data set included 78 escitalopram overdose events (median dose, 140mg [10-560mg]). SDAC was administered 1.0 to 2.6 h after 12 overdoses (15%). A fully Bayesian analysis was undertaken in WinBUGS 1.4.3, first for a population pharmacokinetic (PK) analysis followed by a PKPD analysis. The developed PKPD model was used to predict the probability of having an abnormal QT as a surrogate for torsade de pointes. A one compartment model with first order input and first-order elimination described the PK data, including uncertainty in dose and a baseline concentration for patients taking escitalopram therapeutically. SDAC reduced the fraction absorbed by 31% and reduced the individual predicted area under the curve adjusted for dose (AUC(i) /dose). The absolute QT interval was related to the observed heart rate with an estimated individual heart rate correction factor (α= 0.35). The heart rate corrected QT interval (QT(c) ) was linearly dependent on predicted escitalopram concentration [slope = 87ms/(mgl(-1) )], using a hypothetical effect-compartment (half-life of effect-delay, 1.0h). Administration of SDAC significantly reduced QT prolongation and was shown to reduce the risk of having an abnormal QT by approximately 35% for escitalopram doses above 200mg. There was a dose-related lengthening of the QT interval that lagged the increase in drug concentration. SDAC resulted in a moderate reduction in fraction of escitalopram absorbed and reduced the risk of the QT interval being abnormal.

Mechanism-based PKPD modelling of CNS-active drugs

Event Abstract Back to Event Mechanism-based PKPD modelling of CNS-active drugs Elizabeth C. De Lange1* 1 Leiden University, LACDR/Pharmacology, Gorlaeus Laboratories, Netherlands Our ultimate goal is to develop mechanism-based pharmacokinetic (PK)-pharmacodynamic (PD) models to characterize and to predict CNS drug responses in both physiologic and pathologic conditions. To this end, it is essential to have information on the target site (biophase) pharmacokinetics, because it may significantly differ from plasma pharmacokinetics. It is anticipated that the biophase kinetics of CNS drugs in many cases is strongly influenced by transport across the blood-brain barrier (BBB). In vivo microdialysis enables the determination of free-drug concentrations as a function of time in extracellular fluid of the brain, thereby providing important data to determine BBB transport characteristics of drugs. This is important for delineating the mechanisms that govern biophase pharmacokinetics when combined with CNS effect measurements, and therefore provides an indispensable tool in mechanism-based PKPD modeling of CNS drugs. The biophase kinetics of a CNS drug is an important determinant of the time course and intensity of its CNS effects. Biophase pharmacokinetics can be estimated by PKPD modeling by using a hypothetical effect compartment. This hypothetical effect compartment is linked to the plasma compartment by a rate constant for influx and a rate constant for drug efflux such that there is no time delay between the biophase pharmacokinetics in the effect compartment and the time course of the effect. These data on biophase pharmacokinetics can be related to the effect, whereby it is possible to gain information on the true ability of a drug to activate the receptor. This is typically done using the biophase pharmacokinetics of a number of drugs within a same class, in combination with the receptor theory (operational model of agonism).However, the use of the effect compartment model does not provide insight into mechanisms that govern biophase pharmacokinetics which is needed for more generally applicable PKPD models. Apart from plasma pharmacokinetics, mechanisms that govern CNS biophase kinetics include: the rate and extent of blood-brain barrier (BBB) transport; the kinetics of processes of distribution and elimination within the brain; target interaction, and signal transduction (fig 1). All the mechanisms may vary in their contribution to the dose-effect relationship and therefore need to be taken into consideration1. As BBB transport and brain distribution often do not occur instantaneously and to a full extent, this may contribute to a delay of the pharmacologic effect versus time profile relative to the plasma profile. In order to develop more generally applicable models with more power for extrapolation to other conditions, it is of importance to explicitly investigate BBB transport. BBB transport is related to BBB functionality and occurs by passive diffusion, as well as by active transport. Active transport occurs by many membrane transporters such as the Pglycoprotein (Pgp) and the multidrug resistance-associated proteins (MRPs). BBB functionality is dynamically controlled by blood components and the surrounding brain cells by direct contact or indirectly by their extracellular products. Thus, BBB functionality may vary among different physiologic, pathologic, and chronic drug treatment conditions. It is anticipated that such variations in BBB functionality will ultimately affect the biophase kinetics of CNS drugs and therewith the CNS effect-time profile of the drug. In vivo microdialysis is a technique that enables the determination of the free drug in plasma and its concentrations in extracellular fluid (ECF) the brain as a function of time. Herewith, it provides important information for the determination of BBB transport and brain distribution. A prerequisite for this application is that BBB transport characteristics will not be significantly influenced by microdialysis probe implantation and presence in the brain. This was an initial concern. But based on a series of studies performed to validate the usefulness of intracerebral microdialysis in measurements of passive, as well as active, BBB transport, this prerequisite appears to hold, provided that this technique is used under well-controlled surgical and experimental conditions. In this presentation the main principles of mechanism-based PKPD modeling of CNS active drugs will be presented, including arguments for the need to include biophase kinetics, followed by the description of factors that govern biophase kinetics of CNS drugs. Then, two examples on studies in rats that include investigations on the impact of BBB transport will be discussed. The first example is on the EEG effects of opioids2, while the second one deals with BBB transport of L-DOPA and its brain conversion to HVA and DOPAC in Parkinson’s diseased brain3. Acknowledgments We are grateful to GlaxoSmithKline and Eli Lilly for their collaboration and financing of the studies on the opioids and Parkinson’s disease, respectively. Fig 1

Pharmacokinetic–pharmacodynamic modelling of QT interval prolongation following citalopram overdoses

To develop a pharmacokinetic-pharmacodynamic model describing the time-course of QT interval prolongation after citalopram overdose and to evaluate the effect of charcoal on the relative risk of developing abnormal QT and heart-rate combinations. Plasma concentrations and electrocardiograph (ECG) data from 52 patients after 62 citalopram overdose events were analysed in WinBUGS using a Bayesian approach. The reported doses ranged from 20 to 1700 mg and on 17 of the events a single dose of activated charcoal was administered. The developed pharmacokinetic-pharmacodynamic model was used for predicting the probability of having abnormal combinations of QT-RR, which was assumed to be related to an increased risk for torsade de pointes (TdP). The absolute QT interval was related to the observed heart rate with an estimated individual heart-rate correction factor [alpha = 0.36, between-subject coefficient of variation (CV) = 29%]. The heart-rate corrected QT interval was linearly dependent on the predicted citalopram concentration (slope = 40 ms l mg(-1), between-subject CV = 70%) in a hypothetical effect-compartment (half-life of effect-delay = 1.4 h). The heart-rate corrected QT was predicted to be higher in women than in men and to increase with age. Administration of activated charcoal resulted in a pronounced reduction of the QT prolongation and was shown to reduce the risk of having abnormal combinations of QT-RR by approximately 60% for citalopram doses above 600 mg. Citalopram caused a delayed lengthening of the QT interval. Administration of activated charcoal was shown to reduce the risk that the QT interval exceeds a previously defined threshold and therefore is expected to reduce the risk of TdP.

Integrated pharmacokinetic-pharmacodynamic modeling and allometric scaling for optimizing the dosage regimen of the monoclonal ior EGF/r3 antibody.

The multiple-dose strategy with the monoclonal ior EGF/r3 antibody, in xenograft bearing nude mice, was supported upon the basis of its integrated pharmacokinetic-pharmacodynamic relationship, according to both the temporal (K(e0)=0.0015+/-0.000035h(-1)) and the time-independent sensitivity (C(50%)(ss), 9.23+/-0.17microg/ml; C(max,eff)(ss), 12.5microg/ml) components of its tumor growth delay action. This relationship was consistent with a sigmoidal E(max) pharmacodynamic model postulating a hypothetical effect compartment that permits us to estimate an effective steady-state concentration range (7.5-12microg/ml). Using this information we calculated both the cumulative and non-cumulative dosage regimens to compare their response patterns with respect to the control group. It follows that the differences in the estimated tumor growth inhibition ratio were statistically significant between the control group and either of the treated ones (P<0.05). The median survival time in treated mice under non-cumulative regimen (72+/-10 days), predicted an increase in this parameter as compared to the control one (55+/-6 days). Finally, using the allometric paradigm, the empiric power equation for dose scaling across mammalian species allowed the calculation of the dosage schedule for further clinical trial. The estimated maintenance dose in human (70kg) was 200mg/m(2) to be given weekly, and the corresponding loading dose was 600mg/m(2).

Monitoring of L-dopa concentrations in parkinson’s disease

Although it is the treatment of choice in the management of idiopathic Parkinson’s disease, l-DOPA (LD) shows a decline in its efficacy after years of prolonged use, with the appearance of severe motor disturbances. These complications have been interpreted on pharmacokinetic and pharmacodynamic grounds. The main pharmacokinetic reason is considered to be the decreased capacity in LD activation to dopamine along with reduction of its storage ability in the nigrostriatal terminals, as a result of disease progression. At this stage the LD action in the extrapyramidal system is thought to be closely dependent on its synaptic cleft concentrations, being directly related to those in the systemic circulation and to the events possibly perturbing them. Therapeutic drug monitoring might be useful to explain these modifications in relation to the clinical effect and even to possible problems in transport competition and so to define the LD dosage regimen. Recently LD threshold concentrations have been suggested by means of sophisticated pharmacokinetic–pharmacodynamic approaches. Unfortunately they do not correspond to real therapeutic ranges but to levels in a hypothetical effect compartment in no steady-state conditions, due to remarkable LD fluctuations. However they are considered helpful to the functional state interpretation of the nigrostriatal system.

Comparative Population Pharmacokinetic‐Pharmacodynamic Analysis for Piroxicam‐β‐Cyclodextrin and Piroxicam

Piroxicam (Feldene) is indicated for osteoarthritis and rheumatoid arthritis but not analgesia due to its delayed onset of pain relief. Piroxicam-beta-cyclodextrin (PBCD) was developed for pain indication by virtue of the increased absorption rate of piroxicam. Forty-eight patients received a single dose of PBCD or Feldene (10, 20, and 40 mg) in a randomized study, and piroxicam plasma concentration and pain relief were measured. The purpose of the study was to investigate the PK-PD relationship of piroxicam, determine the optimal dose, and evaluate the effect of increased absorption rate on analgesic effect of piroxicam for the pain model studied. The pharmacokinetic data were best described by a two-compartment model with first-order absorption. The absorption rate of PBCD (5/h) was faster than Feldene (1.41/h). Pain relief was found to be increasing with drug concentration in a hypothetical effect compartment (Emax model). The estimated half-life of the equilibration between plasma and effect site was about 2.34 hours. Monte Carlo simulation showed that the time when at least 50% of the patients have a 75% probability of achieving meaningful pain relief (pain intensity difference (PID > or = 1) for PBCD and Feldene at a dose of 20 mg was about 0.5 and 1.5 hours, respectively. PBCD demonstrated an advantage with an onset of pain relief 1 hour earlier than Feldene.

Pharmacokinetic-pharmacodynamic modeling of risperidone effects on electroencephalography in healthy volunteers.

CNS-active drugs produce specific electroencephalographic changes and the concentration-effect relationship of antipsychotics may be elucidated by adopting electroencephalography (EEG) as an effect measurement tool. The purpose of the present study was to determine the concentration-effect relationship of risperidone by assessing the EEG effect after oral administrations of single dose risperidone in healthy young males. Nine healthy male volunteers received a 1 mg single oral dose of risperidone according to a placebo controlled crossover design. Plasma levels of risperidone and its active metabolite 9-hydroxyrisperidone were measured by radioimmunoassay. Quantitative EEG parameters were obtained for each of four frequency bands through spectral EEG analysis. The difference in the absolute power in the delta frequency band for the F3 lead between risperidone and placebo was used as a drug effect parameter. For pharmacokinetic-pharmacodynamic modeling, the hypothetical effect compartment kinetically linked to plasma by a first-order process was postulated. All curve fittings were done with the non-linear curve-fitting program NONLIN. Our results showed that absolute powers in delta and theta frequency bands were higher for risperidone administration than for placebo at all EEG leads, and the maximum effects were detected at about 3 h after administration of the drug. The hysteresis loop was observed in the plot of plasma concentration of risperidone or sum of risperidone and 9-hydroxyrisperidone (Cp) versus EEG effect for each subject. A linear model adequately described the relationship between the effect compartment concentrations (Ce) and EEG effects, and the two limbs of hysteresis in the Cp-effect plot were collapsed in the Ce-effect plot for risperidone or risperidone plus 9-hydroxyrisperidone. The increases of absolute power for delta and theta frequency bands of EEG were induced by single oral administration of risperidone. The linear PK-PD model fit well with the relationship between effect compartment concentrations (Ce) and EEG effects of risperidone.

Speed of Onset and Offset and Mechanisms of Ventilatory Depression from Sevoflurane

Inhalational anesthetics depress breathing dose dependently. The authors studied the dynamics of ventilation on changes in end-tidal sevoflurane partial pressure. To learn more about the mechanisms of sevoflurane-induced respiratory depression, the authors also studied its influence on the dynamic ventilatory response to carbon dioxide. Experiments were performed in cats anesthetized with alpha chloralose-urethane. For protocol 1, step changes in end-tidal sevoflurane partial pressure were applied and inspired ventilation was measured. Breath-to-breath inspired ventilation was related to the sevoflurane concentration in a hypothetical effect compartment based on an inhibitory sigmoid Emax model. For protocol 2, step changes in the end-tidal partial pressure of carbon dioxide were applied at 0, 0.5, and 1% end-tidal sevoflurane. The inspired ventilation-end-tidal partial pressure of carbon dioxide data were analyzed using a two-compartment model of the respiratory controller, which consisted of a fast peripheral and slow central compartment. Values are the mean +/- SD. In protocol 1, the effect-site half-life of respiratory changes caused by alterations in end-tidal sevoflurane partial pressure was 3.6+/-1.0 min. In protocol 2, at 0.50% sevoflurane, the central and peripheral carbon dioxide sensitivities decreased to 43+/-20% and 36+/-18% of control. At 1% sevoflurane, the peripheral carbon dioxide sensitivity decreased further, to 12+/-13% of control, whereas the central carbon dioxide sensitivity showed no further decrease. Steady state inspired ventilation is reached after 18 min (i.e., 5 half-lives) on stepwise changes in end-tidal sevoflurane. Anesthetic concentrations of sevoflurane have, in addition to an effect on pathways common to the peripheral and central chemoreflex loops, a selective effect on the peripheral chemoreflex loop. Sevoflurane has similar effects on ventilatory control in humans and cats.

Physiologic indirect response models characterize diverse types of pharmacodynamic effects.

A family of four basic physiologic indirect response models has been proposed to account for the pharmacodynamics of drugs that act by way of inhibition or stimulation of the production or loss of endogenous substances or mediators. Such models were applied previously to account for the anticoagulant effects of warfarin, adrenal suppression by corticosteroids, cell trafficking effects of corticosteroids, antipyretic effects of ibuprofen, and aldose reductase inhibition. Additional responses that can be readily characterized with such models include muscular contraction from pyridostigmine, diuresis from furosemide, bronchodilation from terbutaline, prolactin secretion after cimetidine, and potassium suppression by terbutaline. This report shows that indirect response models, rather than "link" or "hypothetical effect compartment" models, may be more appropriate for diverse drugs when time lags exist between plasma or biophase drug concentrations and the time course of pharmacodynamic responses.

The concentration-effect relationship of quinine-induced hearing impairment

Quinine-induced reversible hearing impairment at the frequencies of 1000 and 2000 Hz was investigated in healthy volunteers to analyze the plasma concentration-effect relationship of the drug. Six subjects were given two identical oral doses of quinine and a constant rate infusion of quinine over 6 hours (15 mg.kg-1) on three separate occasions. A simple pharmacodynamic model, E = k.C gamma (in which E is effect, k is a proportionality constant, C is drug concentration, and the exponent gamma is a fitting parameter), was found to describe well the relationship between hearing impairment and quinine concentrations in a hypothetical effect compartment. No statistical differences were found in the estimated parameters when the three dosings were compared, indicating that quinine-induced hearing impairment is independent of route of administration. The first-order rate constant (keo), linking plasma concentrations to the concentrations in the effect compartment, was (mean +/- SD) 0.71 +/- 0.19 and 0.99 +/- 0.37 hr-1 for 1000 and 2000 Hz, respectively. The corresponding values of k were 0.15 +/- 0.10 and 0.12 +/- 0.19 and the values of gamma were 2.13 +/- 0.57 and 3.44 +/- 1.04 for 1000 and 2000 Hz, respectively. Effect was also analyzed by semiparametric pharmacodynamic modeling, which gave results comparable to those obtained with the link model. We conclude that a simple power function is a reliable pharmacodynamic model for describing quinine-induced hearing impairment in healthy subjects.

Effect modelling for drugs undergoing enterohepatic circulation.

A multi-compartment pharmacokinetic model with enterohepatic circulation, was used in simulations and in a clinical trial with morphine. A hypothetical effect compartment was linked to either the central or the peripheral disposition compartment.

Conceptualization of drug distribution to a hypothetical pharmacodynamic effect compartment

Clinical Pharmacology and Therapeutics (1993) 54, 112–113; doi:10.1038/clpt.1993.119

Semiparametric analysis of non-steady-state pharmacodynamic data

We present an approach to the analysis of pharmacodynamic (PD) data arising from non-steady-state experiments, meant to be used when only PD data, not pharmacokinetic (PK) data, are available. The approach allows estimation of the steady-state relationship between drug input and effect. The analysis is based on a model describing the time dependence of drug effect (E) on (unobserved) drug concentration (Ce) in an hypothetical effect compartment. The model consists of (i) a known model for the input rate of drug I(t), (ii) a parametric model; L(t, alpha) (a function of time t, and vector of parameters alpha), relating I to an observed variable X, (iii) a nonparametric model relating X to E. Ce is proportional to X. X (t) is given by I(t) * L(t, alpha)/AL, where L(t, alpha) = e-alpha 1t * sigma k m = 1 alpha 2k e-alpha 2k + 1t, sigma k m = 1 alpha 2k = 1, AL = integral of 0 infinity L(t) dt, and * indicates convolution. The nonparametric model relating X to E is a cubic spline, a function of X and a vector of (linear) parameters beta. The values of alpha and beta are chosen to minimize the sum of squared residuals between predicted and observed E. We also describe a similar model, generalizing a previously described one, to analyze PK/PD data. Applications of the approach to different drug-effect relationships (verapamil-PR interval, hydroxazine-wheal and flare, flecainide and/or verapamil-PR, and left ventricular ejection fraction) are reported.

Concentration-effect relations of 5-hydroxypropafenone in normal subjects

To evaluate the pharmacologic activity of 5-hydroxypropafenone, electrocardiographic changes (PQ and QRS duration) and blood pressure levels were measured in 6 healthy extensive metabolizers of debrisoquine after a single oral dose of 300 mg of this metabolite as a solution in a placebo-controlled, double-blind crossover study. Well-absorbed, with a lag time of 4.4 to 9.8 minutes, 5-hydroxypropafenone reached peak concentrations of 153 to 337 ng/ml after 20 to 51 minutes. The terminal half-life was 506 to 963 minutes. To describe the temporal aspects of the concentration-effect relation, a pharmacokinetic-pharmacodynamic model with a hypothetical effect compartment was applied. The relation between electrocardiographic changes and drug concentration at the effect site could be described by a linear regression model. Significant prolongations of PQ and QRS duration were found in 5 of 6 subjects. There were no changes in QTc interval, blood pressure measurements and heart rate in the supine position. However, blood pressure measurements in the upright position revealed a greater percent decrease of systolic blood pressure than with placebo (mean ± standard deviation −25.6 ± 13.8% vs −3.4 ± 13.1%, p < 0.05). It is concluded that 5-hydroxypropafenone exerts significant pharmacologic activity in humans as well as animals. Because QRS prolongation in patients treated with class IC antiarrhythmic drugs correlates with the antiarrhythmic effect, our data suggest that 5-hydroxypropafenone may contribute to the therapeutic activity of propafenone in humans.

Simultaneous modeling of the pharmacokinetic and pharmacodynamic properties of benzodiazepines I: Lorazepam

This investigation compares the time course changes in the central nervous system (CNS) impairment effects on psychomotor and cognitive skills and relates these changes to the plasma lorazepam concentrations in a pharmacokinetic-pharmacodynamic (PK-PD) model. Six male subjects received a single oral dose of lorazepam or placebo. The CNS effects were measured by using computerized continuous tracking (TRKN), body sway with eyes open (SWAY OPEN), and digit symbol substitution (DSS) tests. Plasma lorazepam concentrations were best characterized by a two-compartment model with first-order absorption. Plotting the plasma lorazepam concentration and measured effect across time revealed a counterclockwise hysteresis loop. Fitting the time course of the effects in an integrated PK-PD model required an effect compartment with the equilibrium rate constant between it and the plasma compartment. The magnitude of the temporal lag was quantified by the half-time of equilibration between concentration in the hypothetical effect compartment and the plasma lorazepam level (t1/2keo). The CNS effect measured by TRKN was characterized by a mean estimate of maximum predicted effect (Emax) of 418 with a t1/2keo of 0.43 hr, an estimate of effect site drug level to produce 50% of Emax (EC50) of 35.8 ng/ml and a power parameter (gamma) of 6.29. Corresponding parameter mean estimates for SWAY OPEN and DSS as measures of drug CNS effect were quite similar.