The population pharmacokinetics of citalopram after deliberate self-poisoning: a Bayesian approach

One-compartment model with Michaelis-Menten elimination kinetics and therapeutic window: an analytical approach

The purpose of this article is to provide the analytical solutions of one-compartment models with Michaelis-Menten elimination kinetics for three different inputs (single intravenous dose, multiple-dose bolus injection and constant). All analytical solutions obtained in present paper can be described by the well defined Lambert W function which can be easily implemented in most mathematical softwares such as Matlab and Maple. These results will play an important role in fitting the Michaelis-Menten parameters and in designing a dosing regimen to maintain steady-state plasma concentrations. In particular, the analytical periodic solution for multi-dose inputs is also given, and we note that the maximum and minimum values of the periodic solution depends on the Michaelis-Menten parameters, dose and time interval of drug administration. In practice, it is important to maintain a concentration above the minimum therapeutic level at all times without exceeding the minimum toxic concentration. Therefore, the one-compartment model with therapeutic window is proposed, and further the existence of periodic solution, analytical expression and its period are analyzed. The analytical formula of period plays a key role in designing a dose regimen to maintain the plasma concentration within a specified range over long periods of therapy. Finally, the completely analytical solution for the constant input rate is derived and discussed which depends on the relations between constant input rate and maximum rate of change of concentration.

Pharmacokinetics of Quetiapine in Overdose and the Effect of Activated Charcoal

The aim of the study was to investigate the pharmacokinetics of quetiapine overdose and the effect of charcoal. The data set included 204 concentration-time points from 54 quetiapine overdose events (median dose 2,700 mg (300-24,000 mg)). Charcoal was administered 0.5-6 h after 19 overdoses. A fully Bayesian methodology for population pharmacokinetic analysis was used and data were modelled using WinBUGS. Uncertainty in the dose history was considered in model building by estimating dose amount and dose time within a possible range. Inclusion of informative priors stabilized the model and population parameter values could be estimated well. A one-compartment model with first-order input and first-order elimination described the data. The final model included uncertainty in dose time. The median and interquartile range of the half-life for individual patients was 6.6 h (4.9-8.4 h). Charcoal was estimated to reduce fraction absorbed by 35%. Co-ingested CYP3A4 inhibitors appeared to decrease clearance and CYP3A4 inducers increase clearance. Charcoal administration may be beneficial after quetiapine overdose.

A Bayesian approach for population pharmacokinetic modelling of sirolimus

AIMS

To explore a Bayesian approach for the pharmacokinetic analysis of sirolimus concentration data arising from therapeutic drug monitoring (poorly informative concentration-time point design), and to explore possible covariate relationships for sirolimus pharmacokinetics.

METHODS

Sirolimus concentration-time data were available as part of routine clinical care from 25 kidney transplant recipients. Most samples were taken at or near the trough time point at steady state. The data were analyzed using a fully conditional Bayesian approach with PKBUGS (v 1.1)/WinBUGS (v 1.3). Features of the data included noncompliance and missing concentration measurements below the limit of sensitivity of the assay. Informative priors were used.

RESULTS

A two-compartment model with proportional residual error provided the best fit to the data (consisting of 315 sirolimus concentration-time points). The typical value for the apparent clearance (CL/F ) was 12.5 l h(-1) at the median age of 44 years. Apparent CL was found to be inversely related to age with a posterior probability of a clinically significant effect of 0.734.

CONCLUSIONS

A population pharmacokinetic model was developed for sirolimus using a novel approach. Bayesian modelling with informative priors allowed interpretation of a significant covariate relationship, even using poorly informative data.

Pharmacokinetic-pharmacodynamic modelling of QT interval prolongation following citalopram overdoses

AIMS

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.

METHODS

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).

RESULTS

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.

CONCLUSION

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.

Application of pharmacokinetic-pharmacodynamic modelling in management of QT abnormalities after citalopram overdose

OBJECTIVE

To develop guidelines for the management of QT prolongation after citalopram overdose, including decontamination with single-dose activated charcoal (SDAC) and cardiac monitoring.

DESIGN

Simulation study using a previously developed pharmacokinetic-pharmacodynamic (PKPD) model which predicted the time-course of QT prolongation and the effect of citalopram dose and use of SDAC on QT prolongation.

MAIN MEASURES AND RESULTS

The previously developed PKPD model was used to address the following in patients following citalopram overdose: (1) Above what dose should patients be decontaminated? (2) Above what dose should patients have cardiac monitoring? (3) For what period of time should patients be monitored? The primary outcome was QT,RR combinations above an abnormal threshold as a surrogate predictor of torsades de pointes. Simulations were performed using MATLAB for an overdose patient with typical demographics: 30-year-old female with a heart rate of 79 bpm taking citalopram therapeutically. The simulations showed: (1) There was significant benefit associated with the administration of SDAC to patients following citalopram overdose ingesting >600 mg; (2) With citalopram overdoses >1,000mg it was advisable to give SDAC and cardiac monitor the patient; (3) The risk of developing future abnormal QT,RR combinations was less than 1% in patients with normal QT,RR combinations up to 13 h post-dose, so the minimum monitoring time for citalopram overdoses >1,000mg should be 13h. Recommended dose levels for intervention should be lowered in older patients and patients with tachycardia, while men are less sensitive to QT prolongation.

CONCLUSIONS

Guidelines for the management of QT prolongation after citalopram overdose were developed. We believe the model will help clinicians to decide which patients to decontaminate and monitor.