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

Abstract

Background and purpose: 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 beta-adrenoceptors (beta-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.

Experimental approach: Groups of WKY rats received a 15 min i.v. infusion of 5 mg kg(-1) S(-)-atenolol, with or without i.v. infusion of 5 microg kg(-1) h(-1) isoprenaline. Heart rate was continuously monitored and blood samples were taken.

Key results: A three-compartment model best described the pharmacokinetics of S(-)-atenolol. The PK-PD relationship was described by a sigmoid Emax model and an effect compartment was used to resolve the observed hysteresis. In the group without isoprenaline, the variability in heart rate (30 b.p.m.) approximated the maximal effect (Emax=43+/-18 b.p.m.), leaving the parameter estimate of potency (EC50=28+/-27 ng ml(-1)) unreliable. Both precise and reliable parameter estimates were obtained during isoprenaline-induced tachycardia: 517+/-13 b.p.m. (E0), 168+/-15 b.p.m. (Emax), 49+/-14 ng ml(-1) (EC50), 0.042+/-0.012 min(-1) (k(eo)) and 0.95+/-0.34 (n).

Conclusions and implications: Reduction of heart rate during isoprenaline-induced tachycardia is a reliable pharmacodynamic endpoint for beta-blockers in vivo in rats. Consequently this experimental approach will be used to investigate the relationship between drug characteristics and in vivo effects of different beta-blockers.

Figure 1

Visual predictive check of the population PK model for isoprenaline. The range between the dashed lines depicts the 90% interquantile range. The solid line presents the population prediction. The solid dots are the observed concentrations.

Figure 2

Population prediction (solid line) and observations (symbols) for the concentration–effect relationship for isoprenaline. The range between the dashed lines depicts the 90% interquantile range.

Figure 3

Visual predictive check of the population PK model for S(−)-atenolol. The range between the dashed lines depicts the 90% interquantile range. The solid line presents the population prediction. The solid dots are the observed concentrations.

Figure 4

Individual plots of the PD of S(−)-atenolol in the rat, without isoprenaline-induced tachycardia. The solid line, the dashed line and the symbols represent the individual prediction, the population prediction and the heart rate observations respectively.

Figure 5

Concentration–effect relationship for S(−)-atenolol for a typical individual rat with isoprenaline-induced tachycardia. (a) Hysteresis loop – observed heart rate plotted against the C_p (b) Collapsed hysteresis loop – observed heart rate plotted against the concentration in the effect compartment (C_e). The solid line, the dashed line and the symbols represent the individual prediction, the population prediction and the heart rate observations respectively.

Figure 6

Individual plots of the PDs of S(−)-atenolol during isoprenaline-induced tachycardia. The solid line, the dashed line and the symbols represent the individual prediction, the population prediction and the heart rate observations respectively.