Assessment of the use of complex baseline models in preclinical safety screening: Application of the van der Pol oscillator model to describe heart rate effects in rats
Tamara van Steeg, Ashley Strougo, Bart Ploeger and Piet Hein van der Graaf
Objectives: Many physiological variables (e.g. heart rate, body temperature) are subject to chronobiological (e.g. circadian) rhythms in both humans and animals. From a pharmacokinetic-pharmacodynamic (PKPD) modelling perspective, correct description of circadian rhythms is critical to avoid biased or imprecise results in the quantification of drug effect. Over the years, several baseline models, both simple and complex, have been proposed for the description of the circadian cycles. Recently, a novel negative feedback PKPD model (based on the van der Poll oscillator) incorporating external light-dark conditions was reported for the description of the asymmetric circadian rhythm in both heart rate and body temperature in rats [1,2]. The aim of the current study was to evaluate the practical utility of the van der Poll oscillator model in safety pharmacology using heart rate data obtained for a new drug candidate (PF-X).
Methods: All PK and PD experiments were performed in male rats. Heart rate was monitored continuously using telemetry and was used as the pharmacodynamic endpoint. The rats were randomly assigned to four treatment groups (3 active, 1 vehicle). The PK and PD of PF-X were quantified using non-linear mixed-effects modeling as implemented in NONMEM software version V, level 1.1. All data were analysed simultaneously, since precise estimation of the pharmacokinetic parameters was not possible using the sparse PK data alone. The PK and PD were described by a two-compartment model and a simple linear, direct effect model, respectively. The circadian cycle was incorporated by means of a descriptive or the van der Pol oscillator model (complex baseline model). The descriptive baseline model contained a simple switch function to define the hours at which the light was turned on (8:00 AM) or off (8:00 PM).
Results: During the activity period (dark) baseline heart rate was estimated to be 52 bpm higher than during the resting period (light). The PKPD model including the descriptive baseline model resulted in an adequate and precise estimation of both PK and PD parameters. Nearly all model runs using the complex baseline model terminated due to rounding errors. The parameters of the van der Pol oscillator (alpha & beta) varied greatly between the single model fits. Overall, the results indicated overparametrisation of the PKPD model including the complex baseline model. This overparametrisation was confirmed by the fact that precise PD parameter estimates were only obtained if the population PK parameters were fixed (to the values obtained with the descriptive baseline PKPD model). Comparison of the parameter estimates for both models showed that the drug effect (slope) was not significantly different. In addition, the description of the heart rate profiles by the complex model was comparable to the description by the simple model.
Conclusions: The objective of this study was to evaluate the practical utility of the van der Pol PKPD model for routine use in safety pharmacology testing in preclinical drug development. Although the van der Pol model clearly has some attractive features compared to simpler models and can better describe some complex circadian cycles, at least in this case study with PF-X we found that its utility was limited in practice. Typically, in safety pharmacology, rich PD data in individual animals is often associated with sparse PK profiles and a simultaneous, population-based, fit of PK and PD data is often required to obtain adequate estimates of exposures profiles. Therefore, a parsimonious approach based on a simpler PD model may be required, since complex baseline models may interfere with the identification of both the pharmacokinetics and pharmacodynamics of the drug under investigations and eventually weaken the conclusions that can be drawn. A possible solution would be adjusting the approach such that the PK parameters are obtained first using the simple baseline model and, thereafter, the complex baseline model is used to describe the profiles.
 Sällström et al., 2005, J Pharmacokinet Pharmacodyn. 32(5-6):835-59
 Visser et al., 2006, J Pharmacol Exp Ther. 317(1):209-19