Modelling the sleep effects of Zolpidem in rats using non-homogeneous Markov chain models
Arianna Madrid(1), Nieves Vélez de Mendizabal(1), Kimberley Jackson(2), Andrew McCarthy(2), Dale Edgar(2), Iñaki F. Trocóniz(1)
(1) Department of Pharmacy and Pharmaceutical Technology; School of Pharmacy; University of Navarra; Pamplona 31080; Spain. (2) Eli Lilly and Company, UK
Objectives: To describe the effects of the hypnotic drug Zolpidem in rats using a semi-mechanistic pharmacokinetic-pharmacodynamic (PK/PD) Markov-chain model
Methods: Experimental. Data were obtained from healthy male Wistar rats in which the electroencephalogram (EEG) was continuously recorded for at least two days of alternating dark/light cycles of 12 h. For each 10 second interval, EEG data were scored into awake, REM or NREM stages. The study consisted of a baseline 24 h period (time -24 to 0). At 6 h clock time (CT) during the second dark cycle, methylcellulose (n=16), zolpidem 10 mg/kg (n=16), 20 mg/kg (n=20), or 30 mg/kg (n=11) were administered orally. PK data were not collected during this study. Data analysis. The time course of the 9 possible transition probabilities between the three sleep stages was described using a non-homogeneous Markov chain model based on piecewise multinomial logistic functions[1]. The PK model used to generate plasma concentrations of zolpidem over time was taken from the literature[2,3]. Analyses were performed under the population approach using the LAPLACIAN estimation method implemented in NONMEM VI. Model evaluation was done by constructing visual predictive checks (VPCs) for the 9 transition probabilities, and other data descriptors.
Results: Baseline model. Location of breakpoints at every hour and incorporating inter-animal differences at some of the breakpoints provided a good description of the baseline data and precise parameter estimates. Methylcellulose (saline) model. The effects of saline administration were reflected mainly as a decrease in the transition probability from NREM to awake and were described with the use of the Bateman function. Drug effect model. Exploration of the time course of raw transition probabilities revealed that zolpidem elicited an initial time dependent decrease in the transition probability from NREM to awake indicating the animals were sleeping more, and at later times an increase which is interpreted as a rebound effect. Drug effects including the rebound phenomena were described with a turnover feedback model. [4] Data were very well described for the three dose levels and parameter estimates were precise.
Conclusions: The model presented here represents an integrated model including baseline, saline, and drug effect models. This type of approach supports the identification and the quantitative description of feedback mechanisms, and represents a promising approach to describe the PD characteristics of different classes of sleep drugs.
References:
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[2] Garrigou-Gadenne D, Burke JT, Durand A, Depoortere H, Thénot JP, Morselli PL. Pharmacokinetics, Brain Distribution and Pharmaco-Electrocorticographic Profile of Zolpidem, a New Hypnotic, in the Rat. J Pharmacol Exp Ther 1989; 248: 1283-88.
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[4] Wakelkamp M, Alván G, Gabrielsson J, Paintaud G. Pharmacodynamic modelling of furosemide tolerance after multiple intravenous administration. Clin Pharmacol Ther 1996; 60: 75-88.
