Modeling Circadian Fluctuations of Pharmacokinetic Parameters

¹ Département de mathématiques et statistique, Université de Montréal, Montréal, Canada H3C 3J7
² Centre for Applied Mathematics in Bioscience and Medicine McGill University, Montréal, Canada

^* Corresponding author. E-mail: belair@dms.umontreal.ca

Abstract

The pharmacokinetic profile of a number of drugs has been shown to vary as a function of the time of day in the administration and thus apparently be under the influence of circadian rhythms: antiasthmatic, anticancer and cardiovascular products are but a few examples. Circadian rhythms may have influence on each of the processes of absorption, distribution, metabolism and elimination (ADME). Variations in pharmacokinetic quantities such as the Area under the curve (AUC), Mean Residence Time (MRT), time to the peak of concentration (t _max ) and value of the peak of concentration (C _max ) may therefore be expected. In this paper, we focus on possible variations in the peak of concentration C _max In contrast to a one-compartment model for time-varying pharmacokinetic quantities which has been shown [6] to display no variations in this quantity, we present a bi-compartmental model for time-varying systems to account for rapid intravenous dose, oral dose and intravenous infusion (zero order input). The effects of circadian rhythms on the maximal concentration of the drug in the body are studied for both single dose and multiple dosing, showing significant changes in values, induced by the time-varying coefficients in the PK model.