Modelling the pharmacokinetics of tramadol: on the difference between CYP2D6 extensive and poor metabolizers

In this work we propose a mathematical model for the kinetics of tramadol, a synthetic opioid commonly used for treating moderate to severe pain. This novel theoretical framework could result in an objective criterion on how to adjust the assigned dose, depending on the genetic polymorphisms of CYP2D6. The model describes the coupled dynamics of tramadol and the metabolite O-desmethyltramadol. The effect of diffusion of the drug in the blood is here accounted for and we further hypothesize the existence of a time delay in the process of chemical translation from tramadol into metabolites. The system of coupled differential equations is solved numerically and the free parameters adjusted so to interpolate the experimental time series for the intravenous injection setting. Theoretical curves are shown to reproduce correctly the experimental profiles obtained from clinical trials. This enables in turn to extract an estimate of the metabolization rate. A difference in metabolization rate between CYP2D6 poor and extensive metabolizers is also found, and the stereoselectivity in the O-demethylation of tramadol highlighted. Our results allow one to quantify the dose of (+)-tramadol (resp. (-)-tramadol) administered to poor or extensive metabolizers, if the same effect is sought. The latter is here quantified through the blood concentration of (+)-metabolites (resp. (-)-metabolites).