Pharmacodynamic model of tolerance: application to nicotine.

The authors propose a model of pharmacodynamic response that, when integrated with a pharmacokinetic model, allows characterization of the development of functional tolerance. The model may be conceived of in several equivalent ways; one of these sees tolerance as a result of (noncompetitive) antagonism of agonist effect by a hypothetical substance (e.g., metabolite) produced by a first-order process, driven by agonist concentration. Tolerance thus lags behind, and is approximately proportional to, agonist concentrations. Two new parameters quantifying tolerance are introduced: kantO, which describes the elimination kinetics of the antagonist and determines the rate of development and disappearance of tolerance, and Cant50, which determines the magnitude of tolerance that can be achieved. The model was tested in eight volunteers on data produced after three sequences of paired i.v. administrations of nicotine separated by different intervals of time. Blood concentrations of nicotine and heart rate were measured. The proposed tolerance model was fitted to the nicotine data. The estimate of kantO suggests a half-life of development and regression of tolerance of 35 min, and the estimate of Cant50 suggests that tolerance, at its full development, causes an approximately 80% reduction of initial (nontolerant) effect. This model provides a quantitative pharmacokinetic-pharmacodynamic description of the development of acute tolerance that also carries physiologic meaning. The quantitative information provided by this model may improve understanding of the temporal patterns of drug abuse and complications thereof.