Modeling a bivariate control system: LH and testosterone response to the GnRH antagonist antide

A pharmacodynamic analysis of the input-response relationship between the gonadotropin-releasing hormone antagonist antide and luteinizing hormone (LH) and testosterone concentrations is presented. A control compartmental model is developed using pharmacokinetic and pharmacodynamic data from experiments in which different short intravenous antide infusions were given to healthy male volunteers. Because of the control interdependence between serum LH and testosterone a separation principle similar to one we have used previously to analyze physiological pharmacokinetic data is used for model exploration: testosterone and LH are first modeled separately, conditioning on the other observed response. This reveals that the LH effect on testosterone depends on previous LH exposure and that LH depends not on current but on previous testosterone exposure, resulting in an LH overshoot after antide-induced suppression. Both submodels are combined into one global model, which in addition includes a model for testosterone circadian variation. This model describes the data well and can be used to predict responses for some nonstudied antide dosages. However, the sensitivity of predictions to model assumptions limits the range of valid extrapolation, and this, too, is illustrated.