Background: Anesthetic drug interactions traditionally have been characterized using isobolographic analysis or multiple logistic regression. Both approaches have significant limitations. The authors propose a model based on response-surface methodology. This model can characterize the entire dose-response relation between combinations of anesthetic drugs and is mathematically consistent with models of the concentration-response relation of single drugs.
Methods: The authors defined a parameter, theta, that describes the concentration ratio of two potentially interacting drugs. The classic sigmoid Emax model was extended by making the model parameters dependent on theta. A computer program was used to estimate response surfaces for the hypnotic interaction between midazolam, propofol, and alfentanil, based on previously published data. The predicted time course of effect was simulated after maximally synergistic bolus dose combinations.
Results: The parameters of the response surface were identifiable. With the test data, each of the paired combinations showed significant synergy. Computer simulations based on interactions at the effect site predicted that the maximally synergistic three-drug combination tripled the duration of effect compared with propofol alone.
Conclusions: Response surfaces can describe anesthetic interactions, even those between agonists, partial agonists, competitive antagonists, and inverse agonists. Application of response-surface methodology permits characterization of the full concentration-response relation and therefore can be used to develop practical guidelines for optimal drug dosing.