Math Biology Seminar Abstracts

Wednesday, March 10, 2004 3:05 pm LCB 225

Steven E. Kern, Ph.D. Department of Pharmaceutics and Anesthesiology University of Utah

Title: ``Modeling multiple-drug interactions with response surfaces''

Drug delivery strategies that maximize positive effects and minimize side effects often employ drug combinations. For cancer chemotherapy, this approach represents the standard of care. There are two primary methods for characterizing pharmacodynamic interactions: isoboles and response surfaces. Isoboles model interactions at a specific level of drug effect. Response surfaces characterize the interaction over a range of effects and are therefore more generally applicable for understanding interactions. Past approaches for modeling response surfaces have presented many problems that limit their generalizability. These include: inability to converge to simple models under constrained conditions, the creation of illogical surfaces, particularly for antagonistic reaction, lack of meaningful parameters that can be compared between different combinations, and the inability to model asymetric interactions surfaces. We have developed a new method for modeling response surfaces of drug interactions that overcome limitations of previous models.

Our proposed model is based on a Hill concentration-response profile that considers each drug combination as a virtual drug acting in a sigmoid manner. The model use polar coordinates to fit synergistic, additive, and antagonistic interactions as defined by Loewe.[1] We have used simulated data sets to assess the ability of the model to fit a number of different types of drug interactions and have compared these results to other response surface models that have been proposed in the literature. The model was also applied to clinical data for the interaction of the opioid alfentanil with the induction agent propofol that was previously reported by Short et al and also modeled by Minto et al. using response surfaces.[2,3] Aikike Information Criteria (AIC) was used to compare the models.

The proposed model has greater flexibility in terms of adequately fitting a number of different interaction conditions from the simulated data. This included asymmetric interactions, competitive antagonistic interactions, and inverse agonist interactions. The model interaction parameter can be statistically assessed to evaluate the significance of the interaction. The proposed model also fit the clinical data well with a comparable AIC to that reported by Minto et al. Further application to antiproliferative agents and leukemia treatments are under way. The flexibility and adequacy of this new model will enhance its application to characterizing the nature and extent of interaction of co-administered drugs.


1. Loewe, S. (1953). The problem of synergism and antagonism of combined drugs. Arzneim. Forsch, 3,2.

2. Short, T.G., Plummer, J.L., Chui, P.T. (1992). Hypnotic and anaesthetic interactions between midazolam, propofol and alfentanil. Br J Anaesth, 69, 162-7.

For more information contact J. Keener, 1-6089