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Updated: Aug 9, 2026

Diagonal Method to Measure Synergy Among Any Number of Drugs
Published on: June 21, 2018
The well-being model: a new drug interaction model for positive and negative effects
Eleonora Zanderigo1, Valentina Sartori, Gorazd Sveticic
1Automatic Control Laboratory, Swiss Federal Institute of Technology, University Hospital, Bern, Switzerland. zanderigo@control.ee.ethz.ch
Background:
Drugs are routinely combined in anesthesia and pain management to obtain an enhancement of the desired effects. However, a parallel enhancement of the undesired effects might take place as well, resulting in a limited therapeutic usefulness. Therefore, when addressing the question of optimal drug combinations, side effects must be taken into account.
Methods:
By extension of a previously published interaction model, the authors propose a method to study drug interactions considering also their side effects. A general outcome parameter identified as patient's well-being is defined by superposition of positive and negative effects. Well-being response surfaces are computed and analyzed for varying drugs pharmacodynamics and interaction types. In particular, the existence of multiple maxima and of optimal drug combinations is investigated for the combination of two drugs.
Results:
Both drug pharmacodynamics and interaction type affect the well-being surface and the deriving optimal combinations. The effect of the interaction parameters can be explained in terms of synergy and antagonism and remains unchanged for varying pharmacodynamics. For all simulations performed for the combination of two drugs, the presence of more than one maximum was never observed.
Conclusions:
The model is consistent with clinical knowledge and supports previously published experimental results on optimal drug combinations. This new framework improves understanding of the characteristics of drug combinations used in clinical practice and can be used in clinical research to identify optimal drug dosing.
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