Anesth Pain Med.  2016 Jan;11(1):1-13. 10.17085/apm.2016.11.1.1.

An overview of pharmacodynamic drug interaction with isobole and response surface model in anesthesia

• Choi BM

• KMID: 2169061
• DOI: http://doi.org/10.17085/apm.2016.11.1.1

Abstract

Drug interaction is the principal concept of anesthetic practice. Typically, drug interactions are divided into three categories i.e., additive, synergistic, or infra-additive interactions. Pharmacodynamic drug interactions are typically described using mathematical models. The traditional model is an isobole, which is an iso-effect curve that shows dose or concentration combinations that result in equal effect. Response surface model is a pharmacodynamic tool that describes all isoboles and concentration effect curves for a given endpoint in one equation. In summarizing concentration-effect relationships, the response surface model allows anesthesiologists the versatility to work with precise and safe drug interactions. The aim of this review is to provide the reader with principal concepts of the isobole and response surface model and evaluate characteristics of most commonly used models, including 4 response surface models i.e., the Greco model, reduced Greco model, Minto model, and the Hierarchy model. In addition, the concept of population analysis using nonlinear mixed effects modeling is introduced.

Keyword

Drug interactions; Pharmacology

MeSH Terms

Anesthesia*
Drug Interactions*
Models, Theoretical
Pharmacology

Figure

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  Fig. 1 Necessity for consideration of drug interaction during general anesthesia. PK: pharmacokinetic, ke0: blood-brain equilibration rate constant, PKPD: pharmacokinetic and pharmacodynamic, CNS: central nervous system.

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  Fig. 2 Isobole. (A) additivity, (B) synergy, (C) infra-additivity. D1, and D2, are isoeffective doses of two drugs administered alone. The administration of the two drugs in combination (d1, d2) results in the same effect. If D1, and D2, are the D50 doses, in each case the line represents the 50% isobole.

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  Fig. 3 Response surface models showing synergistic (A), additive (B), and infra-additive (C) interactions. Each panel contains a response surface (upper) and an isobologram showing the 50% probability isobole (lower).

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  Fig. 4 Response surfaces models. For all figures, the effect with no drug is 0. (A) Additive interaction between two agonists, (B) supra-additive (synergistic) interaction between two agonists, (C) infra-additive interaction between two agonists, (D) partial agonist and full agonist; (E) competitive antagonist and full agonist, (F) inverse agonist and full agonist. The isoboles for 10, 20, 30, 40, 50, 60, 70, 80, and 90% response are shown.

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  Fig. 5 Concepts of population analysis using nonlinear mixed effects modeling. PK: pharmacokinetic, PD: pharmacodynamic, TCI: target-controlled infusion.

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  Fig. 6 The functions for the parameters (Emax(θ), U50(θ), and γ(θ)) for the two drug-interaction showing synergic interaction.

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