Loewe additivity

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In pharmacodynamics, Loewe Additivity (or dose additivity) is one of several common reference models used for measuring the effects of drug combinations.

Let and be doses of compounds 1 and 2 producing in combination an effect . We denote by and the doses of compounds 1 and 2 required to produce effect alone (assuming this conditions uniquely define them, i.e. that the individual dose-response functions are bijective). quantifies the potency of compound 1 relatively to that of compound 2.

can be interpreted as the dose of compound 2 converted into the corresponding dose of compound 1 after accounting for difference in potency.

Loewe additivity is defined as the situation where or .

Geometrically, Loewe additivity is the situation where isoboles are segments joining the points and in the domain .

If we denote by , and the dose-response functions of compound 1, compound 2 and of the mixture respectively, then dose additivity holds when


References[edit]

  • William R Greco, Gregory Bravo, and John Parsons "The Search for Synergy: A Critical Review from a Response Surface Perspective", Pharmacological Reviews 47(2) 331-385 (1995)
  • Loewe and Muischnek. "Effect of combinations: mathematical basis of the problem" Arch. Exp. Pathol. Pharmakol. 114: 313-326, 1926
  • Pamela J. Yeh, Matthew J. Hegreness, Aviva Presser Aiden & Roy Kishony "Nature Reviews Microbiology" 7, 460-466 (June 2009)
  • Tang, J., K. Wennerberg, and T. Aittokallio. "What Is Synergy? The Saariselkä Agreement Revisited." Frontiers in Pharmacology 6. Frontiers: 181. (2015)