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. 2019 Feb 28;9:3002. doi: 10.1038/s41598-019-38907-x

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© The Author(s) 2019

Open Access This article is licensed under a Creative Commons Attribution 4.0 International License, which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made. The images or other third party material in this article are included in the article’s Creative Commons license, unless indicated otherwise in a credit line to the material. If material is not included in the article’s Creative Commons license and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder. To view a copy of this license, visit http://creativecommons.org/licenses/by/4.0/.

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Concept of additivity according to the Hand model. (a) The Hand model specifies how to add the two dose-effect curves of drugs A and B to get the combined dose-effect curve at fixed dose ratio λ (b). (c) f_A and f_B are transformed to effect-sensitivity curves via $s_{A} (x) = {f'}_{A} (f_{A}^{- 1} (x))$ , reflecting the saturation dynamics. (d) The effect-sensitivity curve s_AB,λ of the mixture C_λ is their weighted algebraic sum. f_AB,λ is obtained from s_AB,λ by integration.