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. 2019 Nov 27;9:17674. doi: 10.1038/s41598-019-54117-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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Response cascade used for modelling cell death dynamics in spheroids after combination treatments of radiation and hyperthermia. After treatment, the cell population is divided into surviving and dying cells by drawing random numbers $N$ and $N_{2}$ between 0 and 1 and comparing them to the clonogenic surviving fractions, $S_{R T H T}$ ( $N$ ) and $S_{H T}$ ( $N_{2}$ ). Depending on the random number drawn, a cell will follow the route of radiation-induced cell death, heat-induced cell death, or survival.