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. 2017 Aug 1;7:7069. doi: 10.1038/s41598-017-07302-9

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© The Author(s) 2017

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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Cell-based RBE dose using equation (4) and four Geant4-calculated cellular dose matrices. (a) RBE dose distribution in the scoring plane versus distance from the tumour centre. (b) Transverse RBE dose in the scoring plane versus distance from tumour centre. The transverse profile for x-ray EBRT³⁴ is also shown as a comparison. The statistical uncertainty of the calculated results (the relative error between several runs) was ∼±10%.