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. 2018 Sep 28;8:14558. doi: 10.1038/s41598-018-32347-9

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© The Author(s) 2018

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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Time courses for the volume fraction (solid points) and credible interval (the vertical error bars) of viable tumor cell number for different initial cell concentrations: 100,000 (purple), 50,000 (green), 25,000 (blue), 10,000 (orange), and 5,000 (red) cells/ml. The solid lines represent the cross validation of the calibrated model. The data in panel (a) shows the effects of apoptosis after the cells are treated with 10 μg/ml of Mitomycin-C for two hours. The average error, for each initial condition, is between 10.27% and 15.14%. In panel (b), untreated cells in a serum concentration of 10% display an initial growth phase in which the cells reach the carrying capacity. The average error for this case is between 7.25% and 15.24%. In panels (c–f) the growth or decline of the tumor cells is observed for nutrient concentrations of 7.5% (c), 5% (d), 2.5% (e) and 0% (f). The maximum confluence (i.e., the carrying capacity) decreases as the initial concentration of nutrient is reduced. The average error, for each condition, is between 8.35% and 35.02%, with the highest error for the 25,000 cells/ml in panel (f).