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. 2021 Oct 1;11:19539. doi: 10.1038/s41598-021-98554-z

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© The Author(s) 2021

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 licence, and indicate if changes were made. The images or other third party material in this article are included in the article's Creative Commons licence, unless indicated otherwise in a credit line to the material. If material is not included in the article's Creative Commons licence 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 licence, visit http://creativecommons.org/licenses/by/4.0/.

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Validation cases; (A) Comparison of the fold increase in Dox accumulation in tumor tissue between the present mathematical model and the experimental data²⁶, (B) Estimation of tumor growth onset in the day post-injection in mathematical and experimental models²⁶ (in the mathematical model, tumor growth is based on about 10% increase in cell density), (C) IFV prediction in the present model has been compared with those of Kashkooli et al.³³, and (D) IFP prediction in the present model has been compared with those of Soltani and Chen⁴³, as well as Al-Zu’bi and Mohan⁴⁴ models, which show high compatibility.