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. 2020 May 19;10:8294. doi: 10.1038/s41598-020-65162-2

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© The Author(s) 2020

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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Optimizing nanoparticle designs for tumors of different sizes. (A) Tumors of different sizes at which the treatment starts. Change in optimal nanoparticle diameters that (B) minimizes tumor size after one day of treatment and (C) maximizes percent accumulation of nanoparticles in tumor tissue as a function of tumor size at start of treatment. Black lines represent the second order polynomial fit obtained by minimizing the least linear square. Red: proliferating tumor tissue; blue: hypoxic tissue; brown: necrotic tissue. Orthogonal grid represents pre-existing capillary network surrounding the growing tumor. Irregular lines simulate capillary growth in response to a net balance of pro-angiogenic factors released by hypoxic tumor tissue.