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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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Hybrid framework for optimizing nanoparticle mediated drug delivery. The framework couples a computational “blackbox” model of vascularized tumor growth and nanoparticle treatment^7,25 with an optimization model based on the mesh adaptive direct search (MADS) algorithm^26,27. The computational model²⁵ uses a nanoparticle design (x) selected by MADS and evaluates the objective function f(x) and the constraints g(x). These values are used by MADS to recommend a new trial point for the computational model. This process iterates until the objective function is optimized, so that the result of the hybrid framework generates optimal nanoparticle designs x^*. In the computational model, multiple sub-models interact and exchange parameters, including: (a) angiogenic factors; (b) oxygen and nutrients; (c) location of capillary junctions; (d) wall shear stress, flow stimulus, and intravascular pressure; and (e) vessel radii, vessel surface areas, and flow rate. The tumor is displayed in the computational model at inception, after vascularization, before treatment and after treatment. Colors are as in Fig. 1.