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Biophys J. 2018 Sep 18;115(6):1103-1115. doi: 10.1016/j.bpj.2018.07.038. Epub 2018 Aug 17.

Extravasation of Brownian Spheroidal Nanoparticles through Vascular Pores.

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Department of Mechanical Engineering, Stanford University, Stanford, California.
Department of Chemistry, University of California, Berkeley, California.
Department of Radiology, Stanford University, Stanford, California; Department of Biomedical Engineering and Institute for Quantitative Health Science and Engineering, Michigan State University, East Lansing, Michigan. Electronic address:
Department of Mechanical Engineering, Stanford University, Stanford, California; Department of Chemical Engineering; Institute for Computational and Mathematical Engineering, Stanford University, Stanford, California. Electronic address:


In modern cancer treatment, there is significant interest in studying the use of drug molecules either directly injected into the bloodstream or delivered by nanoparticle (NP) carriers of various shapes and sizes. During treatment, these carriers may extravasate through pores in the tumor vasculature that form during angiogenesis. We provide an analytical, computational, and experimental examination of the extravasation of point particles (e.g., drug molecules) and finite-sized spheroidal particles. We study the advection-diffusion process in a model microvasculature, consisting of a shear flow over and a pressure-driven suction flow into a circular pore in a flat surface. For point particles, we provide an analytical formula [Formula: see text] for the dimensionless Sherwood number S, i.e., the extravasation rate, in terms of the pore entry resistance (Damköhler number κ), the shear rate (Péclet number P), and the suction flow rate (suction strength Q). Brownian dynamics (BD) simulations verify this result, and our simulations are then extended to include finite-sized NPs, in which no analytical solutions are available. BD simulations indicate that particles of different geometries have drastically different extravasation rates in different flow conditions. In general, extreme aspect ratio particles provide a greater flux through the pore because of favorable alignment with streamlines entering the pore and less hindered interaction with the pore. We validate the BD simulations by measuring the in vitro transport of both bacteriophage MS2 (a spherical NP) and free dye (a model drug molecule) across a porous membrane. Despite their vastly different sizes, BD predicts S = 8.53 E-4 and S = 27.6 E-4, and our experiments agree favorably, with Sexp=10.6 E-4± 1.75 E-4 and Sexp=16.3 E-4 ± 3.09 E-4, for MS2 and free dye, respectively, thus demonstrating the practical utility of our simulation framework.

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