261283 Physiologically Based Three-Compartment Model for Anomalous Diffusion of Gold Nanoparticles with a Pulsed Inlet

Wednesday, October 31, 2012
Hall B (Convention Center )
Laura M. Hernandez, Angel A. Galvis, Ruben D. Vargas and Watson L. Vargas, Department of Chemical Engineering, Universidad de los Andes, Bogotá, Colombia

The enhanced permeability and retention (EPR) effect has been explored as an appealing route for nanoparticle transport into tummoral tissues, due to the high rate of angiogenesis in cancerous lymphomas among other neoplasms. The EPR effect allows nanoparticles to penetrate a high number of blood vessels in comparison to non-cancerous tissues. Nevertheless, classical models for diffusive and convective transport of nanoparticles through biological tissues do not achieve the level of detail needed, because there are several restrictions related to the behavior of the mean square displacement (MSD) in such complex media (i.e. anomalous diffusion). In addition, today little is known on how nanoparticles properties affect individual transportation kinetic parameters [1].

This study provides a model and its numerical solution for nanoparticle diffusion in an emulated biological blood vessel with some simplifications, modeled by a three-compartment model, where the nanoparticles mass transport within the tissue is assumed to take place by an anomalous diffusion process, the first compartment is a reservoir  with high concentration of gold nanoparticles and with a pulsed inlet, the second compartment is an emulated biological tissue that allows only a one-dimensional diffusion initially with a null concentration of nanoparticles, through this compartment nanoparticles  reach a well mixed liquid cavity with no particle at the  onset of the experiment.

The effect of the pulsed behavior in the first compartment is an interesting factor that is studied in this model due to the fact that it is not straightforward to develop a prediction of how a pulsed inlet condition could influence the behavior of the particles MSD within the tissue. Fractional calculus strategies arise as the natural model for these kinds of transport phenomena because the time fractional diffusion equation (TFDE) allows the inclusion of memory effects into the model.

The experimental set-up consists of permeation experiments conducted in a Franz diffusion cell with rigorous controlled conditions, the nanoparticles are used without any marker substance in order to provide an accurate prediction of the chemical interaction between the particles and the emulated biological tissue (two types of gold nanoparticle with surface functionalization are used: a biocompatible polymer modified surface and citrate modified surface), the concentration inside the third compartment is measured via HR-UV-VIS spectroscopy. Finally, a finite differences type method is used for obtaining theoretically predicted concentrations in the third compartment, this concentrations are contrasted with the experimental data available through a lest squares optimization which allows the evaluation of  the transport parameters related to the anomalous MSD behavior (fractional derivative order, relaxation time and diffusivity).

Key Words: anomalous diffusion,  nanoparticle diffusion, transport phenomena, gold nanoparticles.


  1. Mingguang Li, Zoi Panagi,  Konstantinos Avgoustakis andJoshua Reineke. Physiologically based pharmacokinetic modeling of PLGA nanoparticles with varied mPEG content. International Journal of Nanomedicine 2012:7 1345–1356

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