Page 221 - Computational Modeling in Biomedical Engineering and Medical Physics
P. 221

210   Computational Modeling in Biomedical Engineering and Medical Physics


                                                                             2
                   The energy group introduced here for the first time, W mg;0 =ρU ,may be used
                                                                             0
                in sizing the magnetic field source (its energy), for a specific situation. This group
                relates the contribution of the magnetic field to the MD transport with respect to
                the kinematic energy of the flow (provided by the “pump”-ing device)asleading
                term. It is an important factor in the MDT design, positioning, and constructal
                optimization the magnet with respect to the ROI. The magnetic to mechanical
                forces group Eq. (6.29) is obtained from the energy group, and it may outline the
                order of magnitude of the forces streamwise or orthogonal to the flow. The
                streamwise velocity scale U 0 is used in general, but the scale for the orthogonal
                velocity may be used too, and aspect ratio of the vessel is the conversion factor.
                   The magnetic velocity, v r , that is used then as a macroscopic quantity to model
                th MNPs transfer in endothelial membrane and tissue is seen as a homogenization
                technique that maps the MNP nanometric physical process onto a macroscopic, con-
                tinuous, magnetizable medium, superparamagnetic like, which is characterized by an
                apparent susceptibility, χ app , that depends on the (constant) viscosity of a Newtonian
                fluid—the coefficient k in Eq. (6.32), which is proportional with the susceptivity of
                the MNP and the dynamic viscosity of the solute fluid.


                References
                Abd Elrahman, A.A., Mansour, F.R., 2019. Targeted magnetic iron oxide nanoparticles: Preparation,
                   functionalization and biomedical application. J. Drug Deliv. Sci. Tech. 52, 702 712.
                Akbar, N.S., Nadeem, S., 2014. Carreau fluid model for blood flow through a tapered artery with a ste-
                   nosis. Ain Shams Eng. J. 5, 1307 1316.
                Alexiou, C., Christoph, A., Arnold, W., Klein, R.J., Parak, F.G., Hulin, P., et al., 2000. Locoregional
                   cancer treatment with magnetic drug targeting. Cancer Res. 60, 6641 6648.
                Alexiou, C., Jurgons, R., Schmid, R.J., Bergemann, C., Henke, J., Erhardt, W., et al., 2003. Magnetic
                   drug targeting-biodistribution of the magnetic carrier and the chemotherapeutic agent mitoxantrone
                   after locoregional cancer treatment. J. Drug Target 11 (3), 139 149.
                Alexiou, C., Diehl, D., Henninger, P., Iro, H., Röckelein, R., Schmidt, W., et al., 2006a. A high field
                   gradient magnet for magnetic drug targeting. IEEE Trans Appl. Supercond. 16 (2), 1527 1530.
                Alexiou, C., Schmid, R.J., Jurgons, R., Kremer, M., Wanner, G., Bergemann, C., et al., 2006b.
                   Targeting cancer cells: magnetic nanoparticles as drug carriers. Eur. Biophys. J. 35 (5), 446 450.
                Ali, A., Zafar, H., Zia, M., ul Haq, I., Phull, A.R., Ali, J.S., et al., 2016. Synthesis, characterization, appli-
                   cations, and challenges of iron oxide nanoparticles. Nanotechnol. Sci. Appl. 9, 49 67 (Review).
                Almaça, J., Weitz, J., Rodriguez-Diaz, R., Pereira, E., Caicedo, A., 2018. The pericyte of the pancreatic
                   islet regulates capillary diameter and local blood flow. Cell Met. 27, 630 644.
                An, J., Zhanga, X., Guo, Q., Zhao, Y., Wu, Z., Li, C., 2015. Glycopolymer modified magnetic
                   mesoporous silica nanoparticles for MR imaging and targeted drug delivery. Colloids Surf.
                   A: Physicochem. Eng. Aspects 482, 98 108.
                Aroesty, J., Gross, J.F., 1972. The mathematics of pulsatile flow in small vessels I. Casson theory.
                   Microvas. Res. 4, 1 12.
                Aslibeiki, B., Kameli, P., Manouchehri, I., Salamati, H., 2012. Strongly interacting superspins in Fe3O4
                   nanoparticles. Curr. Appl. Phys. 12, 812 816.
                Avilés, M.O., Ebner, A.D., Chenb, H., Rosengartb, A.J., Kaminskic, M.D., Ritter, J.A., 2005.
                   Theoretical analysis of a transdermal ferromagnetic implant for retention of magnetic drug carrier par-
                   ticles. J. Magn. Magn. Mater. 293, 605 615.
   216   217   218   219   220   221   222   223   224   225   226