Mathematical Modeling on Capturing of Magnetic Nanoparticles in an Implant Assisted Channel for Magnetic Drug Targeting

Authors: Shashi Sharma, V. K. Katiyar, Uaday Singh

Abstract:

In IA-MDT, the magnetic implants are placed strategically at the target site to greatly and locally increase the magnetic force on MDCPs and help to attract and retain the MDCPs at the targeted region. In the present work, we develop a mathematical model to study the capturing of magnetic nanoparticles flowing within a fluid in an implant assisted cylindrical channel under magnetic field. A coil of ferromagnetic SS-430 has been implanted inside the cylindrical channel to enhance the capturing of magnetic nanoparticles under magnetic field. The dominant magnetic and drag forces, which significantly affect the capturing of nanoparticles, are incorporated in the model. It is observed through model results that capture efficiency increases as we increase the magnetic field from 0.1 to 0.5 T, respectively. The increase in capture efficiency by increase in magnetic field is because as the magnetic field increases, the magnetization force, which is attractive in nature and responsible to attract or capture the magnetic particles, increases and results the capturing of large number of magnetic particles due to high strength of attractive magnetic force.

Keywords: Capture efficiency, Implant assisted-Magnetic drug targeting (IA-MDT), Magnetic nanoparticles (MNPs).

Digital Object Identifier (DOI): doi.org/10.5281/zenodo.1109595

References:

[1] U. O. Häfeli, “Magnetically modulated therapeutic systems.” Int. J. pharm, Vol. 277(1), 2004, pp. 19-24.
[2] C. Alexiou, R. Jurgons, Magnetic drug targeting. In: Magnetism in medicine: a handbook, 2nd edn. 2007 pp. 596–605
[3] K. J. Widder, A. E. Senyei, & D. G. Scarpelli, “Magnetic microspheres: a model system for site specific drug delivery in vivo.” Exp Biol Med, Vol. 158(2), 1978, pp. 141-146.
[4] A. Senyei, K. Widder, & G. Czerlinski, (1978). “Magnetic guidance of drug‐carrying microspheres.” J. Appl Phys, Vol. 49(6), 1978, pp. 3578- 3583.
[5] C. Alexiou, W. Arnold, R. J. Klein, R, F. G. Parak, P. Hulin, C. Bergemann, & A. S. Luebbe, “Locoregional cancer treatment with magnetic drug targeting. Cancer Res, Vol. 60(23), 2000, pp. 6641-6648.
[6] H. Xu, T Song, X. Bao & L. Hu, “Site-directed research of magnetic nanoparticles in magnetic drug targeting. “ J. magn. Magn. Mater, Vol. 293(1), 2005, pp. 514-519.
[7] C. Alexiou, R. J. Schmid, R. Jurgons, M. Kremer, G. Wanner, C. Bergemann, & F. G. Parak, “Targeting cancer cells: magnetic nanoparticles as drug carriers.” Eur Biophys J. Vol. 35(5), 2006, pp. 446-450.
[8] A. S. Lübbe, C. Bergemann, J. Brock, & D. G. McClure. “Physiological aspects in magnetic drug-targeting.” J. magn. Magn. Mater, Vol. 194(1), 1999, pp. 149-155.
[9] A. S, Lübbe, C. Alexiou, & C. Bergemann, “Clinical applications of magnetic drug targeting.” J. Surg. Res, Vol. 95(2), 2001, pp. 200-206.
[10] M. O. Avilés, A. D. Ebner, J.A. & Ritter. “In vitro study of magnetic particle seeding for implant assisted-magnetic drug targeting.” J. magn. Magn. Mater Vol. 320(21), 2008, pp. 2640-2646.
[11] M. O. Avilés, A. D. Ebner, & J. A. Ritter, “In vitro study of magnetic particle seeding for implant-assisted-magnetic drug targeting: Seed and magnetic drug carrier particle capture.” J. magn. Magn. Mater, Vol. 321(10), 2009, pp. 1586-1590.
[12] J. A. Ritter, A. D. Ebner, K. D. Daniel, & K. L. Stewart, “Application of high gradient magnetic separation principles to magnetic drug targeting.” J. magn. Magn. Mater, Vol. 280(2), 2004, pp. 184-201.
[13] M. O. Avilés, A. D. Ebner, H. Chen, A. J. Rosengart, M. D. Kaminski, & J. A. Ritter. “Theoretical analysis of a transdermal ferromagnetic implant for retention of magnetic drug carrier particles.” J. magn. Magn. Mater, Vol. 293(1), 2005, pp. 605-615.
[14] M. O. Avilés, A. D. Ebner, & J. A. Ritter. “Ferromagnetic seeding for the magnetic targeting of drugs and radiation in capillary beds.” J. magn. Magn. Mater, Vol. 310(1), 2007, pp. 131-144.
[15] O. Rotariu, & N. J. Strachan. “Modelling magnetic carrier particle targeting in the tumor microvasculature for cancer treatment.” J. magn. Magn. Mater, Vol. 293(1), 2005, pp. 639-646.
[16] B. B. Yellen, Z. G. Forbes, D. S. Halverson, G. Fridman, K.A. Barbee, M. Chorny & G. Friedman. “Targeted drug delivery to magnetic implants for therapeutic applications.” J. magn. Magn. Mater, Vol. 293(1), 2005, pp. 647-654.
[17] Z. G. Forbes, B. B. Yellen, K. Barbee, & G. Friedman. “An approach to targeted drug delivery based on uniform magnetic fields.” Magnetics, IEEE Transactions on, Vol. 39(5), 2003, pp. 3372-3377.
[18] J. O. Mangual, M.O. Avilés, A. D. Ebner, & J. A. Ritter. “In vitro study of magnetic nanoparticles as the implant for implant assisted magnetic drug targeting.” J. magn. Magn. Mater, Vol. 323(14), 2011, pp. 1903- 1908.
[19] K. Hournkumnuard, & M. Natenapit. “Magnetic drug targeting by ferromagnetic microwires implanted within blood vessels.” Med. Phys, Vol. 40(6), 2013, pp. 062302.
[20] H. Chen, A. D. Ebner, M. D. Kaminski, A. J. Rosengart, J. A. Ritter. “Analysis of magnetic drug carrier particle capture by a magnetizable intravascular stent—2: parametric study with multi-wire twodimensional model.” J Magn Magn Mater, Vol. 293(1), 2005, pp. 616– 632
[21] P. J. Cregg, K. Murphy, & A. Mardinoglu. “Calculation of nanoparticle capture efficiency in magnetic drug targeting.” J. magn. Magn. Mater, Vol. 320(23), 2008, pp. 3272-3275.
[22] M. O. Avilés, A. D. Ebner, & J. A. Ritter. “Implant assisted-magnetic drug targeting: comparison of in vitro experiments with theory.” J. magn. Magn. Mater, Vol. 320(21), 2008, pp. 2704-2713.