Cardiovascular Engineering and Technology

, Volume 10, Issue 2, pp 299–313 | Cite as

Development of a Two-Way Coupled Eulerian–Lagrangian Computational Magnetic Nanoparticle Targeting Model for Pulsatile Flow in a Patient-Specific Diseased Left Carotid Bifurcation Artery

  • Rodward L. HewlinJr.Email author
  • Ashley Ciero
  • John P. Kizito



The aim of the present work is to present the development of a computational two-way coupled (fluid and particle coupled) magnetic nanoparticle targeting model to investigate the efficacy of magnetic drug targeting (MDT) in a patient-specific diseased left carotid bifurcation artery. MDT of therapeutic agents using multifunctional carrier particles has the potential to provide effective treatment of both cancer and cardiovascular disease by enabling a variety of localized treatment and diagnostic modalities while minimizing side effects.


A computational model is developed to analyze pulsatile blood flow, particle motion, and particle capture efficiency in a diseased left carotid bifurcation artery using the magnetic properties of magnetite (Fe3O4) and equations describing the magnetic forces acting on particles produced by an external cylindrical electromagnetic coil. A Eulerian–Lagrangian technique is adopted to resolve the hemodynamic flow and the motion of particles under the influence of a magnetic field (Br= 2T). Particle diameter sizes of 20 nm–4 μm in diameter were considered.


The computational simulations demonstrate that the greatest particle capture efficiency results for particle diameters within the micron range, specifically 4 µm in regions where flow separation and vortices are at a minimum. It was also determined that the capture efficiency of particles decreases substantially with particle diameter, especially in the superparamagnetic regime. Particles larger than 2 μm were targeted and captured at the desired location by the external magnetic field, and the largest capture efficiency observed was approximately 98%.


The simulation results presented in the present work have shown to yield favorable capture efficiencies for micron range particles and a potential for enhancing capture efficiency of superparamagnetic particles in smaller arteries and/or using magnetized implants such as cardiovascular stents. The present work presents results for justifying further investigation of MDT as a treatment technique for cardiovascular disease.


Capture efficiency Carotid artery Diseased Eulerian Lagrangian Magnetic drug targeting Magnetite Patient-specific Pulsatile flow 



The authors would like to acknowledge Dr. Moloy Banerjee from the Future Institute of Engineering and Management Department of Mechanical Engineering in Kolkata India. Dr. Banerjee provided a great deal of insight and advice on developing the user defined function used in this work to describe the magnetic field produced by the external cylindrical coil. The authors would also like to acknowledge the University of North Carolina at Charlotte (UNC-C) Faculty Research Grant (FRG) and the Wells Fargo Faculty Grant through the Charlotte Research Institute (CRI) which funded this work. Lastly, the authors would like to acknowledge the North Carolina Space Grant Graduate fellowship through the National Aeronautics and Space Administration (NASA) which provided summer funding for the graduate student (Ashley Ciero) to work on this research.

Conflict of interests

The authors of this work declare no conflict of interests.

Human Studies/Informed Consent

No human studies were carried out by the authors for this article.

Animal Studies

No animal studies were carried out by the authors for this article.


  1. 1.
    Al-Jamal, T., J. Bai, J. Wang, et al. Magnetic drug targeting: preclinical in vivo studies, mathematical modeling, and extrapolation to humans. Nano Lett. 16:5652–5660, 2016.CrossRefGoogle Scholar
  2. 2.
    Aviles, M. O., H. Chen, A. D. Ebner, et al. In vitro study of ferromagnetic stents for implant assisted-magnetic drug targeting. J. Magn. Mater. 311(1):306–311, 2007.CrossRefGoogle Scholar
  3. 3.
    Boghi, A., F. Russo, and F. Gori. Numerical simulation of magnetic nano drug targeting in a patient-specific coeliac trunk. J. Magn. Magn. Mater. 437:86–97, 2017.CrossRefGoogle Scholar
  4. 4.
    Bose, S., and M. Banerjee. Magnetic particle capture for biomagnetic fluid flow in stenosed aortic bifurcation considering particle-fluid coupling. J. Magn. Magn. Mater. 385:32–46, 2015.CrossRefGoogle Scholar
  5. 5.
    Bose, S., A. Datta, R. Ganguly, and M. Banerjee. Lagrangian magnetic particle tracking through stenosed artery under pulsatile flow condition. J. Nano. Eng. Med. 4(3):1–10, 2014.Google Scholar
  6. 6.
    Buchmann, A. C., M. C. Jeremy, and J. Soria. Tomographic particle image velocimetry investigation of the flow in a modeled human carotid artery bifurcation. Exp. Fluids 50(4):1131–1151, 2011.CrossRefGoogle Scholar
  7. 7.
    Chen, H., A. F. Ebner, A. B. Rosengart, et al. Analysis of magnetic drug carrier particle capture by a magnetizable intravascular stent: 1. parametric study with single wire correlation. J. Magn. Magn. Mater. 284:181–194, 2004.CrossRefGoogle Scholar
  8. 8.
    Cheung, S. C., K. K. Wong, G. H. Yeoh, et al. Experimental and numerical study on the hemodynamics of stenosed carotid bifurcation. Australas. Phys. Eng. Sci. Med. 33(4):319–328, 2011.CrossRefGoogle Scholar
  9. 9.
    Chorny, M., I. Fishbein, I. Alferiev, and R. J. Levy. Magnetically responsive biodegradable nanoparticles enhanced adenoviral gene transfer in cultured smooth muscle and endothelial cells. Mol. Pharm. 6(5):1380–1387, 2009.CrossRefGoogle Scholar
  10. 10.
    Chorny, M., I. Fishbein, S. Forbes, and I. Alferiev. Magnetic nanoparticles for targeted vascular delivery. IUBMB Life 62(8):613–620, 2011.CrossRefGoogle Scholar
  11. 11.
    Chorny, M. F., I. Fishbein, B. B. Yellen, et al. Targeting stents with local delivery of paclitaxel-loaded magnetic nanoparticles using uniform fields. Proc. Natl. Acad. Sci. USA 107(18):8346–8351, 2010.CrossRefGoogle Scholar
  12. 12.
    Chorny, M., B. Polyak, I. S. Alferiev, et al. Magnetically driven plasmid DNA delivery with biodegradable polymeric nanoparticles. FASEB J. 21(10):2510–2519, 2007.CrossRefGoogle Scholar
  13. 13.
    Diaconu, A., A. P. Chiriac, N. Tudorachi, et al. Investigation concerning the possibilities for the deposition of magnetic nanoparticles onto a metallic stent. Rev. Roum. Chim. 62(8–9):677–685, 2017.Google Scholar
  14. 14.
    Forbes, Z. G., B. B. Yellen, D. S. Halverson, et al. Validation of high gradient magnetic field based drug delivery to magnetizable implants under flow. IEEE Trans. Bio-Med. Eng. 55(2):643–649, 2008.CrossRefGoogle Scholar
  15. 15.
    Furlani, E. J., and E. P. Furlani. A model for predicting magnetic targeting of multifunctional particles in the microvasculature. J. Magn. Magn. Mater. 312:187–193, 2007.CrossRefGoogle Scholar
  16. 16.
    Furlani, E. P., and K. C. Ng. Analytical model of magnetic nanoparticle transport and capture in the microvasculature. Phys. Rev. E 73:061919, 2006.CrossRefGoogle Scholar
  17. 17.
    Gay, M., and L. Zhang. Numerical studies of blood flow in healthy, stenosed, and stented carotid arteries. Int. J. Numer. Method Fluid 61(4):453–472, 2009.MathSciNetCrossRefzbMATHGoogle Scholar
  18. 18.
    Gharahi, H., B. Zambrano, D. Zhu, et al. Computational fluid dynamic simulation of human carotid artery bifurcation based on anatomy and volumetric blood flow rate measured with magnetic resonance imaging. Int. J. Adv. Eng. Sci. 8(1):40–60, 2016.MathSciNetzbMATHGoogle Scholar
  19. 19.
    Goya, G. F., V. Grazu, and M. R. Ibarra. Magnetic nanoparticles for cancer therapy. Curr. Nanosci. 4(1):1–16, 2008.CrossRefGoogle Scholar
  20. 20.
    Grief, A., and G. Richardson. Mathematical modelling of magnetically targeted drug delivery. J. Magn. Magn. Mater. 293(1):455–463, 2005.CrossRefGoogle Scholar
  21. 21.
    Haider, A., and O. Levenspiel. Drag coefficient and terminal velocity of spherical and nonspherical particles. Powder Technol. 58:63–70, 1989.CrossRefGoogle Scholar
  22. 22.
    Haverkort, J. W., K. Kenjeres, and C. R. Kleijn. Computational simulations of magnetic particle capture in arterial flows. Ann. Biomed. Eng. 37:2436–2448, 2009.CrossRefGoogle Scholar
  23. 23.
    Hewlin, R. Transient Cardiovascular Hemodynamics in a Patient-Specific Arterial System. New York: ProQuest Dissertation Publishing, 2015.Google Scholar
  24. 24.
    Hewlin, R., and J. Kizito. Comparison of carotid bifurcation hemodynamics in patient-specific geometries at rest and during exercise. ASME Fluids Engineering Division Summer Meeting, vol. 82(74), 2013.Google Scholar
  25. 25.
    Iacob, G., O. Rotariu, N. J. C. Strachan, and U. O. Hafeli. Magnetizable needles and wires-modeling an efficieny way to target magnetic microspheres in vivo. Biorheology 41:599–612, 2004.Google Scholar
  26. 26.
    Liu, Y., J. Tan, A. Thomas, et al. The shape of things to come: importance of design in nanotechnology for drug delivery. Ther. Deliv. 3(2):181–194, 2012.CrossRefGoogle Scholar
  27. 27.
    Lubbe, A. S., C. Bergemann, H. Riess, et al. Clinical experiences with magnetic drug targeting: a phase I study with 4′-epidoxorubicin in 14 patients with advanced solid tumors. Cancer Res. 15(56):4686–4693, 1996.Google Scholar
  28. 28.
    Lunnoo, T., and T. Puangmali. Capture efficiency of biocompatible magnetic nanoparticles in arterial flow: a computer simulation for magnetic drug targeting. Nanoscale Res. Lett. 10(426):1–11, 2015.Google Scholar
  29. 29.
    Morsi, S. A., and A. J. Alexander. An investigation of particle trajectories in two-phase flow systems. J. Fluid Mech. 55(2):193–208, 1972.CrossRefzbMATHGoogle Scholar
  30. 30.
    Ning, P., C. Lanlan, K. Yang, et al. Uniform magnetic targeting of magnetic particles attracted by a new ferromagnetic biological patch. Bioelectromagnetics 39(2):98–107, 2018.CrossRefGoogle Scholar
  31. 31.
    Ounis, H., G. Ahmadi, and J. B. McLaughlin. Brownian diffusion of submicrometer particles in viscous sublayer. J. Colloid Interface Sci 143(1):266–277, 1991.CrossRefGoogle Scholar
  32. 32.
    Polyak, B., I. Fishbein, M. Chorny, et al. High field gradient targeting of magnetic nanoparticle-loaded endothelial cells to the surface of steel stents. Proc. Natl. Acad. Sci. USA 105(2):698–703, 2008.CrossRefGoogle Scholar
  33. 33.
    Russo, F., A. Boghi, and F. Gori. Numerical simulation of magnetic nano drug targeting in patient-specific lower respiratory tact. J. Magn. Magn. Mater. 451:554–564, 2018.CrossRefGoogle Scholar
  34. 34.
    Shubayev, V. I., T. R. Pisanic, and S. Jin. Magnetic nanoparticles for theragnostics. Adv. Drug Deliv. Rev. 61:467–477, 2009.CrossRefGoogle Scholar
  35. 35.
    Sui, B., P. Gao, Y. Lin, et al. Assessment of wall shear stress in the common carotid artery of healthy subjects using 3.0-tesla magnetic resonance. Acta. Radiol. 49(4):442–449, 2008.CrossRefGoogle Scholar
  36. 36.
    Takayasu, M., R. Gerber, and F. J. Friedlaender. Magnetic separation of submicron particles. IEEE Trans. Magn. 19(5):2112–2114, 1983.CrossRefGoogle Scholar
  37. 37.
    Tefft, B. J., S. Uthamaraj, J. J. Harburn, et al. Magnetizable stent-grafts enable endothelial cell capture. J. Magn. Magn. Mater. 427:100–104, 2017.CrossRefGoogle Scholar
  38. 38.
    Tzirtzolakis, E. E., and V. C. Loukopoulos. Biofluid flow in a channel under the action of a uniform localized magnetic field. Comp. Mech. 36(5):360–374, 2005.CrossRefzbMATHGoogle Scholar
  39. 39.
    Vetel, J., A. Garon, and S. Pelletier. Lagrangian coherent structures in the human carotid artery bifurcation. Exp. Fluids 46(6):1067–1079, 2009.CrossRefGoogle Scholar
  40. 40.
    Wong, B. S., Y. G. Low, W. Xin, et al. 3D finite element simulation of magnetic particle inspection. Sustainable Utilization and Development in Engineering and Technology (STUDENT) 2010 IEEE Conference on 20–21 Nov, 2010, p. 50–55.Google Scholar
  41. 41.
    Xiao, L., S. Beibei, Z. Huilin, et al. Retrospective study of hemodynamic changes before and after carotid stenosis formation by vessel surface repairing. Nature 5493:1–8, 2018.Google Scholar

Copyright information

© Biomedical Engineering Society 2019

Authors and Affiliations

  1. 1.Department of Engineering Technology & Construction Management (ETCM)University of North Carolina at CharlotteCharlotteUSA
  2. 2.Center for Biomedical Engineering & Science (CBES)University of North Carolina at CharlotteCharlotteUSA
  3. 3.Department of Mechanical EngineeringNorth Carolina Agricultural & Technical State UniversityGreensboroUSA

Personalised recommendations