Skip to main content
SpringerLink
Log in

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

  • Published:
Cardiovascular Engineering and Technology Aims and scope Submit manuscript

Abstract

Purpose

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.

Methods

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.

Results

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%.

Conclusion

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.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Figure 1
Figure 2
Figure 3
Figure 4
Figure 5
Figure 6
Figure 7
Figure 8
Figure 9
Figure 10
Figure 11
Figure 12
Figure 13

Similar content being viewed by others

References

  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.

    Article  Google Scholar 

  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.

    Article  Google Scholar 

  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.

    Article  Google Scholar 

  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.

    Article  Google Scholar 

  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. 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.

    Article  Google Scholar 

  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.

    Article  Google Scholar 

  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.

    Article  Google Scholar 

  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.

    Article  Google Scholar 

  10. Chorny, M., I. Fishbein, S. Forbes, and I. Alferiev. Magnetic nanoparticles for targeted vascular delivery. IUBMB Life 62(8):613–620, 2011.

    Article  Google Scholar 

  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.

    Article  Google Scholar 

  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.

    Article  Google Scholar 

  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. 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.

    Article  Google Scholar 

  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.

    Article  Google Scholar 

  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.

    Article  Google Scholar 

  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.

    Article  MathSciNet  MATH  Google Scholar 

  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.

    MathSciNet  MATH  Google Scholar 

  19. Goya, G. F., V. Grazu, and M. R. Ibarra. Magnetic nanoparticles for cancer therapy. Curr. Nanosci. 4(1):1–16, 2008.

    Article  Google Scholar 

  20. Grief, A., and G. Richardson. Mathematical modelling of magnetically targeted drug delivery. J. Magn. Magn. Mater. 293(1):455–463, 2005.

    Article  Google Scholar 

  21. Haider, A., and O. Levenspiel. Drag coefficient and terminal velocity of spherical and nonspherical particles. Powder Technol. 58:63–70, 1989.

    Article  Google Scholar 

  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.

    Article  Google Scholar 

  23. Hewlin, R. Transient Cardiovascular Hemodynamics in a Patient-Specific Arterial System. New York: ProQuest Dissertation Publishing, 2015.

    Google Scholar 

  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.

  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. 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.

    Article  Google Scholar 

  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. 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. 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.

    Article  MATH  Google Scholar 

  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.

    Article  Google Scholar 

  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.

    Article  Google Scholar 

  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.

    Article  Google Scholar 

  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.

    Article  Google Scholar 

  34. Shubayev, V. I., T. R. Pisanic, and S. Jin. Magnetic nanoparticles for theragnostics. Adv. Drug Deliv. Rev. 61:467–477, 2009.

    Article  Google Scholar 

  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.

    Article  Google Scholar 

  36. Takayasu, M., R. Gerber, and F. J. Friedlaender. Magnetic separation of submicron particles. IEEE Trans. Magn. 19(5):2112–2114, 1983.

    Article  Google Scholar 

  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.

    Article  Google Scholar 

  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.

    Article  MATH  Google Scholar 

  39. Vetel, J., A. Garon, and S. Pelletier. Lagrangian coherent structures in the human carotid artery bifurcation. Exp. Fluids 46(6):1067–1079, 2009.

    Article  Google Scholar 

  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.

  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 

Download references

Acknowledgments

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.

Author information

Authors and Affiliations

  1. Department of Engineering Technology & Construction Management (ETCM), University of North Carolina at Charlotte, Charlotte, NC, USA

    Rodward L. Hewlin Jr. & Ashley Ciero

  2. Center for Biomedical Engineering & Science (CBES), University of North Carolina at Charlotte, Charlotte, NC, USA

    Rodward L. Hewlin Jr.

  3. Department of Mechanical Engineering, North Carolina Agricultural & Technical State University, Greensboro, NC, USA

    John P. Kizito

Authors
  1. Rodward L. Hewlin Jr.
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Ashley Ciero
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. John P. Kizito
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Rodward L. Hewlin Jr..

Additional information

Associate Editor Ajit P. Yoganathan oversaw the review of this article.

Publisher's Note

Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Hewlin, R.L., Ciero, A. & Kizito, J.P. 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. Cardiovasc Eng Tech 10, 299–313 (2019). https://doi.org/10.1007/s13239-019-00411-8

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s13239-019-00411-8

Keywords

Search

Navigation