# An Optimized Method for 3D Magnetic Navigation of Nanoparticles inside Human Arteries

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## Abstract

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## 1. Introduction

## 2. Materials and Methods

#### 2.1. Governing Equations

#### 2.2. Model Validation

#### 2.3. Determination of the Appropriate Magnetic Gradients

#### 2.4. Driving Process

#### 2.5. Simulation Details

## 3. Results

## 4. Discussion

## 5. Conclusions

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

## References

- Senyei, A.; Widder, K.; Czerlinski, C. Magnetic guidance of drug carrying micro- spheres. Appl. Phys.
**1978**, 49, 3578–3583. [Google Scholar] [CrossRef] - Widder, K.; Senyei, A.; Scarpelli, G. Magnetic microspheres: A model system of site specific drug delivery in vivo. Proc. Soc. Exp. Biol. Med.
**1978**, 158, 141–146. [Google Scholar] [CrossRef] [PubMed] - Patra, J.K.; Das, G.; Fraceto, L.F.; Campos, E.V.R.; Rodriguez-Torres, M.; Acosta-Torres, L.S.; Diaz-Torres, L.A.; Swamy, M.K.; Sharma, S.; Habtemariam, S.; et al. Nano based drug delivery systems: Recent developments and future prospects. J. Nanobiotechnol.
**2018**, 16, 71. [Google Scholar] [CrossRef][Green Version] - Arias, L.S.; Pessan, J.P.; Vieira, A.P.M.; Toito de Lima, T.M.; Delbem, A.C.B.; Monteiro, D.R. Iron Oxide Nanoparticles for Biomedical Applications: A Perspective on Synthesis, Drugs, Antimicrobial Activity, and Toxicity. Antibiotics
**2018**, 7, 46. [Google Scholar] [CrossRef] [PubMed][Green Version] - Ali, A.; Zafar, H.; Zia, M.; Haq, I.U.; Phull, A.R.; Ali, J.S.; Hussain, A. Synthesis, characterization, applications, and challenges of iron oxide nanoparticles. Nanotechnol. Sci. Appl.
**2016**, 9, 49–67. [Google Scholar] [CrossRef][Green Version] - Giustini, A.J.; Petryk, A.A.; Cassim, S.M.; Tate, J.A.; Baker, I.; Hoopes, P.J. Magnetic nanoparticle hyperthermia in cancer treatment. Nano LIFE
**2010**, 1, 17–32. [Google Scholar] [CrossRef] - Daughton, C.G.; Ruhoy, I.S. Lower-dose prescribing: Minimizing “side effects” of pharmaceuticals on society and the environment. Sci. Total Environ.
**2013**, 443, 324–337. [Google Scholar] [CrossRef] [PubMed][Green Version] - Mao, X.; Xu, J.; Cui, H. Functional Nanoparticles for Magnetic Resonance Imaging. Wires Nanomed. Nanobiotechnol.
**2016**, 8, 814–841. [Google Scholar] [CrossRef] [PubMed][Green Version] - Gleich, B.; Hellwig, N.; Bridell, H.; Jurgons, R.; Seliger, C.; Alexiou, C.; Wolf, B.; Weyh, T. Design and evaluation of magnetic fields for nanoparticle drug targeting in cancer. IEEE Trans. Nanotechnol.
**2007**, 6, 164–169. [Google Scholar] [CrossRef] - Kubo, T.; Sugita, T.; Shimose, S.; Nitta, Y.; Ikuta, Y.; Murakami, Y.T. Targeted delivery of anticancer drugs with intravenously administered magnetic liposomes in osteosarcoma-bearing hamsters. Int. J. Oncol.
**2000**, 17, 309–315. [Google Scholar] [CrossRef] [PubMed] - Yellen, B.B.; Forbes, Z.G.; Halverson, D.S.; Fridman, G.; Barbee, K.A.; Chorny, M.; Levy, R.; Friedman, G. Targeted drug delivery to magnetic implants for therapeutic applications. J. Magn. Magn. Mater.
**2005**, 293, 647–654. [Google Scholar] [CrossRef] - Karvelas, E.G.; Lampropoulos, N.K.; Karakasidis, T.E.; Sarris, I.E. A computational tool for the estimation of the optimum gradient magnetic field for the magnetic driving of the spherical particles in the process of cleaning water. Desalin. Water Treat.
**2017**, 99, 27–33. [Google Scholar] [CrossRef] - Mathieu, J.B.; Martel, S. Aggregation of magnetic microparticles in the context of targeted therapies actuated by a magnetic resonance imaging system. J. Appl. Phys.
**2009**, 106, 044904. [Google Scholar] [CrossRef] - Vartholomeos, P.; Mavroidis, C. In silico studies of magnetic microparticle aggregations in fluid environments for MRI-guided drug delivery. IEEE Trans. Biomed. Eng.
**2012**, 59, 3028–3038. [Google Scholar] [CrossRef] - Karvelas, E.G.; Lampropoulos, N.K.; Sarris, I.E. A numerical model for aggregations formation and magnetic driving of spherical particles based on OpenFOAM. Comput. Methods Programs Biomed.
**2017**, 142, 21–30. [Google Scholar] [CrossRef] [PubMed] - Karvelas, E.G.; Karakasidis, T.E.; Sarris, I.E. Computational analysis of paramagnetic spherical Fe
_{3}O_{4}nanoparticles under permanent magnetic fields. Comput. Mater. Sci.**2018**, 154, 464–471. [Google Scholar] [CrossRef] - Karvelas, E.G.; Lampropoulos, N.K.; Benos, L.T.; Karakasidis, T.E.; Sarris, I.E. On the magnetic aggregation of Fe
_{3}O_{4}nanoparticles. Comput. Methods Programs Biomed.**2021**, 178, 105778. [Google Scholar] [CrossRef] - Fogelson, A.L.; Neeves, K.B. Fluid Mechanics of Blood Clot Formation. Annu. Rev. Fluid Mech.
**2015**, 47, 377–403. [Google Scholar] [CrossRef][Green Version] - Jackson, J.D. Classical Electrodynamics, 3rd ed.; Wiley: Hoboken, NJ, USA, 1998. [Google Scholar]
- Agiotis, L.; Theodorakakos, I.; Samothrakitis, S.; Papazoglou, S.; Zergioti, I.; Raptis, Y.S. Magnetic manipulation of superparamagnetic nanoparticles in a microfluidic system for drug delivery applications. J. Magn. Magn. Mater.
**2016**, 401, 956–964. [Google Scholar] [CrossRef] - Hedayatnasab, Z.; Abnisa, F.; Daud, W.M.A.Q. Review on magnetic nanoparticles for magnetic nanofluid hyperthermia application. Mater. Des.
**2017**, 123, 174–196. [Google Scholar] [CrossRef] - Cervadoro, A.; Giverso, C.; Pande, R.; Sarangi, S.; Preziosi, L.; Wosik, J.; Brazdeikis, A. Design Maps for the Hyperthermic Treatment of Tumors with Superparamagnetic Nanoparticles. PLoS ONE
**2013**, 8, e57332. [Google Scholar] [CrossRef][Green Version] - Myrovali, E.; Maniotis, N.; Samaras, T.; Angelakeris, M. Spatial focusing of magnetic particle hyperthermia. Nanoscale Adv.
**2020**, 2, 408–416. [Google Scholar] [CrossRef][Green Version] - Simeonidis, K. In-situ particles reorientation during magnetic hyperthermia application: Shape matters twice. Sci. Rep.
**2016**, 6, 38382. [Google Scholar] [CrossRef][Green Version] - Numata, S.; Itatani, K.; Kawajiri, H.; Yamazaki, S.; Kanda, K.; Yaku, H. Computational fluid dynamics simulation of the right subclavian artery cannulation. J. Thorac. Cardiovasc. Surg.
**2017**, 154, 480–487. [Google Scholar] [CrossRef] [PubMed] - Arjunan, A.; Demetriou, M.; Baroutaji, A.; Wang, C. Mechanical performance of highly permeable laser melted Ti6Al4V bone scaffolds. Behav. Biomed. Mater.
**2020**, 102, 103517. [Google Scholar] [CrossRef] - Erisken, C.; Tsiantis, A.; Papathanasiou, T.D.; Karvelas, E.G. Collagen fibril diameter distribution affects permeability of ligament tissue: A computational study on healthy and injured tissues. Comput. Methods Programs Biomed.
**2020**, 196, 105554. [Google Scholar] [CrossRef] - Zhang, X.; Le, T.A.; Hoshiar, A.K.; Yoon, J. A Soft Magnetic Core can Enhance Navigation Performance of Magnetic Nanoparticles in Targeted Drug Delivery. IEEE/ASME Trans. Mechatron.
**2018**, 23, 1573–1584. [Google Scholar] [CrossRef] - Pouponnea, P.; Leroux, J.-C.; Soulez, G.; Gaboury, L.; Martel, S. Co-encapsulation of magnetic nanoparticles and doxorubicin into biodegradable microcarriers for deep tissue targeting by vascular MRI navigation. Biomaterials
**2011**, 32, 3481–3486. [Google Scholar] [CrossRef] [PubMed] - Zhang, X.; Le, T.A.; Yoon, J. Development of a real time imaging-based guidance system of magnetic nanoparticles for targeted drug delivery. J. Magn. Magn. Mater.
**2017**, 427, 345–351. [Google Scholar] [CrossRef] - Martel, S.; Felfoul, O.; Mathieu, J.-B.; Chanu, A.; Tamaz, S.; Mohammadi, M.; Mankiewicz, M.; Tabatabei, N. MRI-based Medical Nanorobotic Platform for the Control of Magnetic Nanoparticles and Flagellated Bacteria for Target Interventions in Human Capillaries. Int. J. Robot. Res.
**2009**, 28, 1169–1182. [Google Scholar] [CrossRef] - Kafash, A.; Le, T.A.; Yoon, J. Swarm of magnetic nanoparticles steering in multi-bifurcation vessels under fluid flow. J. Micro-Bio Robot.
**2020**, 16, 137–145. [Google Scholar] - Tao, R.; Huang, K. Reducing blood viscosity with magnetic fields. Phys. Rev. E
**2011**, 84, 011905. [Google Scholar] [CrossRef] [PubMed] - Waite, L. Biofluid Mechanics in Cardiovascular Systems; McGraw-Hill’s: New York, NY, USA, 2005. [Google Scholar]
- Hansen, N. The CMA evolution strategy: A comparing review. Adv. Estim. Distrib. Algorithms
**2006**, 192, 1769–1776. [Google Scholar] - Weller, H.G.; Tabor, G.; Jasak, H.; Fureby, C. A tensorial approach to computational continuum mechanics using object-oriented techniques. Comput. Phys.
**2010**, 12, 620–631. [Google Scholar] [CrossRef] - Kennedy, P.; Zheng, R. Flow Analysis of Injection Molds; Hanser: New York, NY, USA, 2013. [Google Scholar]
- Bharadvaj, B.K.; Mabon, R.F.; Giddens, D.P. Steady flow in a model of a human carotid bifurcation. Part 1-Flow visualization. J. Biomech.
**1982**, 15, 349–362. [Google Scholar] [CrossRef] - Geuzaine, C.; Remacle, J.-F. Gmsh: A 3-D finite element mesh generator with built-in pre- and post-processing facilities. Int. J. Numer. Methods Eng.
**2009**, 79, 1309–1331. [Google Scholar] [CrossRef] - Gijsen, F.J.H.; Vosse, F.N.V.; Janssen, J.D. The influence of the non-Newtonian properties of blood on the flow in the large arteries: Steady flow in a carotid bifurcation model. J. Biomech.
**1999**, 32, 601–608. [Google Scholar] [CrossRef] - Nowogrodzki, A. The world’s strongest MRI machines are pushing human imaging to new limits. Nature
**2018**, 563, 24–26. [Google Scholar] [CrossRef] - Segadal, L.; Matre, K. Blood velocity distribution in the human ascending aorta. Circulation
**1987**, 76, 90–100. [Google Scholar] [CrossRef][Green Version] - Pomella, N.; Wilhelm, E.N.; Kolyva, C.; Gonzalez-Alonso, J.; Rakobowchuk, M.; Khir, A.W. Common carotid artery diameter, blood flow velocity and wave intensity responses at rest and during exercise in young healthy humans: A reproducibility study. Ultrasound Med. Biol.
**2017**, 43, 943–957. [Google Scholar] [CrossRef][Green Version] - Koutsiaris, A.G.; Tachmitzi, S.V.; Papavasileiou, P.; Batis, N.; Koutoula, M.G.; Giannoukas, A.D.; Tsironi, E. Blood velocity pulse quantification in the human conjunctival pre-capillary arterioles. Microvasc. Res.
**2010**, 80, 202–208. [Google Scholar] [CrossRef] [PubMed] - Griese, F. Simultaneous Magnetic Particle Imaging and Navigation of large superparamagnetic nanoparticles in bifurcation flow experiments. J. Magn. Magn. Mater.
**2020**, 498, 166206. [Google Scholar] [CrossRef][Green Version] - Manshadi, M.K.D. Delivery of magnetic micro/nanoparticles and magnetic-based drug/cargo into arterial flow for targeted therapy. Drug Deliv.
**2018**, 25, 1963–1973. [Google Scholar] [CrossRef][Green Version] - Grosse-Wortmann, L.; Grabitz, R.; Seghaye, M.C. Magnetic Guide-Wire Navigation in Pulmonary and Systemic Arterial Catheterization: Initial Experience in Pigs. J. Vasc. Interv. Radiol.
**2007**, 18, 545–551. [Google Scholar] [CrossRef] [PubMed]

**Figure 3.**Comparison of axial blood velocity between experimental measurements (black) of Ref [40] and present numerical simulation (red).

**Figure 4.**Projection of the carotid artery. Desired trajectory (purple line) and walls (green dots).

**Figure 5.**Velocity in the outlet 1 of the carotid model under different number of computational cells.

**Figure 6.**Projection of the positions of particles under different time steps of the navigation process for particles with diameter of (

**a**) 200 nm and (

**b**) 500 nm. Desired trajectory (cyan line) and walls (black dots).

**Figure 7.**Projection of the positions of different diameter particles under different time steps of the navigation process.

**Figure 8.**(

**a**,

**b**) Best, (

**c**,

**d**) Average and (

**e**,

**f**) Worst distance of particles in each iteration from the desired trajectory.

**Figure 10.**(

**a**) Gradient magnetic field change from the case of 500 nm, (

**b**) Overall percentage difference from the base case of 500 nm.

**Figure 11.**Distance of particles from the desired trajectory in each iteration of the computational method under inlet velocity of 0.06 m/s.

**Figure 12.**Percentage difference of distance of particles $(\Delta l)$ with diameter of 800 nm from the desired trajectory between inlet velocity 0.08 m/s and 0.06 m/s.

**Figure 13.**Distance of particles from the desired trajectory in each iteration of the computational method under inlet velocity of 0.08 m/s in the minimized carotid artery for the cases of (

**a**) 200, 300 nm, and (

**b**) 400 nm and above.

**Figure 14.**Percentage difference of distance of particles with diameter of 800 nm from the desired trajectory between the original and the minimized carotid artery under inlet velocity of 0.08 m/s.

Bird-Carreau Parameters | ||
---|---|---|

Symbol | Value | Unit |

${\nu}_{\infty}$ | $2.2\times {10}^{-3}$ | Pa·s |

${\nu}_{\mathbf{0}}$ | $22\times {10}^{-3}$ | Pa·s |

$\lambda $ | 0.11 | s |

$\mathit{n}$ | 0.392 | - |

Boundary Conditions | ||
---|---|---|

Boundary | Velocity | Pressure |

Inlet | 0.08 m/s | Zero gradient |

Outlet 1 | Zero gradient | 0 |

Outlet 2 | Zero gradient | 0 |

Walls | 0 | Zero gradient |

Property | Units |
---|---|

Particles’ density | 5000 Kg/m${}^{3}$ |

Young’s modulus | $3.5\times {10}^{9}$ Pa |

Poisson’s ratio | $0.34$ |

Relative magnetic permeability | $1.23$ |

Medium permeability | $1.256\times {10}^{-6}$ |

Temperature | 288 K |

Molecular mean free path | $2.5\times {10}^{-9}$ |

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**MDPI and ACS Style**

Karvelas, E.; Liosis, C.; Theodorakakos, A.; Sarris, I.; Karakasidis, T.
An Optimized Method for 3*D* Magnetic Navigation of Nanoparticles inside Human Arteries. *Fluids* **2021**, *6*, 97.
https://doi.org/10.3390/fluids6030097

**AMA Style**

Karvelas E, Liosis C, Theodorakakos A, Sarris I, Karakasidis T.
An Optimized Method for 3*D* Magnetic Navigation of Nanoparticles inside Human Arteries. *Fluids*. 2021; 6(3):97.
https://doi.org/10.3390/fluids6030097

**Chicago/Turabian Style**

Karvelas, Evangelos, Christos Liosis, Andreas Theodorakakos, Ioannis Sarris, and Theodoros Karakasidis.
2021. "An Optimized Method for 3*D* Magnetic Navigation of Nanoparticles inside Human Arteries" *Fluids* 6, no. 3: 97.
https://doi.org/10.3390/fluids6030097