# 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

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**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